HP 39gs User Manual
HP 3 9gs gr aphing calc ulato r user's guide Ed i t io n 3 P a rt Number F2 2 2 3AA-9 0001 HP 3 9gs Engl ish. book Pa ge i Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Notice REG ISTER Y OUR PRODU CT A T: w ww .register .hp.com TH IS MANUAL AND ANY EXAMPLE S CONT AI NED HEREIN ARE PRO VIDED â AS ISâ AND ARE SUBJECT T O CHANG E WITHOUT NO TICE. HEWLETT-P A CKARD COMP ANY MAKES N O W AR- R ANTY O F ANY KIND WITH REGARD T O TH IS MANU AL , INC L UDING , B UT NO T L IMI TE D T O , TH E IM P LIE D W AR RAN T IES OF MERCHANT ABI LI T Y , NON -INFR ING EMENT AN D FITNESS FOR A P ARTI C ULA R PURPOSE . HEWLET T -P ACKARD CO . SHAL L NO T BE LI ABLE FO R ANY ERRORS OR FOR IN CIDE NT AL OR CONSEQ UENT IAL D AMAGES IN CONNEC TION WI TH T HE FU RNISHING, PE RF ORMA NCE, OR USE OF THI S MANU AL OR THE EXAMPLES CONT AI NED HEREIN. © 19 9 4 -19 9 5, 19 9 9- 2000, 200 3, 2006 He w lett-P ack ar d De v el opment Compan y , L .P . Repr oducti on , adaptati on , or tr anslation o f this manual is pr ohibited w ithout pr ior w ritten per missi on of He w lett -P ack ard C ompan y , e x cept as allo w ed under the cop yr ight law s. Hew let t-P ack ar d Compan y 16 3 9 9 W es t Ber nar do Dri v e MS 8- 600 San Di ego , CA 9 212 7 -18 9 9 US A Pr inting His tory E ditio n 2 December 2003 Ed i t io n 3 J u n e 2 0 05 titl e.fm Pa ge i i T hurs day, July 13, 200 6 1 0:29 AM
i Contents Preface Manual conventions ............. ................ ................ ................. P-1 Notice .. ................. ................ ................ ................. ............. P-2 1 Getting started On/off, cancel o perations ........ ................ ................. ............. 1-1 The display ............... ................ ................. ................ .......... 1-2 The keyboard ...... ................ ................ ................ ............. .... 1-3 Menus ...... ................ ................ ................. ............. ............. 1-8 Input forms ... ................ ................. ................ ................ ....... 1-9 Mode settings ............ ................ ................. ............. ........... 1 -10 Setting a mode ...... ................ ................. ................ ........ 1-11 Aplets (E-lessons) ........... ................. ................ ................ ..... 1-12 Aplet library ............ ................. ................ ................ ..... 1-16 Aplet views ........... ............. ................ ................. ........... 1 -16 Aplet view c onfiguration............. ................ ................ ..... 1-18 Mathematical calcu lations ............... ................ ................ ..... 1-19 Using fraction s ..... ................ ............. ................ ................ .. 1-25 Complex numbers ................... ................ ................. ........... 1 -29 Catalogs and editors ............... ................ ................. ........... 1-30 2 Aplets and their views Aplet views .. ................ ............. ................. ................ .......... 2-1 About the Symbolic view ............... ................ ................ .... 2-1 Defining an expressio n (Symbo lic view) ....................... ....... 2-1 Evaluating exp ressions ........... ................. ................ .......... 2-3 About the Plot view ... ................. ................ ................ ....... 2-5 Setting up the plot (Plot view setup) ........... ................ .......... 2-5 Exploring the graph ...... ................ ................ ................ .... 2-7 Other views fo r scaling and splitting the graph ................ .. 2-13 About the numeric view .............. ................ ................ ..... 2-16 Setting up the table (Numeric view setup) ........ ................ .. 2-16 Exploring the table of numbers .... ................... ................ .. 2-17 Building your o wn table of numbers ... ................ ............... 2-19 âBuild Your Ownâ me nu keys ......... ................ ................ .. 2-20 Example: plotting a circle . ................ ................ ............... 2 -20 Ente rpri seTO C.fm Pa ge i Wed nesd ay, May 3, 2 006 5:01 PM
ii 3 Function aplet About the Function aple t ................. ............. ................ .......... 3-1 Getting started w ith the Function aplet ................ ................ 3-1 Function aplet intera ctive analysis ....... .................... ................ 3-9 Plotting a pie cewise-defined function ..... ................ ........... 3-12 4 Parametric aplet About the Parametric aplet ... ................. ................ ................ 4-1 Getting started w ith the Parametric aplet ................ ............. 4-1 5 Polar aplet Getting started w ith the Polar aplet ............ ................... .......... 5-1 6 Sequence aplet About the Sequence aplet ............... ................ ................. ...... 6-1 Getting started w ith the Sequence aplet .............. ................ 6-1 7 Solve aplet About the Solve aplet .. ................ ................ ................ .......... 7-1 Getting started w ith the Solve aplet .... ................ ................ 7-2 Use an initial gues s ..... ................ ................ ................ .......... 7-5 Interpreting results ...... ................ ................ .................... ...... 7-6 Plotting to find gue sses ...... ................ ................. ................ ... 7-7 Using variables in equations ........... ................ ................. .... 7-10 8 Linear Solver aplet About the Linear Solver aplet ....... ................ ................ .......... 8-1 Getting started w ith the Linear Solver aplet ....... ................... 8-1 9 Triangle Solve aplet About the Triangle Solver aplet .... ................ ................ .......... 9-1 Getting started w ith the Triangle Solver aplet ............. .......... 9-1 10 Statistics aplet About the Statistics aplet ........... ................ ................ ........... 1 0-1 Getting starte d with the Statistic s aplet ......... ................. .... 10-1 Entering and editing s tatistical data .... .................... .............. 10-6 Defining a regression model ....... ................ ................... 10-12 Computed st atistics .............. ................. ................ ............ 10-14 Plotting .................. ................. ................ ................ ......... 10-15 Plot types .............. ................ ............. ................ ......... 10-16 Fitting a curve to 2VAR data ......... .................... ............ 10-17 Setting up the plot (Plot setup view) ................. ............... 10-18 Trouble -shooting a plot .... ................. ................ ............ 10-19 Ente rpri seTO C.fm Pa ge i i We dnes day, May 3, 2006 5:0 1 PM
iii Exploring the graph ...... ................ ................ ................ 10-19 Calculating pre dicted values ....... ................ ................ ... 10-20 11 Inference aplet About the Inference a plet ...... ................ ................ ............... 11-1 Getting started with the Inference aplet ..................... ........ 11-1 Importing samp le statistics fro m the Statistics a plet ...... ........ 11-4 Hypothesis tes ts ... ................ ................ ................ ............... 11-8 One-Sample Z-Test .... ................. ................ ................ ..... 11-8 Two-Samp le Z-Test .... ................. ................ ............. ........ 11-9 One-Propo rtion Z-Test ....... ................ ................ ............. 11-10 Two-Proportion Z-Te st .... ................ ................ ................ 11-11 One-Sample T-Test ........ ................ ................ ................ 11-12 Two-Samp le T-Test ................. ................. ............. ......... 11 -14 Confidence intervals ... ................ ................. ................ ...... 11-1 5 One-Sample Z-Interval ... ................ ................ ................ 11-15 Two-Samp le Z-Interval ......... ............. ................ ............. 1 1-16 One-Propo rtion Z-Interval .. ................ ................ ............. 1 1-17 Two-Proportion Z-Interval ............... ................ ................ 11-17 One-Sample T-Interval ............ ................. ................ ...... 11-18 Two-Samp le T-Interval ................. ................ ................ ... 11-19 12 Using the Finance Solver Backgroun d ..... ................. ................ ................ ............. ..... 12-1 Performing TVM calculations ........... ................ ................ ..... 12-4 Calculating Amo rtizations ........... ................ ................ ..... 12-7 13 Using mathematical functions Math functions ........ ................ ................ ................. ........... 1 3-1 The MATH menu ....................... ................ ................... .. 13-1 Math functions by category ............. ................... ................ .. 13-2 Keyboard function s ................ ................. ................ ........ 13-3 Calculus functions .................. ................. ............. ........... 1 3-6 Complex number fu nctions...... ................. ................ ........ 13-7 Constants ............. ................ ................. ................ ........ 13-8 Conversions ....... ............. ................ ................ ............... 13-8 Hyperbolic trigon ometry ... ................ ................ ............... 13-9 List functions ......... ................ ................. ................ ...... 13-1 0 Loop functions .............. ................ ................ ................ 1 3-10 Matrix functions . ................ ................ ................. ......... 13-11 Polynomial fu nctions . ................. ................ ................ ... 13-11 Probability functions .. ................. ................... ................ 13-12 Real-number functio ns ......... ................ ................. ......... 13 -13 Ente rpri seTO C.fm Pa ge i ii W edne sday , Ma y 3, 200 6 5: 01 P M
iv Two-variab le statistic s ............. ............. ................ ......... 13-17 Symbolic functions .... ................... ................. ............... 13-17 Test functions ......... ................ ............. ................ ......... 13-18 Trigonom etry functions ......... ................ ................ ......... 13-19 Symbolic calc ulations .. ................ ................ ................ ...... 13 -20 Finding derivative s ....... ................ ................. ............... 13-21 Program consta nts and physical constants ..................... ...... 13 -24 Program constants ..... ................ ................ ................. .. 13-24 Physical constants .. ................ ................ ................ ...... 13-25 14 Variables and memory management Introduction ..... ................ ................ ................. ................ . 14-1 Storing and recalling variables .. ................ ................ ........... 14-2 The VARS menu ...... ................. ................ ................ ........... 14-4 Memory Manager ............ ................ ................. ................ . 14-9 15 Matrices Introduction ..... ................ ................ ................. ................ . 15-1 Creating an d storing matrices ...... ................ ................ ........ 1 5-2 Working with matrices ... ................ ................ ................. .... 15-4 Matrix arithmetic . ................ .................... ................ ........... 15-6 Solving systems of linear equa tions .... ................ .............. 15-8 Matrix functions a nd commands ......... .................... ............ 15-10 Argume nt conventions ......... ................ ................ ......... 15-10 Matrix functio ns ..... ................ ............. ................ ......... 15-10 Examples ..... ................. ............. ................ ................ ...... 15 -13 16 Lists Displaying and editing lis ts .......... ................... ................. .... 16-4 Deleting lists ............. ................ ................ ................. .... 16-6 Transmitting lists. ................. ................... ................ ........ 16-6 List functions. ................. ................ ................ ................. .... 16-6 Finding stat istical values for list ele ments........ ................ ........ 1 6-9 17 Notes and sketches Introduction ..... ................ ................ ................. ................ . 17-1 Aplet note view .......... ................ ................ ................ ........ 17-1 Aplet ske tch view.... ................. ................ ................ ........... 17-3 The notepad ....................... ................. ................ .............. 17-6 18 Programming Introduction ..... ................ ................ ................. ................ . 18-1 Program catalog ............. ................. ................ .............. 18-2 Creating an d editing programs .... ................ ................ ........ 18-4 Ente rpri seTO C.fm Pa ge i v We dnes day, May 3, 2006 5:0 1 PM
v Using programs ............ ................. ................ ................ ..... 18-7 Customiz ing an aplet ............ ................ ............. ................ .. 18-9 Aplet naming convention .................. ................ ............. 1 8-10 Example ......... ................ ................ ................ ............. 18-10 Programming co mmands....... ................ .................... ......... 18 -13 Aplet commands ................ ................ ................. ......... 18 -14 Branch commands ................. ................. ................ ...... 18-17 Drawing commands ................... ................ ................ ... 18-19 Graphic co mmands ......... ................ ................ ............. 1 8-21 Loop commands .... ................ ................. ............. ......... 18-23 Matrix commands ..... ................. ................ ................ ... 18-24 Print commands ............... ................ ................ ............. 18-26 Prompt commands . ................ ................. ................ ...... 18-2 6 Stat-One and Stat-Two c ommands ............... ................... 18-30 Stat-Two commands ............ ................ ................. ......... 18 -30 Storing and re trieving variables in programs . ................... 1 8-31 Plot-view variables ........... ................ ................ ............. 1 8-32 Symbolic-vie w variables ... ................ ................ ............. 1 8-39 Numeric-view variables ....... .................... ................ ...... 18-41 Note variable s ......... ................. ................ ................ ... 18-44 Sketch variables ....... ............. ................. ................ ...... 18-44 19 Extending aplets Creating new aplets based on ex isting aplets .... ................ ..... 19-1 Using a cus tomized aplet .............. ................ ................ .. 19-3 Resetting an a plet.... ................ ................ ................. ........... 1 9-3 Annotating an aplet with notes .............. ................ ............... 19-4 Annotating an aplet with sketches .......... ................ ............... 19-4 Downloading e-lessons from the web ... ................ ................ .. 19-4 Sending and re ceiving aplets ................ ................ ............... 19-4 Sorting items in the aplet library menu list ................... ........... 1 9-6 Refere nce information Glossary ......... ................. ................ ................ ................ .... R-1 Resetting the HP 39gs .............. ................ ................. ............. R-3 To erase all memo ry and reset defau lts...... ................ .......... R-3 If the calculator does not turn on ........... ................. ............. R-4 Operating details . ................ ................ ................ ................. R-4 Batteries ............... ................ ................. ................ .......... R-4 Variables ........ ............. ................. ................ ................ ....... R-6 Home variable s .................. ............. ................ ................. R-6 Function aplet variables .............. ................... ................ .... R-7 Parametric aplet variables ................ ................ ................. R-8 Ente rpri seTO C.fm Pa ge v Wed nesd ay, May 3, 2 006 5:01 PM
vi Polar aplet variable s .............. ................ ................ .......... R-9 Sequence aplet variables ........... ................ ................. .... R-10 Solve aplet variab les .............. ................ ................ ........ R-11 Statistic s aplet variables ................ ................. ............. .... R-12 MATH menu ca tegories .. ................ ................ ................. .... R-13 Math functions .......... ................ ................ ................. .... R-13 Program constants ........... .................... ................ ........... R-15 Physical Constants .......... ................. ................ .............. R-16 Program commands ........ ................. ................ .............. R-17 Status message s ............ ................ ................ ................. .... R-18 Limited Warranty Service ... ................. ................ ................ ................. ..... W-3 Regulatory info rmation............ ................ .................... ..... W-5 Index Ente rpri seTO C.fm Pa ge v i We dnes day, May 3, 2006 5:0 1 PM
P-1 Pr eface The HP 39gs is a feature-rich graphing calculator. It i s also a powerful mathematics learning tool. The HP 39gs is designed so that you can use it to explore mathematical functions and their prop erties. You can get more information on the HP 39gs from Hewlett-Packardâs Calcula tors web site. You can download customized aplets from the web site and load them onto your calculator. Customized aplets are special applications developed to p erform certain functions, and to demonstrate mathematical concepts. Hewlett Packardâs Calculators web site can be fou nd at: http://www.hp.com /calculators Manual conventions The following conventions are used in this manual to represent the keys that y ou press and the menu options that you choose to perform the described operations. ⢠K e y pr es se s ar e r epre sen ted a s fo llo w s: , , , et c. ⢠Shift k e y s, that is the k ey f uncti ons that y ou access b y pr essing the k ey f i rst , a r e r epres ented as fo llo w s: CLEAR , MODES , ACO S , et c. ⢠Numbers and letters ar e repr esented normally , as fo llo w s: 5, 7 , A, B , etc . ⢠Menu opti ons , that is, the f uncti ons that y ou se lect using the men u k e y s at the top of the k e yp ad ar e r epre sented as follo ws: , , . ⢠Input form f ields and choose list items are r epre sented as f ollo ws: Function , Polar , Parametric ⢠Y our entr ie s as the y appear on the command line or w ithin input for ms ar e r epr esented as f ollo w s: 2*X 2 -3X 5 HP 3 9gs Engl ish. book Pa ge 1 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
P-2 Notice This manual and any examples contained herein are provided as-is and are subject to change without notice. Except to the extent prohibit ed by law, Hewlett-Packard Company makes no express or implied warranty of any kind with regard to this manu al and specific ally disclaims the implied warranties and conditions of merchantability and fitness for a particular purpose and Hewlett-P ackard Company shall not be liable for any errors or for incidental or consequential damage in connection with the furnishing, performance or use of this manual and the examples herein. © 1994â1995, 1999 â2000, 2003â2006 Hewlett- Packard Developme nt Company, L.P. The programs that control your HP 39gs are copyrighted and all rights are reserved. Reproduction, adaptation, or translation of those programs without prior wri tten permission from Hewlett-Packard Company is also prohi bited. Pref ace. fm Page 2 Thur sday, Jul y 13 , 20 06 10:3 3 AM
Getting started 1-1 1 Get ting star ted On/off, cancel operations To turn on Press to turn on the calculator. To cancel When the calculator is on, the key cancels the current operation. To turn off Press OFF to turn the calculator off. To save power, the calculator turns itself off after sev eral minutes of inactivity. All stored and displayed information is saved. If you see the (( ⢠)) annunciator or the Low Bat message , then the calculator needs fresh batteries . HOME HOME is the calculatorâs home view and is common to all aplets. If you want to perform calculations, or you want to quit the current activity (such as an aplet, a program, or an editor), press . All mathematical functions are available in the HOME. The name of t he current aplet is displayed in the title of the home view. Protective cover The calculator is provided with a slide cover to protect the display and keyb oard. Remove the cover by graspi ng both sides of it and pu lling down. You can re verse the slide cover and slide it onto the back of the calculator. this will help prevent you losing the cover while you are using the calculator. To prolong the life of the calculator, always place the cover over the display an d keyboard when you are not using the calculator. HP 3 9gs Engl ish. book Pa ge 1 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
1-2 Getting started The display To adjust the contrast Simultaneously press and (or ) to increase (or decrease) the contrast. To clear the display ⢠Pr ess CANCEL to c lear the edit line . ⢠Pr ess CLEA R to c lear the edit line and the display history . Parts of the display Menu key or soft key labels. T he labels f or the menu k e ys â cur r ent meaning s. is the label f or the fir st menu k ey in this pi ctur e. âPr ess â means to pr ess the fir st menu k e y , that is , the leftmost top-r ow k ey on the calc ulator k e yboar d. Edit line. The line of c urrent entry. History. The HOME display ( ) shows up to four lines of history: the mo st recent input and output. Older lines scroll off the top of the display but are retained in memory. Title. The name of the current aplet is displayed at the top of the HOME view. RAD, GRD, DEG specify whether Radians, Grads or Degr ees angle mode i s set for HOME. The î and î symbols indicate whether there is more history in the HOME displa y. Press the and to scroll in the HOME display. NOTE This userâs guide contains images from the HP 39gs and does not display the menu key label. Title Edit line History Menu k e y labels HP 3 9gs Engl ish. book Pa ge 2 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Getting started 1-3 Annunciators . Annunciators are sy mbols that appear above the title bar and give you important status information. The keyboard Menu keys Annunciator Description Shift in effect for next keystrok e. To cancel, press again. α Alpha in effect for next keystroke. To cancel, press again. (( ⢠)) Low battery power. Busy. Data is being transferred via infrared or cable. HP 39g s Graphing Calc ulator Menu Key Labels Menu Keys Cursor Aplet Control Alpha Key Shift Key Enter Keys Key Keys HP 3 9gs Engl ish. book Pa ge 3 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
1-4 Getting started ⢠On the calc ulator k e y boar d, the top r ow of k ey s are called menu k ey s . The ir meanings depend on the conte xtâthatâs w h y their to ps ar e blank . The menu k e y s ar e sometimes called â so ft k ey s â . ⢠T he bottom line o f the displa y sho ws the la bels f or the menu k ey s â c u r r ent meanings . Aplet control keys The aplet control keys are: K e y Meaning Displays the Symbolic view for the current aplet. See âSymbolic viewâ on page 1-16. Displays the Plot view for the current aplet. See âPlot viewâ on page 1-16. Displays the Numeric vi ew for the current aplet. See âNumeric vie wâ on page 1-17. Displays the HOME view. See âHOMEâ on page 1 -1. Displays the Aplet Library menu. See âAplet libraryâ on page 1-1 6. Displays the VIEWS menu. See âAplet viewsâ on page 1-16. HP 3 9gs Engl ish. book Pa ge 4 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Getting started 1-5 Entry/Edit keys The entry and edit keys are: K e y Meaning ( CANCEL ) Cancels the current operation if the calculator is on by pressing . Pressing , then OFF turns the calculator off. Accesses the function printed in blue above a key. Returns to the HOME view, for performing calculations. Accesses the alphabetical characters printed in o range below a key. Hold down to enter a string of characters . Enters an input or exec utes an operation. In calculations, acts like â=â. When or is present as a menu key, acts the same as pressing or . Enters a negative number. To enter â25, press 25. Note: this is not the same operation that the subtract button performs () . Enters the independen t variable by inserting X , T, θ, or N into the edit line, depending on the current active aplet. Deletes the character under the cursor. Acts as a backsp ace key if the cursor is at the end of the line. CLEAR Clears all data on the screen. On a settings screen, for example Plot Setup, CLEAR returns all settings to their default values. , , , Moves the cursor around the display. Press first to move to the beginning, end, top or bottom. HP 3 9gs Engl ish. book Pa ge 5 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
1-6 Getting started Shifted ke ystrokes There are two shift keys that you use to access the operations and characters printed above the keys: and . CHARS Displays a menu of all a vailable characters. To type one, use the arrow keys to highlight it, and press . To select multiple character s, select each and press , then press . K e y Meaning (Continued) Key D e sc ri p t io n Press the key to access the operations printed in blue above the keys. F or insta nce, to a ccess th e Modes screen, press , then press . ( MODES is labe led in blue above the key). You do not need to hold down when you press HOME. This acti on is depicted in this manual as âpress MODES .â To cancel a shift, press again. The alphabetic keys are also shifted keystrokes. For instance, to type Z, press Z. (The letters are printed in orange to the lower right of each key.) To cancel Alpha, pre ss again. For a lower case letter, press . For a string of letters, hold down while typing. HP 3 9gs Engl ish. book Pa ge 6 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Getting started 1-7 HELPWITH The HP 39gs built-in help is available i n HOME only. It provides syntax help for bu ilt-in math functions. Access the HELPWITH command by pressing SYNTAX and then the math key for which you require syntax help. Example Pr ess SYNTAX Note: R emo ve the left par enthesis fr om built -in func tio ns such a s sine , cosine , and tangen t bef or e inv oking the HELPWI TH command . Math keys HOME ( ) is the place to do calculations. Keyboard keys. The most common operations are available from the keyboard, such as the arithmetic (like ) and trigonometric (like ) functions. Press to complete the operation: 256 displays 16. . MATH menu. Press to open the MATH menu. The MATH menu is a comprehensive list of math functions that do not appear on the keyboard. It also includes categories for all other functions and constants. The functions are grouped by category, ranging in alphabetical order from Calculus to Trigonometry. ⢠T he arr ow k e y s sc r oll thr ough the list ( , ) and mo ve fr om the category lis t in the left column to the ite m list in the r ight column ( , ) . ⢠Pr ess to ins ert the selected command onto the edit line . ⢠Pr ess to dismis s the MA TH menu w ithout selec ting a command . ⢠Pr essing displa ys the lis t of Pr ogram Co nstants . Y ou can use these in pr ogr ams that yo u de ve l op. HP 3 9gs Engl ish. book Pa ge 7 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
1-8 Getting started ⢠Pr essing displa y s a menu of ph y sical constants f r om the f ields o f chemistry , phy sic s, and quantum mec hanic s. Y ou can u se these consta nts in calc ulati ons . (See âPh ysi cal constants â on page 13- 2 5 f or mor e inf or mation .) ⢠Pr essing tak es yo u to the beginning of the MA TH men u . See âMath functions by categoryâ on page 13-2 for details of the math functions. HINT When using the MA TH menu , or any men u on the hp 3 9gs, pr essing an alpha ke y tak es y ou strai ght to the fir st menu option beg inning with that alpha char acte r . W ith this method , you do n ot need to pr ess fir st . Jus t pre ss the ke y that corr esponds to the commandâs beginning alpha char acter . Program commands Pressing CMDS displays the list of Program Commands. See âProgramming commandsâ on page 18 -13. Inactive keys If you press a key that does not operate in the curre nt context, a warning symbol like this appears. There is no beep. Menus A menu offers you a choice of items. Menus are displayed in one or two columns. ⢠Th e a rrow i n t h e displa y means more items belo w . ⢠Th e a rrow i n t h e display means mor e items abov e. To search a menu ⢠Pr ess or to sc ro ll thr ough the list . If y ou pr es s or , you âll go all the wa y to the end or the beginning o f the list . Highligh t the item y ou wa nt to select , then pres s (or ) . ! HP 3 9gs Engl ish. book Pa ge 8 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Getting started 1-9 ⢠If ther e are tw o columns , the left column sho ws gener al categori es and the righ t column sho w s spec ifi c cont ents w ithin a catego ry . Hi ghligh t a gener al category in the left column, then hi ghligh t an item in the r ight column. T he list in the ri ght column c hanges w hen a diffe r ent catego ry is highligh ted . Pr ess or w hen yo u hav e highlighted y our sele ction. ⢠T o speed-s earc h a list , t y pe the f irst le tter of the w ord . F or ex ample , to f ind the Matr i x category in , pr ess , the Alpha âM â k e y . ⢠T o go up a page , y ou can pr ess . T o go do w n a page, pr ess . To cancel a menu Press (for CANCEL ) or . This cancels the current operation. Input forms An input form shows several fields of information for you to examine and specify. After highlighting the field to edit, you can enter or edit a number (or expression). Yo u can also select options from a list ( ). Some input forms include items to check ( ). See below for examples input forms. Reset input form values To reset a field to its default values in an input form, move the cursor to that field and press . To reset all default field values in the input form, press CLEAR . HP 3 9gs Engl ish. book Pa ge 9 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
1-10 Getting started Mode settings You use the Modes inpu t form to set the modes for HOME. HINT Although the numeric setting in Modes affects only HOME, the angle setting controls HOME and the current aplet. The angle setting selecte d in Modes is the angle setting used in both HOME and current aplet. To further configure an aplet, you u se the SETUP keys ( and ). Press MODES to access the HOME MOD ES input form. Setting Options Angle Measure Angle values are: Degrees . 360 degrees in a circ le. Radians . 2 Ï radians in a circle. Grads . 400 grads in a ci rcle. The angle mode you set is the angle setting used in both HOME and the current aplet. This is done to ensure that trigonometric calculations done in the current aplet and HOME give the same result. Number Format The number format mode you set is the number format used in both HOME and the current aplet. Standard . Full-precision display. Fixed . Displays results rounded to a number of decimal places. Example: 123.456789 becomes 123.46 in Fixed 2 format. Scie ntific . Displays results with an exponent, one digit to the left of the decimal point, and the specified number of decimal places. Example: 123.456789 becomes 1.23E2 in Scientific 2 format. HP 3 9gs Engl ish. book Pa ge 10 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Getting started 1-11 Setting a mode This example demonstrates how to change the angle measure from the default mode, radians, to degrees for the current aplet. The procedure is the s ame for changing number format and decimal mark modes. 1. Pr ess MODES t o o p e n t h e H O M E M O D ES i n p u t form. Engineering . Displays result wit h an exponent that is a multiple of 3, an d the specified number of significant digits beyond the first one. Example: 123.456E7 becomes 1.23E9 i n Engineering 2 format. Fraction . Displays results as fractions based on the spec ified number of decimal places. Examples: 123.456789 becomes 123 in Fraction 2 format, and .333 bec omes 1/3 and 0.14285 7 becomes 1/7. See âUsing fractionsâ on page 1-25. Mixed Fraction . Displays results as mixed fractions based on the specified number of decimal places. A mixed fraction has an integer part and a fractional part. Examples: 123.456789 becomes 123 16/35 in Fraction 2 format, and 7÷ 3 returns 2 1/3. See âUsing fractionsâ on page 1-25. Decimal Mark Dot or Comma . Displays a number as 12456.98 (Dot mode) or as 12456,98 (Comma mode). Dot mode uses commas to separate elements in lists and matrices, and to separate function arguments. Comma mode uses periods (dot) as separators in these contexts. Setting Options (Continued) HP 3 9gs Engl ish. book Pa ge 11 We dnes day, Dec embe r 7, 2005 11 : 24 PM
1-12 Getting started T he cur sor (hi ghlight) is in the fir st f ield , Angle Measur e . 2 . Pr ess to display a li st of choic es. 3. P re s s to select Degrees , and pres s . The angle mea sur e changes to degrees . 4. Pr ess to r eturn to HOME . HINT Whenever an input form has a list of choices for a field, you can press to cycle through them instead of using . Aplets (E-lessons) Aplets are the application environments where you explore different classes of mathematical operations. You select the aplet that you want to work with. Aplets come from a variety of sources: ⢠Built-in the HP 3 9gs (initial pur chase). ⢠Aplets cr eated by sa v ing ex isting aplets, w hic h hav e been modified , with spec ific conf igurati ons. See âCr eating new aplets bas ed on ex isting aplets â on page 19-1. ⢠Do wnloaded fr om HPâs Calc ulators w eb site. ⢠Cop ied f r om another calculato r . Aplets are stored in the Aplet library. See âAplet libraryâ on page 1-16 for further information. You can modify configuration settings for the gr aphical, tabular, and HP 3 9gs Engl ish. book Pa ge 12 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Getting started 1-13 symbolic views of the aplets in the following table. See âAplet view configurationâ on page 1 -18 for further information. In addition to these aplets, wh ich can be u sed in a variety of applications, the HP 39 gs is supplied with two teaching aplets: Quad Explorer and Trig Explorer. You cannot modify configurati on settings for these aplets. A great many more teachi ng ap lets can be found at HPâs web site and other web sites created by educators, together with accompanying documentation, often with student work sheets. These ca n be download ed free of Aplet name Use this aplet to e xplore: Function Real-valued, rectangular functions y in terms of x . Example: . Inference Confidence intervals and Hypothes is tests based on the Normal and Students-t distributions. Parametric Parametric relations x and y in terms of t . Example: x = cos(t ) and y = sin(t ). Polar Polar functions r in terms of an angle θ . Example: . Sequence Sequence functions U in terms of n , or in terms of previous terms in the same or another sequence, such as and . Example: , and . Solve Equations in one or more real-valued variables. Example : . Finance Time Value of Money (TVM) calculatio ns. Linear Solver Solutions to sets of two or three linear equations. Triangle Solver Unknown values for the lengths and angles of triangles. Statistics One-variable ( x ) or two-variable ( x and y ) statistical data. y 2 x 2 3 x 5 = r 24 θ () cos = U n 1 â U n 2 â U 1 0 = U 2 1 = U n U n 2 â U n 1 â = x 1 x 2 x â2 â = HP 3 9gs Engl ish. book Pa ge 13 We dnes day, Dec embe r 7, 2005 11 : 24 PM
1-14 Getting started charge and transferred to the HP 39gs using the provided Connectivity Kit. Quad Explorer aplet The Quad Explorer aplet is used to investigate the behaviour of as the values of a , h and v change, both by manipulati ng the equation and seeing the change in the graph, and by manipulating the grap h and seein g the chang e in the eq uation. HINT More detailed documentation, and an accompanying student work sheet can be found at HPâs web site. Pr ess , selec t Quad Explorer , and then press . The Qu ad Exp lorer aplet opens in mode, in which the arro w keys, the and keys, and the key are used to change the shape of the graph. This changing shape is reflected in the equation displayed at the top right corner of the screen, while the original graph is retained for comparison. In this mode the graph controls the equation. It is also possible to have the equation control the graph. Pressing displays a sub-expression of your equation. Pressing the and key moves between sub- expressions, while pressing the and key changes their values. Pressing allows t he user to select whether all three sub-expressions will be explored at once or only one at a time. A button is provided to evaluate the studentâs knowledge. Pres sing displays a target q uadratic graph. The student must manipulate the equationâs parameters to make the equation match the target graph. When a student feels that they have correctly chosen the parameters a button eva luates the answer and provide f eedback. A n button is provided for those who give up! ya x h () 2 v = HP 3 9gs Engl ish. book Pa ge 14 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Getting started 1-15 Trig Explorer aplet The Trig Explorer aplet is used to investigate the behaviour of the graph of as the values of a , b , c and d change, both by manipulating the equation and seeing the change in the graph, or by manipulating the graph and seeing the change in the equation. Press , select Trig Explorer , and then press to display the screen shown right. In this mode, the graph controls the equation. Pressing the and keys transforms the graph, with these transformations reflected in the equation. The button labelled is a toggle between and . When is chosen, the âpoint of controlâ is at the origin (0,0) and the a nd keys control vertical and horizontal transformations. When is chosen the âpoint of controlâ is on the fir st extremum of the graph (i.e. for the sine graph at . The arrow keys change the amplitude and frequency of the graph. This is most easily seen by experimenting. Pressing displays the equation at the top of the screen. The equation is controlled by the graph. Pressing the and keys moves from parameter to parameter. Pressing the o r key changes the parameterâs values. The default angle setting for this aplet is radians. The angle setting can be changed to degrees by pressing . ya b x c () d sin = Origin Ï 21 , â () Extremum HP 3 9gs Engl ish. book Pa ge 15 We dnes day, Dec embe r 7, 2005 11 : 24 PM
1-16 Getting started Aplet library Aplets are stored in the Aplet library. To open an aplet Press to display the Aplet library menu. Se lect the aplet and press or . From within an aplet, you can return to HOME any time by pressing . Aplet views When you have configured an aplet to define th e relation or data that you want to explore, you c an display it in differ ent views. Here are illu strations of the three major aplet views (Symbolic, Plot, and Numeric), the six supporting aplet views (from the VIEWS menu ), and the two user-defined views (Note and Ske tch). Note : some apletsâsuch as the Linear Solver aplet an d the Triangle Solver apletâonly have a single view, the Numeric view. Symbolic view Pres s to display the apletâs S ymbolic v iew . Y ou use this v ie w to define the func tio n(s) or equati on(s) that y ou w ant to explor e. See âAbout the Symbolic viewâ on page 2-1 f or further information. Plot view Pr ess to display the apletâ s P l ot v ie w . In this v iew , the f uncti ons that y ou hav e defined ar e displa y ed gr aphi cally . See âAbout the Plot viewâ on page 2-5 for further information. HP 3 9gs Engl ish. book Pa ge 16 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Getting started 1-17 Numeric view Press to display the apletâs Numeric view. In this view, the functions that you have defined are displayed in tabular format. See âAbout the numeric viewâ on page 2 -16 for further information. Plot-Table view The VIEWS menu contains the Plot-Table view. Select Plot-Table Splits the screen into the plot and the data table. See âOther views for scaling and splitting the graphâ on page 2-13 for futher information. Plot-Detail view The VIEWS menu contains the Plot-Detail view. Select Plot-Detail Splits the screen into the plot and a close-up. See âOther views for s caling and splitting the graphâ on page 2-13 for further information . Overlay Plot view The VIEWS menu contains the Overlay Plot view. Select Overlay Plot Plots the current expression(s) without erasing any pre-existing plot(s). See âOther views for s caling and splitting the graphâ on page 2-13 for further information . HP 3 9gs Engl ish. book Pa ge 17 We dnes day, Dec embe r 7, 2005 11 : 24 PM
1-18 Getting started Note view Press NOTE to display the apletâs note view. This note is transferred with the aplet if it is sent to another calculator or to a PC. A note view contains text to supplement an aplet. See âNotes and ske tchesâ on page 17-1 for further information. Sketch view Press SKETCH to dis play the ap letâs sk etch view . Display s pictur es to supplement an aplet. See âNotes and sketchesâ on page 17-1 for further information. Aplet view configuration You use the SETUP keys ( , and ) to configure the aplet. For example, press SETUP - PLOT ( ) to display the input form for setting the apletâs plot settings. Angle measure is controlled using the MODES view. Plot Setup Press SETUP - PLOT . Sets parameters to plot a graph. Numeric Setup Press SE TUP - NUM . Sets parameters for building a table of numeric values. Symbolic S etup This vi ew is only availa ble in the Statistics aplet in mode, where it plays an important role in choosing data models. Press SETUP - SYMB . HP 3 9gs Engl ish. book Pa ge 18 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Getting started 1-19 To change views Each view is a separate environment. To change a view, select a different view by pressing , , keys or select a view from the VIEWS menu. To change to HOME, press . You do not explicitly close the current view, you just ente r another oneâlike passing from one room into another in a house. Data that you enter is automatically saved as you enter it. To save aplet configuration You can save an aplet config uration that you ha ve used, and transfer the aplet to other HP 39gs calculators. See âCreating new aplets based on existing apletsâ on page 19-1. Mathematical calculations The most commonly used math operations are available from the keyboard. Access to the rest of the math functions is via the MATH menu ( ). To access programming commands, press CMDS . See âProgramming commandsâ on page 18-13 for further information. Where to start The home base for the calculator is the HOME view ( ). You can do all calculations here, and you can access all operations. Entering expressions ⢠Enter an e xpre ssion int o the HP 3 9gs in the same left- to -ri ght order that y ou w ould wr i te the e x pr essi on. T his is ca lled algebr aic entry . ⢠T o enter functions, select the k e y or MA TH menu i tem fo r that functi on . Y ou can also enter a func tion b y using the A lpha k e y s to spell o ut its name . ⢠Pr ess to e valuate the e x pr ession y ou have in the edit line (w her e the blinking c urso r is) . An exp re ss io n can contain numbers , func tions , and va riab le s. HP 3 9gs Engl ish. book Pa ge 19 We dnes day, Dec embe r 7, 2005 11 : 24 PM
1-20 Getting started Example Calculate : Long results If the result is too long to fit on the display line, or if you want to see an expression in textbook format, press to highlight it and then press . Negative numbers Type to start a negative number or to insert a negative sign. To raise a negative number to a power, enclose it in parentheses. For example, (â5) 2 = 25, whereas â5 2 = â25. Scientific notation (powers of 10) A number like or is written in scientific notation , that is, in terms of powers of ten. This is simpler to work with than 50000 or 0.0 00000321. To enter numbers like these, use EEX . (This is easier than using 10 .) Example Calculate 4 EEX 13 6 EEX 23 3 EEX 5 Explicit and implicit multiplication Implied multiplication takes pl ace when two operands appear with no op erator in between. If you enter AB , fo r example, the result is A*B . 23 2 14 8 â 3 â --------------------------- - 45 () ln 23 14 8 3 45 51 0 4 Ã 3.21 10 7 â Ã 41 0 13 â Ã () 61 0 23 Ã () 31 0 5 â Ã ---------------------------------------------------- HP 3 9gs Engl ish. book Pa ge 20 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Getting started 1-21 However, for clarity, it is better to include the multiplication sign where you expect multiplication in an expression. It is clearest to enter AB as A*B . HINT Implied multiplication will not always work as expecte d. For example, entering A(B 4 ) will not give A*(B 4) . Instead an error message is displayed: âI nvalid User Functionâ. This is because the calculator interprets A(B 4) as meaning âevaluate function A at the value B 4 â, and function A does not exist. When in doubt, insert the * sign manually. Parentheses You need to use parentheses to enclose arguments for functions, such as SIN(45). You can omit the final parenthesis at the end of an edit line. The calculator inserts it automatically. Parentheses are also important in specifying the order of operation. Without parentheses, the HP 39gs calculates according to the order of algebraic precedence (the next topic). Following are some examples using parentheses. Entering ... Calculates... 45 Ï si n (45 Ï) 45 Ï sin (45) Ï 85 9 85 9 85 9 Ã 85 9 Ã HP 3 9gs Engl ish. book Pa ge 21 We dnes day, Dec embe r 7, 2005 11 : 24 PM
1-22 Getting started Algebraic precedence order of evaluation Functions within an expression are evaluated in the following order of precedence. Functions with the same precedence are evaluated in order from left to right. 1. E xpressions w it hin parenthe ses. Neste d p ar ent heses ar e ev aluated fr om inner to outer . 2 . Pr efi x functio ns, suc h as S IN and L OG . 3 . P ostfi x func tions , such a s ! 4. P o we r functi on , ^, NTHROO T . 5 . Negati on , multiplicati on , and di v ision . 6 . Additio n and subtr action . 7. A N D a n d N O T . 8. OR and X OR. 9 . L eft ar gument of | ( w her e) . 10. E quals, =. Largest and smallest numbers The smallest number the HP 39gs can represent is 1Ã1 0 â499 (1Eâ499). A sma ller result is displayed as zero. The largest number is 9.99999999999 à 10 499 (1E499). A greater result is displayed as this num ber. Clearing numbers ⢠c lears the char acter under the cu rso r . When the c urso r is positio ned after the last c har acte r , delete s the char acter t o the left of the c ursor , that is, it performs the same as a bac kspace ke y . ⢠CANCEL ( ) clear s the edit line . ⢠CLEAR c lears all inpu t and outpu t in the display , in c luding th e display history . Using previous results The HOME display ( ) shows you four lines of input/output history. An un limited (except by memory) number of previous lines c a n be displayed by scrolling. You can retrieve and reuse any of these values or expressions. Output Last output Inpu t Last input Edit line HP 3 9gs Engl ish. book Pa ge 22 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Getting started 1-23 When you highlight a previous input or result (by pressing ), the and menu labels appear. To copy a previous line Highlight the line (press ) and press . The number (or expression) is co pied into the e dit line. To reuse the last result Press AN S (last answer) to put the last result from the HOME display into an expression. ANS is a variable that is updated each time you press . To repeat a previous line To repeat the very last line, just press . Otherwise, highlight the line (press ) first, and then press . The highlighted expression or nu mber is re-entered. If the previous line is an expression c ontaining the ANS , the calculation is repeated it eratively. Example See how ANS retrieves and reuses the last result (50), and updates ANS (from 50 to 75 to 100). 50 25 You can use the last result as the first expression in the edit line without pressing ANS . Pressing , , , or , (or other operators th at require a preceding argument) automatically enters ANS before the operator. You can reuse any other expression or valu e in the HOME display by highlighting the expression (using the arrow keys), then pressing . See âUsing previous resultsâ on page 1-22 for more details. The variable ANS is different from the numbers in HOMEâs display history. A value in ANS is stored internally with the full precision of the calculated result, whereas the displayed numbers match the display mode. HP 3 9gs Engl ish. book Pa ge 23 We dnes day, Dec embe r 7, 2005 11 : 24 PM
1-24 Getting started HINT When you retrieve a number from ANS , you obtain the result to its full precision. When you retrieve a number from the HOMEâs display history, you obtain exactly what was displaye d. Pressing evaluates (or re-evaluates) the last input, whereas pressing ANS copies the last result (as ANS ) into the edit line. Storing a value in a variable You can save an answer in a variable and use the variable in later calculation s. There are 27 variables available for storing real values. These are A to Z and θ . See Chapter 14, âVariables and memory managementâ for more information on variables. For example: 1. P erf orm a calc ulation . 45 8 3 2 . Stor e the result in the A vari ab le. A 3 . P er f or m another calc ulatio n using the A v ari able . 95 2 A HP 3 9gs Engl ish. book Pa ge 24 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Getting started 1-25 Accessing the display history Pressing enables the highlight bar in the display history. While the highlight bar is active, the following menu and keyboard keys are very useful: Clearing the display history Itâs a good habit to cl ear the display his tory ( CLEAR ) whenever you have finish e d working in HOME. It saves calculator memory to clear the display history. Remember that all your previous inputs and results are saved until you clear them. Using fractions To work with fractions in HOME, you set the number format to Fraction or Mixed Fraction , as follows: Setting Fraction mode 1. In HOME , open the HO ME MODE S input f orm . MODES Key F u n c t i o n , Scrolls through the di splay history. Copies the highlighted expression to the position of the curso r in the edit line. Displays the current expre ssion in standard mathematical for m. Deletes the highlighted expression from the display history , unless there is a cursor in the edit line. CLEAR Clears all lines of display history and the edit line. HP 3 9gs Engl ish. book Pa ge 25 We dnes day, Dec embe r 7, 2005 11 : 24 PM
1-26 Getting started 2 . Select Number Format , pr ess to display the optio ns, and hi ghlight Fract ion or Mixed Fraction . 3 . Pr ess to sele ct the Number F ormat option , then mo ve to the prec ision value field . 4. Enter the prec ision v alue that yo u want to us e , and pr ess to set the pr ecisi on . Pres s to retur n to HOME . See âSetting fr action pr ec i si on â belo w for mor e infor mation . Setting fraction precision The fraction precision setting determines the pr ecision in which the HP 39gs converts a decimal value to a fraction. The greater the precision value that is set, the closer the fraction is to the decimal value. By choosing a precision o f 1 you are saying that the fraction only has to match 0.234 to at least 1 decimal place (3/13 is 0.23076... ). The fractions used are found using the technique of continued fractions. When converting recurring decimals this can be important. For ex ample, at precision 6 the decimal 0.6666 becomes 3333/5 000 (6666/10000) wher eas at precision 3, 0.6666 becomes 2/3 , which is probably what you would want. For example, when converting .234 to a fraction, the precis ion value has th e following effect: HP 3 9gs Engl ish. book Pa ge 26 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Getting started 1-27 ⢠Pr ec ision set to 1: ⢠Pr ec ision set to 2 : ⢠Pr ec ision set to 3: ⢠Pr ec ision set to 4 Fraction calculations When entering fractions: ⢠Y ou use the ke y to separate the numerator part and the denominator par t of the fr action. ⢠T o ent er a mi xed f r acti on , f or e x ample , 1 1 / 2 , y ou enter it in the f ormat (1 1 / 2 ). For example, to perform the following calc ulation: 3(2 3 / 4 5 7 / 8 ) 1. Set the Number f or mat mode to Fraction or Mixed Fraction and sp ec ify a pr ec ision v alue of 4. In this ex ample, w eâll select Fraction as our form a t.) MODES Select Fraction 4 HP 3 9gs Engl ish. book Pa ge 27 We dnes day, Dec embe r 7, 2005 11 : 24 PM
1-28 Getting started 2. E n t e r t h e c a l c u l a t i o n . 32 3 45 7 8 Note: Ensur e y ou ar e in the HOME v ie w . 3 . E valuat e the calc ulation . Note that if you had selected Mixed Fraction instead of Fraction as the Number format, the answer would have been expressed as 25 7/8. Converting decimals to fractions To convert a decimal value to a fraction: 1. Set the number f ormat mode to Fraction or Mixed Fraction . 2 . Eithe r r etr ie v e the v alue fr om the Hist ory , or en ter the v alue on the command line. 3 . Pres s to conv ert the number t o a fr action . When converting a decimal to a fraction, keep the following points in mind: ⢠When con v erting a rec u r r ing dec imal to a fr acti on , set the f r actio n pr ec ision to abou t 6, and e nsur e that y ou include mor e than six dec imal places in the r ec urr ing dec imal that y ou ent er . In this e x ample , the fr action pr ecisi on is set to 6. T he top calc ulation r eturns the corr ect r esult . The bottom one does no t . ⢠T o con vert an ex act decimal to a fr action, set the fr action pr ecisi on to at lea st two mor e than the number of dec imal plac es in the dec imal . HP 3 9gs Engl ish. book Pa ge 28 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Getting started 1-29 In this e x ample , the fr action pr ec ision is s et to 6. Complex numbers Complex results The HP 39gs can return a complex number as a result for some math functions. A comp lex number appears a s an ordered pair ( x, y ), where x is the real part and y is the imaginary part. For example, entering returns (0,1). To enter complex numbers Enter the number in either of these forms , where x is the real part, y is the imaginar y part, and i is th e imagina ry constant, : ⢠( x, y ) or ⢠x iy . To enter i : ⢠pr ess or ⢠pr ess , or keys t o sel e c t Cons tant , to mo v e to the r ight column o f the menu , to sele ct i , and . Storing comp lex numbers There are 10 variables available for storing complex numbers: Z0 to Z9. To store a complex number in a variable: ⢠Enter th e complex numb er , p r ess , enter the v ari able to s tor e the number i n , and pr ess . 45 Z 0 1 â 1 â HP 3 9gs Engl ish. book Pa ge 29 We dnes day, Dec embe r 7, 2005 11 : 24 PM
1-30 Getting started Catalogs and editors The HP 39gs has several catalogs and editors. You use them to create and manipulate objects. They access features and stored values (numbe rs or text or other items) that are independent of aplets. ⢠A catalog lists items, w hich y ou can delete or tr ansmit , for e xampl e an aplet . ⢠An edito r lets you c reate or modify items and number s, for e xample a no te or a matr i x . Catalog/Editor Contents Aplet library () Aplets. Sketch editor ( SKETCH ) Sketches and diagrams, See Chapter 17, âN otes and sketchesâ. List ( LIST ) Lists. In HOME, lists are enclosed in {}. See Chapter 16, âListsâ. Matrix ( MATRIX ) One- and two-dimensional arrays. In HOME, arrays are enclosed in []. See Chapter 15, âMatricesâ. Notepad ( NOTEPAD ) Notes (short text entries). See Chapter 17, âN otes and sketchesâ. Program ( PROGRM ) Programs that you create, or associated with user-defined aplets. See Chapter 18, âProgrammingâ. HP 3 9gs Engl ish. book Pa ge 30 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Aplets and their views 2-1 2 Aplets and t heir v ie w s Aplet views This section examines the options an d functionality of the three main views for the Function, Polar, Parametric, and Sequence aplets: Symbolic, Plot, and Numeric views. About the Symbolic view The Symbolic view is the defining view for the Functi on, Parametric, Polar, and Seque nce aplets. The other views are derived from the symbolic expression. You can create up to 10 different definitions for each Function, Parametric, Polar, and Sequence aplet. You can graph any of the relations (in the same aplet) simultaneously by selecting them. Defining an expression (Symbolic view) Choose the aplet from the Aplet Library. Pr ess or to select an aplet . T he F uncti on , P ar ametri c, P olar , and Sequence aplets s tart in the S ymbolic v ie w . If the highli ght is on an e x isting expr essio n , sc r oll to an empty lineâunless y ou don ât mind wr i ting o ver the e xpr essionâ or , clear o ne line ( ) or all line s ( CLEAR ). Expr es sions ar e selected (c heck mar ked) on entry . T o deselect an e xpressi on, pr ess . All selected e xpres sions ar e plotted. HP 3 9gs Engl ish. book Pa ge 1 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
2-2 Aplets and the ir views â For a Function definiti on , e nt er an e xpr es sio n to def ine F(X) . The only independent variab le in th e ex pre ss i on i s X. â Fo r a P arametric definiti on , e nt er a pair of e xpr essi ons to def ine X(T) and Y(T) . The o nly independent v ari able in the e xpr es sions is T . â Fo r a Pol a r definiti on , e nt er an e xpr es sio n to def ine R ( θ ). T h e only independent variab le in th e ex pre ss i on i s θ . â Fo r a S eq u e n c e definiti on , e ither enter the f irst ter m , or the fi rst and second terms, for U (U1 , or ... U9 , or U0 ) . Then def i ne the n th ter m of the seq uence in ter ms of N or of the pr ior t erm s, U(Nâ1) and/or U(Nâ2) . The e xpres sions should pr oduce r eal- v alued sequences w ith integer domains . Or define the n th ter m as a non-r ec ursi ve e xpr essi on in terms o f n onl y . In this case , the calc ulator inserts the f irs t two te rms bas ed on the expr essi on that y ou def ine. â Note : Y ou w i ll hav e to enter t he second term if the hp 3 9gs is unable to calc ulate it automatically . T y picall y if U x(N) depends on U x(Nâ2) then y ou must enter U x(2) . HP 3 9gs Engl ish. book Pa ge 2 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Aplets and their views 2-3 Evaluating expressions In aplets In the Symbolic view, a variable is a symbol only, and does not represent one specif ic value. To evaluate a function in Symbolic view, press . If a function calls another function, then reso lves all references to other functions in terms of their independent variable. 1. Choo se the F unction apl et . Sele ct Function 2 . Enter the e xpr es sions in the F unction ap letâs S y mbolic vi ew . A B F1 F2 3 . Highligh t F3(X) . 4. Pr ess Note h o w the value s fo r F1(X) and F2(X) ar e sub stituted in to F3(X) . HP 3 9gs Engl ish. book Pa ge 3 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
2-4 Aplets and the ir views In HOME You can also evaluate any expression in HOME by entering it into the edit line and pressing . For example, define F4 as below. In HOME, type F4(9) and press . This evaluates the expression, substituting 9 in place of X into F4 . SYMB view keys The following table details the menu keys that you use to work with the Symbolic view. K e y Meaning Copies the highlighted expression to the edit line for editing. Press when done. Checks/unchecks the current expression (or set of expressions). Only checked expression(s) are evaluated in the Plot and Numeric views. Enters the independent variable in the Function aplet. Or, you can use the key on the keyboard. Enters the independent variable in the Parametric aplet. Or, you can use the key on the keyboard. Enters the independent variable in the Polar aplet. Or, you can use the key on the keyboard. Enters the independent variable in the Sequence aple t. Or, you can use the key on the keyboard. Displays the curren t expression in text book form. Resolves all references to other definitions in terms of va riables and evaluates all arithmetic express ions. Displays a menu for entering variable names or contents of variables. HP 3 9gs Engl ish. book Pa ge 4 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Aplets and their views 2-5 About the Plot view After entering and selecting (check marking) the expression in the Symbolic view, press . To adjust the appearance of the graph or the interval that is displayed, you can change the Plot view settings. You can plot up to ten expressions at the same time. Select the expressions you want to be plotted together. Setting up the plot (Plot view setup) Press SETUP - PLOT to define any of the se ttings shown in the next two table s. 1. Hi ghlight the f ield to edit . â If there is a n umber to enter , t y pe it in and pr ess or . â If there is an opti on to ch oose , pre ss , highli ght y our c hoi ce , and pres s or . As a shortcut to , j ust highlight the field to change and pr ess to cy cle thr ough the optio ns. â If there is an option to select or deselect, pr ess t o ch e ck o r u nch e ck i t. 2 . Pr ess to vi e w mor e settings . 3 . When done , pr ess to vi ew the ne w plot . Displays the menu for en tering math operations. CHARS Di splays special characters. To enter one, place the cursor on it and press . To remain in the CHARS menu and enter another special character, press . Deletes the highlighted expression or the current character in the edit line. CLEAR Deletes all expressions in the list or clears the edit line. K e y Meaning (Continued) HP 3 9gs Engl ish. book Pa ge 5 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
2-6 Aplets and the ir views Plot view settings The plot view settings are: Those items with space for a checkmark are settings you can turn on or off. Press to display the second page. F ield Meaning XRNG, YRNG Specifies the minimum and maximum horizontal ( X ) and vertical ( Y ) values for the plotting window. RES For function plots: Resolution; âFasterâ plots in alternate pixel columns; âDetailâ plots in every pixel column. TRNG Parametric aplet: Specifies the t- values ( T ) for the graph. θ RNG Polar aplet: Specifies the angle (θ ) value range for the graph. NRNG Sequence aplet: Specifies the index ( N ) values for the graph. TSTEP For Parametric plots: the increment for the independent variab le. θ STEP For Polar plots: the increment value for the independent variable. SEQPLOT For Sequen ce aplet: Stairste p or Cobweb types. XTICK Horizontal spacing for tickmarks. YTICK Vertical spacing for tickmarks. F ield Meaning SIMULT If more than one relation is being plotted, plots them simultaneously (otherwise sequentially). INV. CROSS Cursor crosshairs invert the status of the pixels they cover. HP 3 9gs Engl ish. book Pa ge 6 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Aplets and their views 2-7 Reset plot settings To reset the default values for all plot settings, press CLEAR in the Plot Setup view. To reset the default value for a field, highlight the field, and pres s . Exploring the graph Pl o t v i ew g iv e s y ou a se l ec t io n of k ey s a n d m e nu k ey s to explore a graph further. The options vary from aplet to aplet. PLOT view keys The following table details the keys that you use to work with the graph. CONNECT Connect the plotted points. (The Sequence aplet always connects them.) LABELS Label the axes with XRNG and YRNG values. AXES Draw the axes. GRID Draw grid points using XTICK and YTICK spacing. F ield Meaning (Continued) K e y Meaning CLEAR Erases the plot and ax es. Offers additional pre-defined views for splitting the screen and for scaling (âzoomingâ) the axes. Moves cursor to far left or far right. Moves cursor between relations. or Interrupts plotting. Continues plotting if interr upted. HP 3 9gs Engl ish. book Pa ge 7 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
2-8 Aplets and the ir views Trace a graph You can trace along a function using the or key which moves the cur sor along the graph. The display also shows the current coordinate position ( x, y ) of the cursor. Trace mode and the coordinate di splay are automatically set when a plot is drawn. Note: Tracing might not appe ar to exactly follow your plot if the resolution (in Plot Setup view) is set to Faster. This is because RES: FASTER plots in only every other column, whereas tracing al ways uses every column. In Function and Sequence Aplets: Yo u can also scroll (move the cursor) left or right beyond the edge of the display window in trace mode, giving you a vi ew of more of the plot. To move between relations If there is more than one relation displayed, press or to move between relations. Turns menu-key labels on and off. When the labels are off, pressing turns th em back on. ⢠Pr essing once display s the full r ow o f labels . ⢠Pr essing a second time r emo ves the r ow of labels to displa y onl y the gr aph . ⢠Pr essing a thir d time displa y s the coordinate mode . Displays the ZOOM menu list. Turns trace mode on/off. A white box appears over the on . Opens an input form for you to enter an X (or T or N or θ ) value. Enter the value and press . The cursor jumps to the point on the graph that you entered. Function aplet only: turns on menu list for root-finding functions (see âAnalyse graph with FCN functionsâ on page 3-4). Displays the current, defining expression. Press to restore the menu. K e y Meaning (Continued) HP 3 9gs Engl ish. book Pa ge 8 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Aplets and their views 2-9 To jump directly to a value To jump straight to a value rather than using the Trace function, use the menu key. Press , then enter a value. Press to jump to the value. To turn trace on/off If the menu labels are no t displayed, press first. ⢠T urn o ff tr ace mode by pr essing . ⢠T urn on tr ac e mode by pre ssing . ⢠T o turn the c oor dinate displ a y off , pr ess . Zoom within a graph One of the menu key options is . Zooming redraws the plot on a larger or smaller scale. It is a shortcut for changing the Plot Setup. The Set Factors... option enables you to set the factors by which you zoom in or zoom out, and whether the zoom is centered about the cursor. ZOOM options Press , select an option, and press . (If is not displayed, press .) Not all options are available in all aplets. Option Meaning Center Re-centers the plot around the current position of the cursor without changing the scale. Box... Lets you draw a box to zoom in on. See âOther views for scaling and splitting the graphâ on page 2-13. In Divides horizontal and vertical scales by the X-factor and Y-factor. For instance, if zoom factors are 4, then zooming in results in 1 /4 as many units depicted per pixel. (see Set Factors... ) Out Multiplies horizontal and vertical scales by the X-factor and Y-factor (see Set Factors... ). X-Zoom In Divides horizontal scale only, using X-factor. X-Zoom Out Multiplies horizontal scale, using X-factor. HP 3 9gs Engl ish. book Pa ge 9 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
2-10 Aplets and the ir views Y-Zoom In Divides vertical sc ale only, using Y-factor. Y-Zoom Out Multiplies v ertical scale only, using Y-factor. Square Changes the vertical scale to match the horizontal scale. (Use this after doing a Box Zoo m, X-Zoom, or Y-Zoom.) Set Factors... Sets the X-Zoom and Y-Zoom factors for zooming in or zooming out. Includes option to recenter the plot before zooming. Auto Scale Rescales the vertical axis so that the display shows a representative piece of the plot, for the supplied x axis settings. (For Sequence and Statistics aplets, autoscaling rescales both axes.) The autoscale process uses the first selected function only to determine the best scale to use. Decimal Rescales both axes so each pixel = 0.1 units. Resets defaul t values for XRNG (â6.5 to 6.5) and YRNG (â3.1 to 3.2). (Not in Sequence or Statistics aplets.) Integer Rescales horizontal axis only, making each pixel =1 unit. (Not available in Sequence or Statistics aplets.) Trig Rescales horizontal axis so 1 pixel = Ï /24 radians, 7 .58, or 8 1 / 3 grads; rescales vertic al axis so 1 pixel = 0.1 uni t. (Not in Sequence or Statistics aplets.) Option M eaning (Continued) HP 3 9gs Engl ish. book Pa ge 10 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Aplets and their views 2-11 ZOOM examples The following screens show the effects of zooming options on a plot of . Plot of Zoom In : In Un-zoom : Un-zoom Note: Press to move to the bottom of the Zoom list. Zoom Out : Out Now un -zoom . X-Zoom In : X-Zoom In Now un -zoom . X-Zoom Out : X-Zoom Out Now un -zoom . Un-zoom Returns the display to the previous zoom, or if there has been only one zoom, un-zoom displays the graph with the original plot settings. Option M eaning (Continued) 3 x sin 3 x sin HP 3 9gs Engl ish. book Pa ge 11 We dnes day, Dec embe r 7, 2005 11 : 24 PM
2-12 Aplets and the ir views Y-Zoom In: Y-Zoom In Now un-zoom. Y-Zoom Out: Y-Zoom Out Zoom Square: Square To box zoom The Box Zoom option lets you dr aw a box aroun d the area you want to zoom in on by selecting the endpoints of one diagonal of the zoom rectangle. 1. If necessary , pr ess to tur n on the menu -k ey labels . 2. P r e s s a n d s e l e c t Box... 3 . P osition the c ursor on one cor ner of the r ectangle . Pr ess . 4. Use the cursor k ey s ( , etc.) to drag to the op posite corner . 5 . Pr ess to z oom in on the box e d ar ea . HP 3 9gs Engl ish. book Pa ge 12 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Aplets and their views 2-13 To set zoom factors 1. In the P lot v iew , pr ess . 2. P r e s s . 3. Se l e c t Set Factors... and pr es s . 4. Enter the z oom fac tors . Ther e is one z oom fac tor f or the hor i z ontal sc ale ( XZOOM ) and one f or the vertical sca le ( YZOOM ). Z ooming out multipli es the s cale by the fac tor , so that a gr eater scale distance appears on the sc r een. Z ooming in div ide s the scale b y the fact or , so that a shorter s cale dist ance appear s on the sc r een . Other views for scaling and splitting the graph The preset viewing options menu ( ) contains options for drawing the plot using certain pre-defined configurations. This is a shortcut for changing Plot vi ew settings. For instance, if you have define d a trigonometric function, then you could select Trig to plot your function on a trigonometric scale. It also contains split-screen options. In certain aplets, fo r example those that you download from the world wide web, the preset viewing options menu can also contain options that relate to the aplet. VIEWS menu options Press , select an option, and press . Option Meaning Plot- Detail Splits the screen into the plot and a close-up. Plot-Table Splits the screen into the plot and the data table. Overlay Plot Plots the current expression(s) without erasing any pre-existing plot(s). HP 3 9gs Engl ish. book Pa ge 13 We dnes day, Dec embe r 7, 2005 11 : 24 PM
2-14 Aplets and the ir views Split the screen The Plot-Detail view can give you two simultaneous views of the plot. 1. Pr ess . Se lect Plot-Detai l and pr ess . The gr aph i s plotted twi ce. Y ou can no w z oom in on the r ight si de. 2. P r e s s , selec t the z oom method and pres s or . This z ooms the r ight si de. Her e is an e x ample of s plit scr een w ith Zoom In . â The P lot menu k e ys are a vailable as f or the f ull plot (f or tr ac ing, coor dinate displa y , equation displa y , and so on) . Auto Scale Rescales the vertical axis so that the display shows a representative piece of the plot, for the supplied x axis settings. (For Sequence and Statistics aplets, autoscaling rescales both axes.) The autoscale process uses the first selected function only to determine the best scale to use. Decimal Rescales both axes so each pixel = 0.1 unit. Resets default values for XRNG (â6.5 to 6.5) and YRNG (â3.1 to 3.2). (Not in Sequence or Statistics aplets.) Integer Rescales horizontal axis only, making each pixel = 1 unit. (Not available in Sequence or Statistics aplets.) Trig Rescales horizontal axis so 1 pixel = Ï /24 r adian, 7 .58, o r 8 1 / 3 grads; rescales vertical axis so 1 pixel = 0.1 unit. (Not in Sequence or Statistics aplets.) Option M eaning (Continued) HP 3 9gs Engl ish. book Pa ge 14 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Aplets and their views 2-15 â mo ves the leftmost c ursor to the scr eenâs left edge an d mo ves the ri ghtmost c ursor to the s cr een âs ri ght edge . â The menu k e y copi es the r ight plot t o the left plot . 3 . T o un -split the sc reen , pre ss . The left si de tak es o ver the wh ole scr e en . The Plot-Table view gives you two simultaneous views of the pl ot . 1. Pr ess . Select Plot-Table and pr ess . The scr een display s the plot on th e left side and a table of numbers on the right side. 2 . T o mov e up and do wn the ta ble , use the and c urso r k ey s. T hese k ey s mo ve the tr a.ce point le ft or r ight along the plot , and in the table , the cor r espo nding value s ar e highlighted . 3 . T o mo ve between f uncti ons, us e the and c urso r k e y s to mo v e the c ursor fr om one graph to another . 4. T o r eturn to a full Nume r ic (o r P lot) v ie w , pr ess (or ). Overlay plots If you w ant to pl ot over an ex isting plot withou t erasing that plot, then use Overlay Plot inste ad of . Note that tracing follows only the curre nt functions from the current aplet. Decimal scaling Decimal scaling is the default scaling. If you have changed the scaling to Trig or Integer, you can change it back with Decimal. Integer scaling Integer scaling compresses the axes so that e ach pixel is and the origin is near the scr een center. Trigonometric scaling Use trigonometric scaling whenever you are plotting an expression that includes trigonometric functions. Trigonometric plots are more li kely to intersect the axis at points factored by Ï . 11 Ã HP 3 9gs Engl ish. book Pa ge 15 We dnes day, Dec embe r 7, 2005 11 : 24 PM
2-16 Aplets and the ir views About the numeric view After entering and selecting (check marking) the expression or expressions that you want to explore in the Symbolic view, press to view a table of data values for the independent variable ( X , T, θ , or N ) and dependent variables. Setting up the table (Numeric view setup) Press NUM to define any of the table settings. Use the Numeric Setup input form to configure the table. 1. Hi ghlight the f ield to edit . Use the ar r ow k ey s to mo ve f r om f ield to f ield . â If there is a n u mber to en ter , t y pe it in and pr ess or . T o modi fy an ex isting number , press . â If there is an opti on to choos e , pre ss , highli ght y our c hoi ce, and pr ess or . â Shortc ut : Pr ess the ke y to copy v a lue s fr om the Plot Setup into NUMSTART and NUMSTEP . Effecti vel y , the menu k ey allo ws y ou to mak e the table match the p i x el columns in the gr aph v ie w . 2 . When do ne , pr ess to v ie w the table o f numbers. HP 3 9gs Engl ish. book Pa ge 16 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Aplets and their views 2-17 Numeric view settings The following table details the fields on the Numeric Setup input form. Reset numeric settings To reset the default values for all table settings, press CLEAR . Exploring the table of numbers NUM view menu keys The following table details the menu keys that you use to work with the table of numbers. Zoom within a table Zooming redraws the table of numbers in greater or lesser detail. F ield Meaning NUMSTART The independent variableâ s starting value. NUMSTEP The size of the increment from one independent v ariable value to the next. NUMTYPE Type of numeric table: Automatic or Build Your Own. To build your own table, you must type each independent value into the table yourself. NUMZOOM Allows you to zoom in or out on a selected value of the independent variable. K ey Meaning Displays ZOOM menu list. Toggles between two character sizes . Displays th e defining function expression for the highlighted column. To cancel this display, press . HP 3 9gs Engl ish. book Pa ge 17 We dnes day, Dec embe r 7, 2005 11 : 24 PM
2-18 Aplets and the ir views ZOOM options The following table lists the zoom options: The display on the right is a Zoom In of the display on the left. The ZOOM factor is 4. HINT To jump to an independent va riable value in the table, use the arrow keys to place the cursor in the independent variable column, then enter the value to jump to. Automatic recalculation You can enter any new value in the X column. When you press , the values for the dependent variables are recalculated, and the entire table is regenerated with the same interval between X values . Option Meaning In Decreases the intervals for the independent variable so a narrower range is show n. Uses the NUMZOOM factor in Numeric Setup. Out Increases the intervals for the independent variable so that a wider range is shown. Uses the NUMZOOM factor in Numeric Setup. Decimal Changes intervals for the independent variable to 0.1 units. Starts at zero. (Shortcut to changing NUMSTART and NUMSTEP .) Integer Changes intervals for the independent variable to 1 un it. Starts at zero. (Shortcut to changing NUMSTEP .) Trig Changes interv als for independent variable to Ï /24 radian o r 7.5 degrees or 8 1 / 3 grads. Starts at zero. Un-zoom Returns the display to the previous zoom. HP 3 9gs Engl ish. book Pa ge 18 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Aplets and their views 2-19 Building your own table of numbers The default NUMTYPE is âAutomaticâ, which fills the table with data for regular intervals of the independent ( X , T , θ , or N ) variable. With the NUMTYPE option set to âBuild Your Ownâ, you fill the table yourself by typing in the independent-variable values yo u want. The dependent values are then calculated and displayed. Build a table 1. S tart with an e xpressi on def ined (in S ymboli c v ie w) in th e ap let of you r choic e . Not e: F uncti on , P olar , P ar ametric , and Sequenc e aplets onl y . 2 . In the Numer ic Setup ( NUM ) , choo se NUMTYPE: Build Your Own . 3 . Open the Numeri c v ie w ( ) . 4. Clear e xisting dat a in the table ( CLEAR ). 5 . Ente r the independent v alues in the left -hand column . T ype in a number and pr ess . Y ou do not hav e to enter them in or der , becaus e the functi on can rear r ange them . T o inser t a number bet w een two others , use . Clear data Press CLEAR , to er ase the data from a table. F1 and F2 entries are generated automatically You enter numbers into the X column HP 3 9gs Engl ish. book Pa ge 19 We dnes day, Dec embe r 7, 2005 11 : 24 PM
2-20 Aplets and the ir views âBuild Your Ownâ menu keys Example: plotting a circle Plot the circle, x 2 y 2 = 9 . First rearrange it to read . To plot both the positive and negative y values, you need to define two equations as follows: and K e y Meaning Puts the highlighted independent value ( X , T , θ , or N ) into the edit line. Pressing replaces this variable with its current value. Inserts a zero value at the position of the highlight. Replace a zero by typing the number you want and pressing . Sorts the independent variable values into ascending or descending order. Press and select the ascending or descending option from the menu, and press . Toggles between two character sizes. Displays the defining function expression for the highlighted column. Deletes the highlighted row. CLEAR Clears all data from the table. y 9 x 2 â ± = y 9 x 2 â = y 9 x 2 â â = HP 3 9gs Engl ish. book Pa ge 20 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Aplets and their views 2-21 1. In the F unction aplet , spec ify the functi ons . Select Function 9 9 2 . Rese t the gr aph se tup to the de fa ult setting s. SETUP - PLOT CLEAR 3 . P lot the two func tions and hide the men u so that y ou can see all the ci rc l e. 4. R eset the n umer ic s etup to the def ault se ttings. SETUP - NUM CLEAR 5 . Displa y the functio ns in numer ic f orm . HP 3 9gs Engl ish. book Pa ge 21 We dnes day, Dec embe r 7, 2005 11 : 24 PM
HP 3 9gs Engl ish. book Pa ge 22 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Function aplet 3-1 3 F unc tion aplet About the Function aplet The Function aplet enables you to explore up to 10 real-valued, rectangu lar functions y in terms of x . For example . Once you have defined a function you can: ⢠cr eate gr aphs to fi nd r oots, int er cepts, slope , signed ar ea, and e x tr ema ⢠cr eate tables to evaluate f uncti ons at par tic ular va lu es . This chapter demonstrates the basic tools of the Function aplet by stepping you through an example. See âAplet viewsâ on page 2-1 for furth er information about the functionality of the Symbolic, Numeric , and Plot views. Getting started with the Function aplet The following example involves two functions: a linear function and a quadratic equati on . Open the Function aplet 1. Open the Functi on aplet . Select Fun ction T he F uncti on aple t starts in the S ymboli c v ie w . The Symbolic view is the defining view for Function, Parametric, Polar, and Seq uence aplets. The other views are derived from the symbolic expression. y 2 x 3 = y 1 x â = yx 3 () 2 2 â = HP 3 9gs Engl ish. book Pa ge 1 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
3-2 Function aplet Define the expressions 2 . T her e are 10 f uncti on def inition f ields on the F uncti on apletâs S y mbolic v ie w sc r een . Th ey ar e labeled F1(X) to F0(X). Highligh t the func tion de f inition f ield y ou w ant to use , and en ter a n e xpr es si on . (Y o u can pr ess to delete an e xis ting line , or CLEAR to clear all lines .) 1 3 2 Set up the plot You can change the scales of the x and y axes, graph resolution, and the spacing of the axis ticks. 3 . Display plot s ettings. SETUP - PLOT Note: F or our e x ample , you can lea v e the plot settings at t heir def ault values since we w ill be using the Auto Scale f eatur e to c hoose an appr opr iate y ax is fo r our x axis s ettings. If y our settings do not matc h this e x ample , pre ss CLEAR to r estor e th e defau lt valu es. 4. Spec ify a gri d f or the gr aph . Plot the functions 5 . P lot the functi ons. HP 3 9gs Engl ish. book Pa ge 2 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Function aplet 3-3 Change the scale 6 . Y ou can chan ge the scale to see mo r e or le ss of your gr aphs . In this e xam ple , ch oose Auto Scale . (See âVIEW S menu options â on page 2 -13 f or a de scr ip t ion of Aut o Sc al e) . Select Auto Scale Trace a graph 7 . T race the linear f uncti on . 6 times Note: B y default , the tr acer is acti ve . 8. Jum p fr om the linear functi on to the q uadra tic func tion . HP 3 9gs Engl ish. book Pa ge 3 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
3-4 Function aplet Analyse graph with FCN functions 9. Display the Plot view menu. From the Plot view menu, you can use the functions on the FCN menu to find roots, intersections, slopes, and areas for a function defined in the Function aplet (and any Function-based ap lets). The FCN fun ctions act on the currently selecte d graph. See âFCN func tions â on page 3-10 fo r further infor matio n. To find a root of the quadratic function 10. Mov e the cur sor to the gr aph of the quadr atic equati on by pr es sing the or ke y . Then mo ve the c urs or so that it is near by pr essing the or ke y . Sele ct Root T he root v alue is display ed a t the bottom of the sc r een. Note: If ther e is more tha n one root (a s in our exam p l e ) , t he coor dinates of the r oot c lose st to the c urr ent c ursor position ar e display ed. To find the intersection of the two functions 11. F ind the inte rsec tion o f the two f uncti ons . x 1 â = HP 3 9gs Engl ish. book Pa ge 4 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Function aplet 3-5 12 . Cho ose the linear f unction w hose int ers ecti on w ith the quadr atic functi on you w ish to f ind. T he coor dinates o f the inters ecti on poin t ar e display ed at the bottom of the scr een. Note: If ther e is more than one inter secti on (as in our e xam ple) , the coor dinates of the inter sec tion po int c lose st to the c urr ent c ursor po sition ar e displa ye d. To find the slope of the quadratic functio n 13 . F ind the slope of the quadr atic f uncti on at the inters ecti on poin t . Sele ct Slope T he slope v alue is display ed at the bottom of th e sc r een. To find the signed area of the two functio ns 14. To find the area between the two functions in the range â2 ⤠x ⤠â1, fir st mo v e the c urso r to and selec t the signed ar ea optio n . Sele ct Signed area F 1 x () 1 x â = HP 3 9gs Engl ish. book Pa ge 5 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
3-6 Function aplet 15 . Mo v e the c urso r to x = â2 by pr essing the or key . 16 . Pr es s to acce pt using F2(x) = (x 3) 2 â 2 as the other boundar y for the integr al. 17 . Choo se the end v alue for x . 1 Th e cu rs or ju mps t o x = â 1 on the linear func tion . 18. Displa y the numerical value of the integral. Note: See âShading ar eaâ o n page 3-11 for ano ther method of calc ulating ar ea . To find the extremum of the quadratic 19 . Mov e the cu rso r to the quadr atic equati on and f ind the e xtr emum o f the quadrati c . Select Extremum The coordina tes of t he ext re mu m a re display ed a t the bottom of the sc r een . HP 3 9gs Engl ish. book Pa ge 6 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Function aplet 3-7 HINT The Root and Extremum functions return one value only even if the function has more than one r oot or extremum. The function finds the value closest to the position of the cursor. You need to re- locate the cursor to find oth er roots or extrema that may exist. Display the numeric view 20. Display the numer ic v ie w . Set up the table 21. Display the n umer ic se tup . SETUP - NUM See âSettin g up the table (Numeric v iew s etup)â on page 2 -16 for mor e infor mation . 2 2 . Matc h the table settings to the pi xel co lumns in the gr aph v iew . Explore the table 2 3 . Displa y the ta ble of v alues. HP 3 9gs Engl ish. book Pa ge 7 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
3-8 Function aplet To navigate around a table 2 4. Mo v e to X = â5 .9 . 6 times To go directly to a value 2 5. Mov e direc tly to X = 10. 1 0 To access the zoom options 2 6 . Z oom in on X = 10 by a fact or of 4. Note: NUMZOOM has a setting of 4 . In To change font size 2 7 . Displa y table n umbers in lar ge fon t . To display the symbolic definition of a column 2 8. Displa y the s ymboli c def initio n for the F1 column . The symbolic definition of F1 is display ed at the bottom of the screen. HP 3 9gs Engl ish. book Pa ge 8 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Function aplet 3-9 Function aplet interactive analysis From the Plot view ( ), you can use the functions on the FCN menu to find r oots, intersections, slopes, and areas for a function defined in the Function aplet (and any Function-based aplets). See âFCN functionsâ on page 3- 10. The FCN operations act on the currently sele cted graph. The results of the FCN function s are saved in the following variables: ⢠Area ⢠Extr emum ⢠Isec t ⢠R oot ⢠Slope For example, if you use the Root function to find the root of a plot, you can use the result in calculations in HOME. Access FCN variables The FCN variables are cont ained on the VARS menu. To access FCN variables in HOME: Sele ct Plot FCN or to choo se a va riab l e To access FCN variable in th e Function apletâs Symbolic view: Sele ct Plot FCN or to choo se a var iable HP 3 9gs Engl ish. book Pa ge 9 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
3-10 Function aplet FCN functions The FCN functions are: Function Description Root Select Root to find the root of the current function nearest the cursor. If no root is found, but only an extremum, then the result is labeled EXTR: instead of ROOT: . (The root-finder is also used in the Solve aplet. See also âInterpreting resultsâ on page 7-6.) The cursor is moved to the root value on the x-axis and the resu lting x -value is saved in a variable named ROOT. Extremum Sel ect Extremum to find the maximum or minimum of the current function nearest the cursor. This displays the coordinate values and mov es the cursor to the extremum. The resulting value is saved in a variable named EXTREMUM . Slope Select Slope to find the numeric derivative at the current position of the cursor. The result is saved in a variable named SLOPE. Signed area Select Signed area to find the numeric integral. (If there are two or more expressions checkmarked, then you will be asked to choose the second expression from a list that includes the x -axis.) Select a starting point, then move the cursor to selection ending point. The result is saved in a variable named AREA. HP 3 9gs Engl ish. book Pa ge 10 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Function aplet 3-11 Shading area You can shade a selected area between functio ns. This process also gi ves you an appro ximate measurement of the area shaded. 1. Open the F unction aplet. T he Func tion aplet opens in the S ymbolic v ie w . 2 . Select the e xpr essi ons wh ose c ur v es y ou w ant to stu dy . 3 . Pres s to plot the f unctions . 4. Pr es s or to po sitio n the c ursor at the starting point o f the area y ou want to shade . 5. P re s s . 6 . Pr ess , t hen select Signed area and pr ess . 7 . Pr ess , ch oose the f uncti on that w ill act as the boun dary of the shaded ar ea , and pr es s . 8. Pr ess the or k e y to shade i n the ar ea . 9 . Pr ess to calculat e the ar ea . The ar ea measur ement is display ed near the bottom of the screen. To remove the shading, press to re-draw the plot. Intersection Select Intersection to find the intersection of two graphs nearest the cursor. (You need to have at least two selected expressions in Symbolic view.) Disp lays the coordinate values and moves the cursor to the intersection. (Uses Solve function.) The resulting x - value is saved in a variab le named ISECT. Function Description (Continued) HP 3 9gs Engl ish. book Pa ge 11 We dnes day, Dec embe r 7, 2005 11 : 24 PM
3-12 Function aplet Plotting a piecewise-defined function Suppose you wanted to plot the following piecewise- defined function. 1. Open the F unction apl et . Sele ct Function 2 . Highlight the line you wan t to us e , and ente r the e xpre ssion . (Y ou can pre ss to delete an e xisting line , or CLEAR to c lear all lines .) 2 CHARS ⤠1 CHARS > 1 AND CHARS ⤠1 4 CHARS > 1 Note: Y ou can us e the menu k ey to as sist in the entry of equations . It has the same e ffect as pr essing . fx () x 2 x 1 â ⤠; x 2 1 â x 1 ⤠< ; 4 xx 1 ⥠; â ⩠⪠⨠⪠⧠= HP 3 9gs Engl ish. book Pa ge 12 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Parametric aplet 4-1 4 Pa r a m e t r i c a p l e t About the Parametric aplet The Parametric aplet allows you to explore parametric equations. These are equ ations in which both x and y are defined as functions of t . They take the forms and . Getting started with the Parametric aplet The following example uses the parametric equations Note: This examp le will produce a circle. For this example to work, the angle measure must be set to degrees. Open the Parametric aplet 1. Open the P arametri c aplet. Select Parametric Define the expressions 2 . Define the e xpre ssio ns. 3 3 xf t () = yg t () = xt () 3 t yt () 3 t cos = sin = HP 3 9gs Engl ish. book Pa ge 1 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
4-2 Parametric aple t Set angle measure 3 . Set the angle measu r e to degrees. MODES Select Degrees Set up the plot 4. Display the graphing options. PLOT T he P lot Setu p inpu t for m has t w o f ields n ot inc luded in the Func tion aplet , TRNG and TSTEP . TRNG spec if ies the r ange of t val ue s. TSTEP spec if ies the step value between t values. 5 . Set the TRNG and TSTEP so that t steps fr om 0 ° to 360 ° in 5 ° steps. 360 5 Plot the expression 6 . P lot the e xpre ssion . 7 . T o see all the c irc le, pr ess tw ice . HP 3 9gs Engl ish. book Pa ge 2 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Parametric aplet 4-3 Overlay plot 8. Plot a triangle graph over the existing circle graph. PLOT 120 Sele ct Overlay Plot A tri angle is displa yed r ather than a c irc le ( with out c hanging the equati on) becaus e the c hanged value o f TSTEP ensur es that points be ing plot ted ar e 120 ° apart instea d of near l y continuou s. Y ou ar e able to e xplor e the graph u sing tr ace, z oom , split sc reen , and scaling func tio nality available in the F unction aplet . See âExplor ing the gr aph â on page 2 - 7 fo r fur t h er i nfo rma t ion. Display the numbers 9 . Displa y the table of v alues. Y ou can highli ght a t -value , t y pe in a r eplac ement v alue, and see the table j ump to that v alue . Y ou can also z oom in or z oom out on an y t -v alue in t he ta ble . You are able to explore the table using , , build your own table, and split screen functionality available in the Function aplet. See âExploring the table of numbersâ on page 2-17 for further information. HP 3 9gs Engl ish. book Pa ge 3 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
HP 3 9gs Engl ish. book Pa ge 4 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Polar aplet 5-1 5 Po l a r a p l e t Getting started with the Polar aplet Open the Polar aplet 1. Open the P olar aplet . Sele ct Polar L ik e the F unction aple t , the P o lar aplet opens in the S ymboli c v ie w . Define the expression 2 . Define the po lar equati on . 2 Ï 2 Specify plot settings 3 . S pec ify the plot settings . In this ex ample, w e w ill use the def ault se ttings, e x cept f or the θ RNG fi el d s. SETUP - PLOT CLEAR 4 Ï Plot the expression 4. P lot the expr essi on . r 2 Ïθ 2 â () θ () 2 cos cos = HP 3 9gs Engl ish. book Pa ge 1 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
5-2 Polar aplet Explore the graph 5 . Displa y the Plot v ie w menu k ey labels . Th e Pl ot vi ew op t i on s av ailable ar e the same as those f ound in the F u ncti on aplet . See âExplor ing the gra ph â on page 2 - 7 fo r further informati on . Display the numbers 6 . Displa y the table of v alue s for θ and R1. Th e N u m eric view optio ns av ailable ar e the same as th o se fo und in the F uncti on aplet . See âExplor ing the table of n umber s â on pa g e 2-1 7 fo r fur t h er in for ma t ion. HP 3 9gs Engl ish. book Pa ge 2 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Sequence aplet 6-1 6 Sequence aplet About the Sequence aplet The Sequence aplet allows you to explore sequences. You can define a sequence named, for example, U1: ⢠in terms of n ⢠in terms of U1 ( nâ1) â¢i n ter ms of U1 ( nâ2) ⢠in ter ms of another sequence , for e xample , U2 ( n) ⢠in an y combination of the a bov e. The Sequence aplet allows you to create two types of graphs: â A Stairstep s gr aph pl ots n o n the hor i z ontal ax is and U n on the ve rtical ax is. â A Cob web gr aph plots U nâ 1 on the hor iz ont al ax is and U n on the v ertical ax is. Getting started with the Sequence aplet The following example defines and then plots an expression in the Sequence aplet. The sequence illustrated is the well-known Fibonacci sequ ence where each term, from the third term on, is the sum of the preceding two terms. In this example, we specify three sequence fields: the first term, the second te rm and a rule for generating all subsequent terms. However, you can also define a sequence by specifying just the first term and the rule for generating all subsequent terms. Y ou w ill , though , hav e to enter the second te rm if the hp3 9gs is unable to calc ulate it automatical l y . T ypically if the n th t erm in the s equence depends on n â 2 , then you must enter the second term . HP 3 9gs Engl ish. book Pa ge 1 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
6-2 Sequence aple t Open the Sequence ap let 1. Open the Sequ ence aplet . Sele ct Sequence The Sequence ap let starts in the S ymboli c view . Define the expression 2 . Def ine the F ibonacc i sequence, in w hich eac h term (after the f irst tw o) is the sum of the pr eceding tw o terms: , , for . In the S ymboli c v ie w of the Seq uence aplet , highlight the U 1 (1) fi eld and begin def ining y our sequence . 1 1 Note: Y ou can us e the , , , , and menu k ey s to assist in the entry of equati ons . Specify plot settings 3. In Plo t Setup , fir st se t the SEQPLOT optio n to Stairstep . Re set the de fa ult plot settings b y clear i ng the P lot Setup v iew . SETUP - PLOT CLEA R 8 8 U 1 1 = U 2 1 = U n U n 1 â U n 2 â = n 3 > HP 3 9gs Engl ish. book Pa ge 2 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Sequence aplet 6-3 Plot the sequence 4. P lot the Fibonacc i sequ ence. 5. In Plot Setup, set the SEQPLOT option to Cobweb. SETUP - PLOT Select Cobweb Display the table 6 . Di spla y the table of values f or this ex amp le . HP 3 9gs Engl ish. book Pa ge 3 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
HP 3 9gs Engl ish. book Pa ge 4 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Solve aple t 7-1 7 Solve aplet About the Solve aplet The Solve aplet solves an equation or an expression for its unknown variable . You define an equation or expression in the symbolic view, then supply values for all the variables exce pt one in the numeric view. Solve works only with real numbers. Note the differences between an equation and an expression: ⢠An equati on contains an equals si gn. Its s oluti on is a v alue for the unkno wn v ari able that mak es bo th sides hav e the same value . ⢠An ex p res si on does not contain an eq uals sign . Its solu tion is a r oot , a v alue fo r the unkno w n v ari able that mak es the e x pr ession hav e a value of z er o . You can use the Solve aplet to solve an equation for any one of its variables. When the Solve aplet is started, it opens in the Solve Symbolic view. ⢠In S ymbolic v ie w , you spec if y the e xpr ession or equation to solve . Y ou can d ef ine up to ten equations (or e xpr essions), named E0 to E9 . E ach equati on can contain up to 2 7 r eal vari ables, named A to Z and θ. ⢠In Numeri c vi ew , y ou spec ify the values of the know n v ari ables , hi ghlight the v ariable that y ou w ant to sol v e fo r , and pr ess . You can s olve the e quation as many times as you want, using new values for the knowns and highlighting a different unknown. Note: It is not possible to solv e for more than one variable at once. Simultaneous linear equations, for example, should be solved using the Li near Solver aplet, matrices or graphs in the Function aplet. HP 3 9gs Engl ish. book Pa ge 1 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
7-2 Solve ap let Getting started with the Solve aplet Suppose you want to find th e acceleration needed to increase the speed of a car from 16.67 m/sec (60 kph) to 27.78 m/sec (100 kph) in a distance of 1 00 m. The equation to solve is: Open the Solve aplet 1. Open the Solv e aplet. Sele ct Solve T he Sol v e aplet st arts in the s y mbolic v iew . Define the equation 2. Define the equ ation. V U 2 A D Note: Y ou can us e the menu k ey to as sist in the entry of eq uations . Enter known variables 3 . Display the Solve numer ic vie w scr een. V 2 U 2 2 AD = HP 3 9gs Engl ish. book Pa ge 2 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Solve aple t 7-3 4. Enter the v alues f or the kno wn var iables . 2 7 7 8 1 6 6 7 1 0 0 HINT If the Decimal Mark setting in the Modes input form ( MODES ) is set to Comma, use instead of . Solve the unknown variable 5. Sol v e f or the unkno wn var iable ( A ). T her ef or e , the accelerati on needed to inc r ease the speed of a car fr om 16.6 7 m/sec (6 0 kph) to 2 7 .7 8 m/sec (100 kph) in a di st ance of 100 m is appro ximatel y 2 .4 7 m/s 2 . Becaus e the va ri able A in the equati on is linear w e kno w that we need not loo k fo r an y other soluti ons . Plot the equation T he P lot v ie w sho w s one gr aph for eac h side of the selected equation. Y ou can choose an y of the v ari able s to be the independen t va ri able . T he c urr ent equati on is . One of these is , w i th , that is, . This gr aph w ill be a hor i z ontal line . T he other gr aph w ill be , w ith and , that is, . This gr aph is also a line . The desir ed solutio n is the va lue of A w here these two lines intersect . V 2 U 2 2 AD = YV 2 = V 27.78 = Y 771.7284 = YU 2 2 AD = U 16.67 = D 100 = Y 200 A 277.8889 = HP 3 9gs Engl ish. book Pa ge 3 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
7-4 Solve ap let 6. Plo t the equati on fo r var iable A . Sele ct Auto Scale 7 . T race along the gr aph r epr esen ting the left side of the equati on until the c ursor nears the inter sec tion . 20 times Note the v alue o f A display ed near the bottom left corner of the scr een. T he Plo t vi e w pr o v ides a con v enien t wa y to f ind an appr ox imation to a solu tion instead of u sing the Numer ic v ie w Sol ve opti on . See âPlotting to f ind gu esses â o n pa ge 7 - 7 for m ore inform at ion. Solve apletâs NUM view keys The Solve apletâs NUM view keys are: Key M e a n i n g Copies the highlighted value to the edit line for editing. Press when done. Displays a message about the solution (see âInterpreting resultsâ on page 7-6). Displays other pages of variable s, if any. Displays the symbolic definition of the current expression. Press when done. Finds a solution for the highlighted variable, based on the values of the other var iables. HP 3 9gs Engl ish. book Pa ge 4 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Solve aple t 7-5 Use an initial guess You can usually obtain a fa ster and more accurate solution if you supply an estimated valu e for the unknown variable before pressing . Solve starts looking for a solution at the initial guess. Bef or e plottin g , make sur e the unkno wn v ariable is highli ghted in the nume ri c v ie w . P lot the equati on to help y ou s elect an initi al gues s w hen y ou don ât kno w the r ange in whi c h to look fo r the solution . See âP lotting to find guesses â on pa ge 7 - 7 for f urt her infor mation. HINT An initial guess is especially important in the case of a curve that could have more than one solution. In this case, only the solution closest to the initial guess is re turned. Number format Yo u can change the number fo rmat for the Solve aplet in the Numeric Setup view. The options are the same as in HOME MODES: Standard, Fixed, Scientific , and Engineering. For the latter three, you also specify how many digits of accuracy you want. See âMode settings â on page 1-10 for more information. You might find it handy to set a different number format for the Solve aplet if, for example, you define equations to solve for the value of money. A number format of Fixed 2 would be appropriate i n this case. Clears highlighted variable to zero or deletes current character in edit line, if edit line is active . CLEAR Resets all variable values to zero or clears the edit line, if cursor is in edit line. K ey M eaning (Continued) HP 3 9gs Engl ish. book Pa ge 5 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
7-6 Solve ap let Interpreting results After Solve has returned a solution, press in the Numeric view for more information. You will see one of the following three messages. Press to clear the message. Messa ge Condition Zero The Solve aplet found a point where both sides of the equation were equal , or wher e the expression was zero (a root), within the calculator's 12-digit accuracy. Sign Reversal Solve found two points where the difference between the two side s of the equation has opposite signs, bu t it cannot find a point in between where the value is zero. Similarly, for an expression, where the value of the express ion has different si gns but is not precisely zero. This might be because either the two points are neighbours (they differ by one in the twelfth digit), or the equation is not real-valued between the two points. Solve returns the point where the value or difference is closer to zero. If the equation or expression is continuously real, this poi nt is Solveâs best approximation of an actual solution. Extremum Solve found a point where the value of the expression approximates a local minimum (for posi tive values) or maximum (for negative values). This point may or may not be a solution. Or: Solv e stopped sea rching at 9.99999999999E4 99, the largest number the calculator can represent. Note that the value returned is probably not valid. HP 3 9gs Engl ish. book Pa ge 6 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Solve aple t 7-7 If Solve could not find a solution, you will see one of the following two messages. HINT It is important to check the information relating to the solve process. For example, the solution that the Solve aplet finds is not a solution, but the closest that the function gets to zero. Only by checking the information will you know that this is the case. The Root-Finder at work You can watch the process of the root-finder calculating and searching for a root. Immediately after pressing to start the root-finder, press any key except . You will see two intermediate guesses and, to the left, the sign of the expression evaluated at each gue ss. For example : 2 2.2193305 55745 â 1 21.31111111149 You can watch as the root-finder either finds a sign reversal or converges on a local extrema or does not converge at all. If there is no convergence in process, you might want to cancel the operation (press ) and start over with a different initial guess. Plotting to find guesses The main reason for plotting in the Solve aplet is to help you find initial guesses and so lutions for thos e equations that have difficult-to-find or multi ple solutions. Consider the equation of motion for an ac celerating body: Message Condition Bad Guess(es) The initial guess lies outside the domain of the equation. Therefore, the solution was not a real number or it caused an error. Constant? The value o f the equation is the same at every point sampled. 2 2 0 AT T V X = HP 3 9gs Engl ish. book Pa ge 7 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
7-8 Solve ap let where X is distance, V 0 is initial velocity, T is time, and A is acceleration. This is actually two equations, Y = X and Y = V 0 T (AT 2 ) / 2 . Since this equation is quadratic for T , there can be both a positive and a negative solution. However, we are concerned only with posi tive so lutions, since only positive distance makes sense. 1. Selec t the Sol v e aplet and ente r the equati on . Sele ct Solve X V T A T 2 2. Find the solution for T (time) when X = 30, V =2 , and A =4 . Enter the values for X , V , and A ; then highlight the independent variable, T . 30 2 4 to highlight T 3. Use the Plot view to find an initial guess for T . First set appropriate X and Y ranges in the Plot Setup. With equation X = V x T A x T 2 /2 , the plot will produce two graphs: one for and one for X = V x T A x T 2 /2 . Since we have set in this example, one of the graphs will be . Therefor e, make the YRNG â 5 to 35. Keep the XRNG default of â 6.5 to 6.5. SETUP- PLOT 5 35 4. P lot the gr aph. YX = X 30 = Y 30 = HP 3 9gs Engl ish. book Pa ge 8 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Solve aple t 7-9 5. Move the cursor near the positive (right-side) intersection. This cursor value will be an initial guess for T . Pr ess until the c urs or is at the inters ecti on. Th e t wo p oi nt s of inter sec tion sho w that ther e ar e tw o soluti ons f or this equati on . Ho w e ve r , on ly po si t ive va l ue s fo r X mak e sense , so we w ant to fi nd the soluti on f or the int ers ecti on on the r ight side of the y -ax is . 6 . R etur n to the Numer ic vi ew . Note: the T -value is fi lled in w ith the positi on of the c ursor from the Plot vie w . 7. Ensur e that the T value is highli ghted , and solv e the equati on . Use this equation to solve fo r another variab le, such as velocity. How fast must a bodyâs initial velocity be in order for it to travel 50 m within 3 seconds ? Assume the same acceleration, 4 m/s 2 . Leave the last value of V as the initial guess. 3 50 HP 3 9gs Engl ish. book Pa ge 9 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
7-10 Solve ap let Using variables in equations You can use any of the real variable names, A to Z and θ . Do not use variable nam es defined for other type s, such as M 1 (a matrix variable). Home variables All home variables (other than t hose for aplet settings, like Xmin and Ytick ) are globa l , which means they are shared throughout the different aplets of the calcu lator . A value that is assigned to a home variable anywhere remains with that variable wh erever its name is used. Therefore, if you have defined a value for T (as in the above example) in another aplet or even another Solve equation, that value shows up in the Numeric view for this Solve equation. When you th en redefine the value for T in this Solve equation, that value is applied to T in all other contexts (until it is changed again). This sharing allows you to work on the same problem in different plac es (such as HOME and the Solve aplet) without having to update the value whenever it is recalculated. HINT As the Solve aplet uses existing variable values, be sure to check for existing variable values that may affec t the solve process. (You can use CLEAR to reset all values to zero in the Solve apletâs Numeric view if you wish.) Aplet variables Functions defined in other aplets can also be referenc ed in the Solve aplet. For example, if, in the Function aplet, you define F1(X)=X 2 10 , you can enter F1(X)=50 in the Solve aplet to solve the equation X 2 10=50 . HP 3 9gs Engl ish. book Pa ge 10 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Linear Solve r aplet 8-1 8 Li n e a r S o lve r a p l e t About the Linear Solver aplet The Linear Solver aplet allows you to solve a set of Linear Equations. The set can contain two or three linear equations. In a two-equation set, each equation must be in the form . In a three-equation set, e ach equation must be in the form . You provide values for a , b , and k (and c in three- equation sets) for each equation, and the Linear Solver aplet will attempt to solve for x and y (and z in three- equation sets). The hp39gs will alert you if no solution can be found, or if there is an infinite number of solutions. Note that the Linear Solver aplet only has a nume ric view. Getting started with the Linear Solver aplet The following example defines a set of three equations and then solves for the unknown variables. Open the Linear Solver aplet 1. Open the Linear Sequence ap let . Select Linear Solver T he L inear E quati on Sol ver opens . ax by k = ax by cz k = HP 3 9gs Engl ish. book Pa ge 1 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
8-2 Linear Solver aplet Choose the equation set 2 . If the last time y ou us ed the L inear Sol v er aplet yo u so l ve d fo r t wo equati ons, the tw o - equati on input f orm is display ed (as in the e x ample in the pr ev ious step) . T o solv e a th r e e -equation set , pre ss . No w the input f or m displa y s thr ee equati ons . If the three-equation input fo rm is displaye d and you want to solve a two-equation set, press . In this example, we are going to solve the following equation set: Hence we need the three-equation input form. Define and solve the equations 3 . Y o u def ine the equati ons y ou w ant to so lv e by ente r ing the co -eff ic ients o f eac h var iable in eac h equati on and the const ant ter m . Notice that the c urso r is immediately positi oned at the co -effi c ient of x in the fir st equation . Enter that co -eff ic ient and pr ess or . 4. T he cur sor mo v es to the ne xt co -effi c ient . Enter that co - eff ic ient , pres s or , and contin ue doing lik e w i se un til y ou ha v e def ined all the equati ons . Note : y ou can enter the name of a var iable f or any co -effi c ient or consta nt . Pr ess and begin enter ing the name. T he menu k e y appears. Pr ess that k ey to lock alphabetic entry mode. Pr ess it again to cancel the lock . Once y ou ha v e enter ed enough values f or the sol ver to be able to gener ate soluti ons, those solutions appear on the displa y . In the e x ample at the r ight , the so lv er wa s able t o f ind so lutio ns f or x , y , and z as 6 x 9 y 6 z 5 = 7 x 10 y 8 z 1 0 = 6 x 4 y 6 = HP 3 9gs Engl ish. book Pa ge 2 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Linear Solve r aplet 8-3 soon as the f irst co -eff ic ient o f the last eq uation was enter ed. As you enter each of the r emaining kno wn v alues , the soluti on c hanges . T he ex ample at the ri ght sho ws the fi nal soluti on once all th e c o - efficient s a nd constants are e nter ed for the set o f equati ons w e set out to solve . HP 3 9gs Engl ish. book Pa ge 3 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
HP 3 9gs Engl ish. book Pa ge 4 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Triangle Solve apl et 9-1 9 T riangle Solv e aplet About the Triangle Solver aplet The Triangle Solver aplet a llows you to determine the length of a side of a triangle, or the ang le at the vertex of a triangle, from information you supply about the other lengths and/or other angles. You need to specify at leas t three of the six possible valuesâthe lengths of the three sides and the size of the three ang lesâbefore the solver ca n calculate t he other values. Moreover, at least one valu e you specify must be a length. For example, you could specify the lengths of two sides and one of the angl es; or you could specify two angles and one length; or all three lengths. In each case, the solver will calculate the remaining lengths or angles. The hp39gs will alert you if no solution can be found, or if you have provided insuffi cient data. If you are determining the properties of a right-angled triangle, a simpler input for m is available by pressing the menu key. Note that the Triangle Solver aplet only has a numeric view. Getting started with the Triangle Solver aplet The following example solves f or the unk nown le ngth of the side of a triangle whose two known sidesâof lengths 4 and 6âmeet at an angle of 30 degrees. Before you begin : You should make sure that your angle measure mode is appro priate. If the angle information you have is in degrees (as in this example) and your current angle measure mode is ra dians or grads, change the mode to degrees before running the solver. (See âMode settingsâ on page 1-10 for instructions.) Because the angle measure mode is associated with the aplet, you should start the aplet first and then change the setting. HP 3 9gs Engl ish. book Pa ge 1 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
9-2 Triangle Solv e aplet Open the Triangle Solver aplet 1. Open the T r iangle S olv er aplet. Sele ct Triangle Solver The T r iangle Solv er aplet open s . Note : if y ou h a v e alr eady u sed the T ri angle Sol v er , the entries and re sul ts fr om the pre v ious use w i ll still be display ed. T o start the T r iangle Solv er a fr esh, c lear the pr ev ious entr ies and results b y pr es sing CLEAR . Choose the triangle type 2 . If the last time y ou us ed the T r iangle S olv er aplet you used the ri ght -angled tr iangle input f orm , that input form i s di sp l ayed again (as in the e x ample at the r ight). If the tri angle y ou ar e inv estigating is n ot a ri ght -angled tr iangle , or you ar e not sur e what ty pe it is, y ou should use the gener al input f orm (illustr ated in the pr e v i ous st ep) . T o s witc h to the gener al input f orm , pres s . If the gener al input for m is display ed an d y ou ar e inv estigating a r ight-angled tri angle , pr es s to displa y the simpler input f orm . Specify the known values 3 . Using the arr ow k e ys , mov e to a f ie ld wh os e value y ou know , enter the value and pr ess or . Repeat f or each kno w n value . Note that the lengths of the side s ar e labeled A , B , and C , and the angles are la beled α , β , and δ . It is important that y ou enter the kno wn value s in the appr opr iate f ields . In our e xam ple , w e kno w the length of tw o sides and the angle at w hic h thos e side s meet . Hence if w e spec if y the le ngths of si des A and B, w e must enter the angle as δ (since δ is the angle wher e A an d B meet) . If instead we enter ed the HP 3 9gs Engl ish. book Pa ge 2 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Triangle Solve apl et 9-3 lengths as B and C, w e would ne ed to spec if y the angle as α . T he illustr a ti on on the displa y w ill help y ou determine wher e to enter t he know n values. Note: if y ou need to change the angle measur e mode , pres s MOD E S , c hange the mode , and then pr ess to r etur n to the aplet . 4. Pr ess . T he solv er calc ulates the values of the unkno w n va r iab les and display s. As the illustr ation at the r igh t sho w s, the lengt h of the unkno wn side in our e x ample is 3 .2 29 6. (The other two angle s hav e also been calc ulated.) Note: if two si des and an adjacent ac ute angle ar e enter ed and ther e are tw o solu tion s, onl y one w ill be display ed initially . In this case , an menu k ey is display ed (as in this e x ample) . Yo u p r e s s t o display the second solu tion , and again to r eturn to the fir st soluti on. Errors No solution with given data If you are using the general input form and you enter more than 3 values, the values might not be consistent, that is, no triangle could poss ibly have all the values you specified. In these cases, No sol with give n data appear s on the screen. The situation is similar if you are using the simpler input form (for a right-angled tria ngle) and you enter more than two values. HP 3 9gs Engl ish. book Pa ge 3 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
9-4 Triangle Solv e aplet Not enough data If you are using the general input form, you need to specify at least three values for the Triangle Solver to be able to calculate the remaining attributes of the triangle. If you specify less than three , Not enough data appears on the screen. If you are using the simplified input form (for a right- angled triangle), you must specify at least two values. In addition, you cannot specify only angles and n o lengths. HP 3 9gs Engl ish. book Pa ge 4 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Statistics aplet 10-1 10 Statis tic s a ple t About the Statistics aplet The Statistics aplet can store up to ten data sets at one time. It can perform one- variab le or two-variable statistical analysis of one or more sets of data. The Statistics aplet starts with the Numeric view which is used to enter data. The Symbol ic view is used to specify which columns contain data and which column contains frequencies. You can also compute stat istics values in HOME and recall the values of specif ic statistics variables. The values computed in the Stat istics aplet are saved in variables, and many of these variables are listed by the function accessible from the Statistics apletâs Numeric view screen. Getting started with the Statistics aplet The following example asks y ou to enter and analyze the advertising and sales data (i n the table below), compute statistics, fit a curve to the data, and predict the effect of more advertising on sales. Adver tisin g mi nute s (independent, x) Resulting Sales ($) (dependent, y) 21 4 0 0 1 9 2 0 31 1 0 0 52 2 6 5 52 8 9 0 42 2 0 0 HP 3 9gs Engl ish. book Pa ge 1 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
10-2 Statistics aplet Open the Statistics aplet 1. Open the S tatisti cs a plet and c lear ex isting data b y pr essing . Select Statistics Th e S ta t is ti cs ap l et starts in the Numer ical view . At an y time the Statisti cs aplet is conf igur ed for o nly one of t wo types of sta tistical explorations: one - var iable ( ) or tw o-v ariable ( ) . The 5th menu k ey label in the Numer ic vi e w toggles betw een these tw o options and show s the cur r ent opti on . 2 . Select . Y ou need to selec t because in this e x ample w e are anal yzing a dataset compr ising two v ar iable s: ad v ertising minut es and r esulting s ales . Enter data 3 . Ente r the data into the columns . 2 1 3 5 5 4 to mo ve to the ne xt column 1400 9 20 1100 2 2 6 5 2 8 90 2 200 1VAR/2VAR men u k ey l abel HP 3 9gs Engl ish. book Pa ge 2 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Statistics aplet 10-3 Choose fit and data columns 4. Selec t a fit in the S ymboli c setup v ie w . SETUP - SYMB Sele ct Linear Y ou c a n cre at e u p t o five ex p lo ra t io n s of t wo - va ri ab l e data , named S1 to S5 . I n t hi s exa m pl e, we wil l cre a te jus t o n e: S1 . 5 . Spec ify the columns that hold the data yo u w ant to analyz e. Yo u c o u l d h a v e e n t e r e d y our data int o columns other than C1 and C2 . Explore statistics 6 . F ind the mean adv ertising time ( MEANX ) and the mean sales ( MEANY ). MEANX is 3 .3 minu tes and MEANY is ab out $17 9 6 . 7 . Sc r oll dow n to dis play the v alue for the corr elatio n coeff ic ient ( CORR ). T he CORR v alue i ndicates ho w w ell the linear model f its the data . 9 times T he value is .8 99 5 . HP 3 9gs Engl ish. book Pa ge 3 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
10-4 Statistics aplet Setup plot 8. Change the plo tting range to e nsur e all the data points ar e plot ted (and select a diff er ent point mar k, if yo u wi s h ) . SETUP - PLOT 7 100 400 0 Plot the graph 9 . P lot the gr aph. Draw the regression curve 10. Dra w the reg r essi on c urve (a c ur ve to fi t the data points). T his dra w s the r egr ession line fo r the best linear f it. Display the equation for best linear fit 11. Retur n to the S ymbo lic v ie w . 12 . Displa y the equ ation f or the be st linear f it . to mov e to the FIT1 fie l d T he full FIT1 e xpr essi on is sho wn . T he slope ( m ) i s 425.87 5. Th e y -inter cept ( b ) is 3 7 6. 25. HP 3 9gs Engl ish. book Pa ge 4 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Statistics aplet 10-5 Predict values 13 . T o f ind the pr edic ted sales f igur e if ad v ertising w er e to go up to 6 minute s: S ( to highlight Stat-Two ) (to highligh t PREDY ) 6 14. Retu rn to the P lot vi e w . 15 . Jum p to the indicat ed point on the r egr essi on line . 6 Observ e the pr edict ed y -v alue in the left bottom corner of the screen. HP 3 9gs Engl ish. book Pa ge 5 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
10-6 Statistics aplet Entering and editing statistical data The Numeric view ( ) is used to enter dat a into the Statistics aplet. Each column represents a variable named C0 to C9 . After entering the data, you must define the data set in the Symbolic view ( ). HINT A data column must have at least four data points to provide vali d two-variable statistics, or two data points for one-var iable stat istics. You can also store statistical da ta values by copying lists from HOME into Statistics data columns. For ex ample, in HOME, L1 C1 stores a copy of the list L1 into the data-column var iable C1 . Statistics apletâ s NUM view keys The Statistics apletâs Numeric view keys are: Key M e a n i n g Copies the highlighted item into the edit line. Inserts a zero value above the highlighted cell. Sorts the specified independ ent data column in ascending o r descending order, and rearr anges a specified dependent (o r frequency) data column accordingly. Switches between larger and smaller font sizes. A toggle switch to select one- variable or two-variable statistic s. This setting affects the statistical calculations and plots. The label indicates which setting is current. Computes descriptive statistics for each data set specified in Symbolic view. HP 3 9gs Engl ish. book Pa ge 6 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Statistics aplet 10-7 Example Yo u are measuring the height of students in a classroom to find the mean height. The first five students have the following measurements 160cm, 165cm, 1 70cm, 175cm, 180cm. 1. Open the Stati stics aplet . Sele ct Statistics 2 . Enter the measurement data. 160 16 5 17 0 17 5 180 3 . F ind the mean of the sampl e. Ensur e the / menu k ey label re a ds . Pr ess to see the statis tic s calc ulated fr om the sample data in C1 . Deletes the currently highlighted value. CLEAR Clears the current column or all columns of data. Pregss CLEAR to display a menu list, then select the current colu mn or all columns option, and press . cursor key Moves to the first or last row, or first or last column. K ey Meaning (Conti nued) HP 3 9gs Engl ish. book Pa ge 7 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
10-8 Statistics aplet Note that the title o f the colu mn o f st atis ti cs i s H1 . Ther e a r e 5 data set de f initions a vailable for one -v ari able sta tis tics : H1âH5 . If data is entered in C1 , H1 is automatically set to use C1 fo r data , and the fr equency of eac h data point is set to 1. Y ou can select other columns o f data fr om the St atisti cs S ymbo lic s etup v ie w . 4. Pr ess to c lose the statisti cs w indow and pr ess k ey to see the data set definiti ons. T he firs t column indicates the ass oc iated column of data for eac h data set def inition , and the second column indicate s the constant f r equenc y , or the column that holds the frequ en c ies. T he ke ys y ou can use f r om this w indo w ar e: Key M e a n i n g Copies the column variable (or variable expression) to the edit line for editing. Press when done. Checks/unchecks the current data set. Only the checkmarked data set(s) are computed and plotted. or Typing aid for the column variables ( ) or for the Fit expressions ( ). Displays the current variable expression in standard mathematical form. Press when done. Evaluates the variables in the highlighted column (C1, etc.) expression. HP 3 9gs Engl ish. book Pa ge 8 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Statistics aplet 10-9 To continue our example, supp ose that the heights of the rest of the students in the class are measured, but each one is rounded to the nearest of the five values first recorded. Instead of entering all the new data in C1 , we shall simply add another column, C2 , that holds the frequencies of our five data points in C1 . 5 . Mo ve the highli ght bar into the r ight column of the H1 def inition and r eplace the f r equenc y v alue of 1 w ith the name C2 . 2 Displays the menu for en tering variable names or contents of variables. Displays the menu for entering math operations. Deletes the highlighted variable or the current character in the edit line. CLEAR Resets default specifications for the data sets or clears the edit line (if it was ac tive). Note: If CLEAR is used the data sets will need to be selected again before re-use. K ey Meaning (Conti nued) Heig ht (cm) Freq ue ncy 160 5 165 3 170 8 175 2 180 1 HP 3 9gs Engl ish. book Pa ge 9 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
10-10 Statistics aplet 6 . R eturn t o the numer ic vi ew . 7 . Ente r the fr equency data sho wn in the a bo ve t able . 5 3 8 2 1 8. Displa y the computed sta tis tics. The mean height is approxim ately 167.63cm. 9 . Setup a histogr am plot for the data . SETUP - PLOT Enter s et up inf or matio n appropriate to your data. 10. P lot a histogr am of the data. Save data The data that you enter is automatically saved. When you are finished entering data values, y ou can press a ke y for another Statistics view (like ), or you can switch to another aplet o r HOME. Edit a data set In the Numeric view of the Statistics aplet, highlight the data value to change. Type a new value and press , or press to copy the valu e to the edit line for modification. Press after modifying the value on the edit line. HP 3 9gs Engl ish. book Pa ge 10 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Statistics aplet 10-11 Delete data ⢠T o delete a single data item, highli ght it and pr ess . T he value s belo w the delet ed cell w ill scr oll up one ro w . ⢠T o delete a column of data , highli ght an entry in that column and press CLEAR . Select the co lumn name . ⢠T o delete all columns of data , pres s CLEAR . Sele ct All columns . Insert data Highlight the entry following the point of insertion. Press , then enter a numbe r. It will write over t he zero that was inserted. Sort data values 1. In Numer ic v ie w , highli ght the column y ou want to sort , and pr ess . 2 . S pec ify the Sort Order . Y ou can choo se either Ascending or Descending . 3 . Spec ify the INDEPENDENT and DEPENDENT data columns. S orting is by the independent column . For instance , if Age is C1 and Income is C2 and y ou w ant to sort by Income , then you mak e C2 the independen t column for the s orting and C1 the dependent column. â T o sort jus t one column , choo se None f or the dependent column . â F or one -v ari able stat istic s w ith two data columns , spec ify the fr equenc y column as the depende nt column. 4. Pr ess . HP 3 9gs Engl ish. book Pa ge 11 We dnes day, Dec embe r 7, 2005 11 : 24 PM
10-12 Statistics aplet Defining a regression model The Symbolic view includes an expression (Fit1 through Fit5) that defines the regression model, or âfitâ, to use for the regression analysis of each two-variable data set. There are three ways to select a regression model: ⢠Accept the d efa ult opt ion to f it th e data to a straight line . ⢠Selec t one of the a v ailable f it options in S y mbolic Setup v ie w . ⢠Enter y our o w n mathematical e xpres sio n in S ymboli c v ie w . This e xpr ession w ill be plot ted, bu t it w ill not be fi tted to the data po ints . Angle Setting You can ignore the angle measurement mode unless your Fit definition (in Symbo lic view) involves a trigonometric function. In this case, you should specify in the mode screen whether the trigonometric units are to be interpreted in degrees, radians, or grads. To choose the fit 1. In Numer ic vi e w , make sur e is set . 2. P r e s s SETUP - SYMB to display the S ymbolic Setup v ie w . Hi ghlight the F it number ( S1FIT to S5FIT ) y ou w ant to define . 3 . Pr ess and select f r om the list. Pr ess when done . Th e r egr essi on f orm ula fo r the fit is displa y ed in S ymboli c v ie w . Fit models T en fit models are available: F it model M eaning Linear (Default.) Fits the data to a straight line, y = mx b . Uses a least-squares fit. Logarithmic Fits to a logarithmic curve, y = m ln x b . Exponential Fits to an exponential curve, y = be mx . Power Fits to a power curve, y = bx m . HP 3 9gs Engl ish. book Pa ge 12 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Statistics aplet 10-13 To define your own fit 1. In Numer ic v ie w , mak e sure is set . 2 . Display the S y mbolic v iew . 3 . Highligh t the F it expr es sion ( Fit1 , et c.) f or the desir ed data set. 4. T ype in an e xpr ess ion an d pr ess . The independent variable must be X , and the e xpr essi on mu st not cont ain any unkn o wn v aria bles. Ex ample: . This automatically changes the Fit type ( S1FIT , etc.) in the Symbolic Setup view to User Defined . Quadratic Fits to a quadratic curve, y = ax 2 bx c . Needs at least three points. Cubic Fits to a cubic curve, y = ax 3 bx 2 cx d . Needs at least four points. Logistic Fits to a logistic curve, , where L is the saturation value for growth. You can store a positive real value in L , orâif L = 0âlet L be computed automatically. Exponent Fits to an exponent curve, . Trigonometric Fits to a trigonometric curve, . Needs at least three points. User Defined Define your own expression (in Symbolic view.) F it model Meaning (Continued) y L 1 ae bx â () ------------------------- - = ya b x = ya b x c () sin â d = 1.5 x cos à 0.3 x sin à HP 3 9gs Engl ish. book Pa ge 13 We dnes day, Dec embe r 7, 2005 11 : 24 PM
10-14 Statistics aplet Computed statistics One-variable When the data set contains an odd number of values, the data setâs median value is no t us ed when calculating Q1 and Q3 in the table above. For example, for the following data set: { 3,5,7,8,15,16,17} only the first three items, 3, 5, and 7 are used to calculate Q1, and only the last three ter ms, 15, 16, and 17 are used to calculate Q3. Statistic Definition N Σ Number of data points. TOT Σ Sum of data values (with their frequencies). MEAN Σ Mean value of data se t. PVAR Σ Population variance of data set. SVAR Σ Sample variance of data set. PSDEV P opulation standard deviation of data set. SSDEV Samp le standard deviation of da ta set. MIN Σ Mi nimum data value in data set. Q1 First quartile: median of values to left of median. MEDIAN Median value of da ta set. Q3 Third quartile: median of values to right of median. MAX Σ Maxi mum data value in data set. HP 3 9gs Engl ish. book Pa ge 14 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Statistics aplet 10-15 Two-variable Plotting You can plot: ⢠histogr ams ( ) ⢠bo x -and-whisk er plots ( ) ⢠scat ter plots ( ) . Once you have ente red your data ( ), defined your data set ( ), and defined your Fit model for two- variable statistics ( SETUP - SYMB ), you can plot your data. You can plot up to five scatter or box-an d-whisker plots at a time. You can plot only one histogram at a time. Statistic Definition MEANX Mean of x - (independent ) values. Σ X Sum of x -values. Σ X2 Sum of x 2 -values. MEANY Mean of y - (dependent) values. Σ Y Sum of y -values. Σ Y2 Sum of y 2 -values. Σ XY Sum of each xy . SCOV Sample covarianc e of independent and dependent data columns. PCOV Population covariance of independent and dependent data columns CORR Correlation c oefficient of the independent and dependent data columns for a linear fit only (regardless of the Fit chosen). Returns a value from 0 to 1, where 1 is the best fit. RELERR The relati ve error for the selected fit. Provides a measure of accuracy for the fit. HP 3 9gs Engl ish. book Pa ge 15 We dnes day, Dec embe r 7, 2005 11 : 24 PM
10-16 Statistics aplet To plot statistical data 1. In S ymboli c v ie w ( ) , select ( ) the data sets y ou w ant to plot . 2 . Fo r one -var iable dat a ( ) , selec t the plot type in P lot Setup ( SETUP - PLOT ) . Highli ght ST A TPLOT , pr ess , select either Histogram or BoxWhisker , and pr es s . 3 . F or any plot , but espec iall y fo r a histogr am, adj ust the plottin g scale and range in th e P l ot Setup v ie w . If y ou find histogr am bars too fat or too thin, y ou can adjus t them b y adj usting the HWIDTH sett in g . 4. Pr ess . If y ou ha ve not adj usted the P lot Se tup y ours elf , you can try se le ct Auto Scale . Auto Scale can be relied upon to give a good starting scale which can then be adjusted in the Plot Setup view. Plot types Histogram One-variable statistics . The numbers below the plot mean that the current bar (where the cursor is) starts at 0 and ends at 2 (not including 2), and the frequency for this column, (that is, the number of data elements that fall between 0 and 2) is 1. You can see information about the n ext bar by pressing the k ey. Box and Whisker Plot One-variable statistics . The left whisker marks the minimum data value. The box marks the first quartile, the median (where the cursor is), and the third quartile. The right whisker marks the maximum data value. The numbers below the plot mean that this column has a median of 13. HP 3 9gs Engl ish. book Pa ge 16 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Statistics aplet 10-17 Scatter Plot Tw o-variable statistics . The numbers below the plot indicate that the cursor is at the first data point for S2, at (1, 6). Press to move to the next data point and display information about it. To connect the data points as they are plotted, checkmark CONNECT in the second page of the Plot Setup. This is not a regression curve. Fitting a curve to 2VAR data In the Plot view, press . This draws a curve to fit the checked two-variable data set(s). See âT o choose the fitâ on page 10-12. The e xpressi on in Fit2 sho ws that the slope = 1.98 08 21917 81 and the y - i n t e r c e p t = 2. 26 57 . Correlation coefficient The correlation coeffici ent is stored in the CORR variable. It is a measure of fit to a line ar curve only. Regardless of the Fit model you have chosen, CORR relates to the linear model. HP 3 9gs Engl ish. book Pa ge 17 We dnes day, Dec embe r 7, 2005 11 : 24 PM
10-18 Statistics aplet Relati ve Error The relative error is a measure of the error between predicted values and actual va lues based on the specified Fit. A smaller number means a better fit. The relative error is stored in a variable named RELERR . The relative error provides a measur e of fit accuracy for all fits, and it does depend on the Fit model you have chosen. HINT In order to access the CORR and RELERR variables after you plot a set of statistics, you must press to access the numeric view and then to display the correlation values. The values are stored in the variables when you access the Symbolic view. Setting up the plot (Plot setup view) The Plot Setup view ( SETUP - PLOT ) sets most of the same plotting parameters as it does for the other built-in aplets. See âAbout the Plot viewâ on page 2-5. Sett ings unique to the Statistics aplet are as follows: Plot type (1VAR) STATPLOT enables you to specify eithe r a histogram or a box-and-whisker plot for one-variable statistics (when is set). Press to change the highlighted setting Histogram width HWIDTH enables you to spec ify the width of a his togram bar. This determines how many bars will fit in the display, as well as how the data is di stributed (how many values each bar represents). Histog ram rang e HRN G enables you to specify th e range of values for a set of histogram bars. The r ange runs from the left edge of the leftmost bar to the right edge of the rightmost bar. You can limit the range to exclude any values you suspe ct are outliers. Plotting mark (2VAR) S1MARK through S5MARK enables you to specify one of five symbols to use to plot each data set. Press to change the highlighted setting. Connected points (2VAR) CONNECT (on the second page), when checkmarked, connects the data points as they are plotted. The resulting line is not the regression curve. The order of plotting is according to the ascending order of independent values. HP 3 9gs Engl ish. book Pa ge 18 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Statistics aplet 10-19 For instance, the data set (1,1 ), (3,9), (4,16), (2,4) would be plotted and traced in the order (1,1), (2,4), (3,9), (4,16). Trouble-shooting a plot If you have problems plotting, check that you have the following: ⢠T he cor r ect or menu label o n (Numer ic vi ew ) . ⢠T he corr ect fit (r egres sion model), if the data set is tw o -v ar ia ble . ⢠Only the data sets to compute or plot are chec kmarked (S y mbolic v iew ) . ⢠T he corr ect plotting r ange . T r y using Auto Scale (instead o f ), or adjust the plotting par ameters (in Plo t Setup) fo r the range s of the ax es and the w idth of hist ogr am bars ( HWIDTH ). In mode, ensure that both paired columns contain data, and that they are the same length. In mode, ensure that a paired column of fre quency values is the same length as th e data column that it refers to. Exploring the graph The Plot view has menu keys for zooming, tracing, and coordinate display. There are also scaling options under . These options are desc ribed inâEx ploring the graphâ on page 2-7. Statistics apletâs PLOT view keys K e y Meaning CLEAR Erases the plot. Offers additional pre-defined views for splitting the screen, overlaying plots, and autoscaling the axes. Moves cursor to far left or far right. HP 3 9gs Engl ish. book Pa ge 19 We dnes day, Dec embe r 7, 2005 11 : 24 PM
10-20 Statistics aplet Calculating predicted values The functions PREDX and PREDY estimate (predict) values for X or Y given a hypothetical value for the other. The estimation is made based on the curve that has been calculated to fit the data a ccording to the specified fit. Find predicted values 1. In P lot v iew , dra w the r egr essi on curve f or the data set. 2 . Pres s to mo ve to the r egr essio n c urve . 3 . Pres s and enter the v alue of X . T he c urso r jumps to the specif ied point on the curve and th e coor dinate displa y sho ws X and the pr edicted v alue of Y . In HOME: ⢠Enter PREDX ( y-value ) to find the pr edic ted v alue for the indepe ndent v ar iable gi ven a h y potheti cal dependen t value . Displays ZOOM menu. Turns trace mode on/off. The white box appears next to the option when Trace mode is active. Turns fit mode on or off. Turning on draws a curve to fit the data points according to the current regression model. (2var statistics only) Enables you to spe cify a value on the line of best fit to jump to or a data point number to jump to. Displays the equation of the regression curve. Hides and displays the menu key labels. When the la bels are hidden, any menu key displays the (x,y) coordinates. Pressing redisplays the menu labels. K e y Meaning (Continued) HP 3 9gs Engl ish. book Pa ge 20 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Statistics aplet 10-21 ⢠Enter P RED Y( x-value ) to f ind the pr edicted v alue of the dependent var iable gi ven a h ypothetical independent va riab l e. You can type PREDX and PREDY into the edit line, or you can copy these function names from the MATH menu under the Stat-Two category. HINT In cases where more than one fit curve is displayed, the P RED Y function uses the most recently calculated curve. In order to avoid errors with th is function, uncheck all fits except the one that you want to work w ith, or use the Plot View method. HP 3 9gs Engl ish. book Pa ge 21 We dnes day, Dec embe r 7, 2005 11 : 24 PM
HP 3 9gs Engl ish. book Pa ge 22 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Inference aplet 11-1 11 Inference aplet About the Inference aplet The Inference capabilities include calculation of confidence intervals and hy pothesis tests based on the Normal Z-distribution or Studentâs t-distribution. Based on the statistics from one or two samples, you can test hypotheses and find confidence intervals for the following quantities: ⢠mean ⢠pro portion ⢠diff erence betw een two means ⢠diff erence between two proportions Example data When you first access an input form for an Inference test, by default, the input form contai ns example data. This example data is designed to return meaningful results that relate to the test. It is useful for gaining an understanding of what the test does, and for demonstrating the test. The calculatorâs on-line help provides a descripti on of what the example data represents. Getting started with the Inference aplet This example describes the Inference apletâs options and functionality by stepping you through an example using the examp le data for the Z-Te st on 1 mean. Open the Inference aplet 1. Open the Inference aplet. Select Inference . The Inference aplet opens in the Symbolic view. HP 3 9gs Engl ish. book Pa ge 1 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
11-2 Inference a plet Inference apletâs SYMB view keys The table below summarizes the options available in Symbolic view. If you choose one of the hypoth esis tes ts, you can choose the alternative hypothesis to test against the null hypothesis. For each test, th ere are three possible choices for an alternative hypothesis based on a quantitative comparison of two quantiti es. The null hypothesis is always that the two quantities are equal.Thus, the alternative hypotheses cover th e various cases for the two quantities being unequal: <, >, and â . In this section, we will use th e example data for the Z-Test on 1 mean to illustrate how the aplet works and what features the various views present . Hypothesis Tests Confidence Intervals Z: 1 μ , the Z-T est on 1 mean Z-Int: 1 μ , the confidence interval for 1 mean, based on the Normal distribution Z: μ 1 â μ 2 , the Z-Test on the difference of two means Z-Int: μ 1 â μ 2 , the confidence interval for the difference of two means, based on the Normal distribution Z: 1 Ï , the Z-Te st on 1 proportion Z-Int: 1 Ï , the confidence interval for 1 proportion, based on the Normal distribution Z: Ï 1 â Ï 2, the Z-Test on the difference in two proportions Z-Int: Ï 1 â Ï 2, the con fidence interval for the difference of two proportions, based on the Normal distribution T: 1 μ , the T-Test on 1 mean T-Int: 1 μ , the confidence interval for 1 mean, based on the Studentâs t-distribution T: μ 1 â μ 2 , the T- Test on the difference of two means T-Int: μ 1 â μ 2 , the confidence interval for the difference of two means, based on the Studentâs t-distribution HP 3 9gs Engl ish. book Pa ge 2 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Inference aplet 11-3 Select the inferential method 2. Select the Hypothesis Test inferential method. Select HYPOTH TEST 3. Define the type of test. ZâTest: 1 μ 4. Select an alternative hypothesis. μ< μ0 Enter data 5. Enter the sample statis tics and population parameters. setup-NUM The table below lists the fields in this view for our current Z-Test: 1 μ example. Field name Definition μ 0 Assumed population mean Ï Population standard deviatio n Sample mean n Sample size α Alpha level for the test x HP 3 9gs Engl ish. book Pa ge 3 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
11-4 Inference a plet By default, each field already contains a value. These values constitu te the example database and are expla ined in the feature of this aplet. Display on-line help 6. To display the on-line help, press 7. To close the on-line help, press . Display test results in numeric format 8. Display the test results in numeric format. The test dis tribution value and its associated probability are displayed, along with the critical value(s) of the test and the associated critical value(s) of the statistic. Note: You can access the on-line help in Numeri c view. Plot test results 9. Display a graphic view of the test results. Horizontal axes are presented for both the distribution variable and the test statistic. A generic bell curve repre sents the probability distribution func tion. Vertical lines mark the critical value(s) of the test, as well as the value of the test statistic. The rejection region is marked and the test numeric results are displayed betwee n the horizontal axes. Importing sample statistics from the Statistics aplet The Inference aplet supports th e calculation of confidence intervals and the testing of hypotheses based on data in the Statistics aplet. Computed statistics for a sample of data in a column in any St atistics-based aplet can be imported for use in the Infe rence aplet. The following example illustrates the process. R HP 3 9gs Engl ish. book Pa ge 4 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Inference aplet 11-5 A calculator produces the following 6 random number s: 0.529, 0.295, 0.95 2, 0.259, 0.925, and 0. 592 Open the Statistics aplet 1. Open the Statistics aplet and reset the current settings. Select Statistics The Statistics aplet opens in the Numeric view. Enter data 2. In the C1 column, enter the random numbers produced by the calculator. 529 295 952 259 925 592 HINT If the Decimal Mark setting in the Modes input form ( modes ) is set to Comma, use instead of . 3. If necessary, select 1-va ri able statistics. Do this by pressing the fifth menu key until is displayed as its menu label. Calculate statistics 4. Calculate statistics. The mean of 0.592 seems a little large compared to the expected value of 0.5. To see if the difference is statistically significant, we will use the statist ics computed here to construct a confidence inter val for the true mean of the population of random numbers and see whether or not this interval contains 0.5. 5. Press to close the computed statistics window. HP 3 9gs Engl ish. book Pa ge 5 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
11-6 Inference a plet Open Inference aplet 6. Open the Inference aplet and clear current s ettings. Select Inference Select inference method and type 7. Select an inference me thod. Select CONF INTERVAL 8. Select a distribution statistic type. Select T-Int: 1 μ Set up the interval calculation 9. Set up the interval calculation. Note: The default values are derived from sample data from the on-line help example. Setup-NUM HP 3 9gs Engl ish. book Pa ge 6 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Inference aplet 11-7 Import the data 10. Import the data from the Statistics aple t. Note: The data from C1 is disp layed by default. Note: Press to see the statistics before importing them into the Numeric Setup view. Also, if there is more than one ap let based on the Statistics aplet, you are prompted to choose one. 11. Specify a 90% confidence interval in the C: field. to move to the C: field 0.9 Display Numeric view 12. Display the confi dence interval in the Numeric view. Note: The interval setting is 0.5. Display Plot view 13. Display the confidence interval in the Plot view. You can see, from the second text row, that the mean is contained within the 90% confidence interval (CI) of 0.346981 4 to 0.8370186. Note: The graph is a simple, generic bell-c urve. It is not meant to accurately represent the t-distribution with 5 degrees of freedom. HP 3 9gs Engl ish. book Pa ge 7 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
11-8 Inference a plet Hypothesis tests You use hypothesis tests to test the validity of hypotheses that relate to the statistical parameters of one or two populations. The tests are base d on statistics of samples of the populations. The HP 39gs hypothesis tests use the Normal Z-distribution or Studentâ s t-distribution to calcula te probabilities. One-Sample Z-Test Menu name Z-Test: 1 μ On the basis of statistics from a single sample, the One-Sample Z-Test measures th e strength of the evidence for a selected hypothesis against the null hypothesis. The null hypothesis is that the population mean equals a specified value Î 0 : μ = μ 0 . You select one of the following alternative hypothese s against which to test the null hypothesis: Inputs The inputs are: H 1 : μ 1 μ 2 < H 1 : μ 1 μ 2 > H 1 : μ 1 μ 2 â Field name Definition Sample mean. n Sample si ze. μ 0 Hypothetical population mean. Ï Population standard devi ation. α Significance level. x HP 3 9gs Engl ish. book Pa ge 8 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Inference aplet 11-9 Results The results are: Two-Sample Z-Test Menu name Z-Test: μ 1â μ 2 On the basis of two samples, each from a separate population, this test measu res the strength of the evidence for a selected hypothesis against the null hypothesis. The null hypothesis is that the mean of the two populations are equal (H 0 : μ 1= μ 2). You select one of the following alternative hypothe ses against which to test the null hypothesis: Inputs The inputs are: Result Description Test Z Z-test statistic. Prob Probability associated with the Z-Test statistic. Critical Z Boundary values of Z associated with the α level that you supplied. Critical Boundary values of required by the α value that you supplied. x x H 1 : μ 1 μ 2 < H 1 : μ 1 μ 2 > H 1 : μ 1 μ 2 â Field name Definiti on Sample 1 mean. Sample 2 mean. n1 Sample 1 size. n2 Sample 2 size. Ï 1 Po pulation 1 standa rd deviation. x 1 x 2 HP 3 9gs Engl ish. book Pa ge 9 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
11-10 Inference a plet Results The results are: One-Proportion Z-Test Menu name Z-Test: 1Ï On the basis of statistics from a single sample, this test measures the strength of the evidence for a selected hypothesis against the null hypothesis. The null hypothesis is that the proportion of su ccesses in the two populations is equal: H 0 : Ï = Ï 0 You select one of the following alternative hypothese s against which to test the null hypothesis: Ï 2 Population 2 standard deviation. α Significance level. Field name Definition (Continued) Result Description Test Z Z-Test statistic. Prob Probability associated with the Z-Test statistic. Critical Z Boundary value of Z associated with the α level that you supplied. H 1 : ÏÏ 0 < H 1 : ÏÏ 0 > H 1 : ÏÏ 0 â HP 3 9gs Engl ish. book Pa ge 10 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Inference aplet 11-11 Inputs The inputs are: Results The results are: Two-Proportion Z-Test Menu name Z-Test: Ï 1 â Ï 2 On the basis of statistics fr om two samples, each from a different population, the Two-Proportion Z-Test measures the stre ngth of the evidence for a selected hypo thesis against the null hypothesis. The null hypothesis is that the proportion of successes in th e two populations is equal H0: Ï 1 = Ï 2 . You select one of the following alternative hypothe ses against which to test the null hypothesis: Field name Definitio n x Number of successes in the sample. n Sample size. Ï 0 Population proportion of successes. α Significance level. Result Description Test P Proportion of successes in the sample. Test Z Z- Test statist ic. Prob Probability associated with the Z-Test statistic. Critical Z Boundary value of Z associ ated with the level you supplied. H 1 : Ï 1 Ï 2 < H 1 : Ï 1 Ï 2 > H 1 : Ï 1 Ï 2 â HP 3 9gs Engl ish. book Pa ge 11 We dnes day, Dec embe r 7, 2005 11 : 24 PM
11-12 Inference a plet Inputs The inputs are: Results The results are: One-Sample T-Test Menu name T-Test: 1 μ The One-sample T-Test is used when the population standard deviation i s not know n. On the basis of statistics from a single sample, this tes t measures the strength of the evidence for a selected hypothesis against the nu ll hypothesis. The null hypothesis is that the sample mean has some assumed value, Î 0 :μ = μ 0 You select one of the following alternative hypothese s against which to test the null hypothesis: Field name Definition X1 Sample 1 mean. X2 Sample 2 mean. n1 Sample 1 size. n2 Sample 2 size. α Significance level. Result Description Test Ï 1â Ï 2 Difference between the proportions of successes in the two samples. Test Z Z-Test statistic. Prob Probability associated with the Z-Test statistic. Critical Z Boundary values of Z associated with the α level that you supplied. H 1 : μμ 0 < H 1 : μμ 0 > H 1 : μμ 0 â HP 3 9gs Engl ish. book Pa ge 12 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Inference aplet 11-13 Inputs The inputs are: Results The results are: Field name Definiti on Sample mean. Sx Sample standard de viation. n Sample size. μ0 Hypothetical population mean. α Significance level. x Result Description Test T T-Test statistic. Prob Probability associated with the T-Test statistic. Critical T Boundary value of T assoc iated with the α level that you supplied. Critical Boundary value of required by the α value that you supplied. x x HP 3 9gs Engl ish. book Pa ge 13 We dnes day, Dec embe r 7, 2005 11 : 24 PM
11-14 Inference a plet Two-Sample T-Test Menu name T-Test: μ 1 â μ 2 The Two-sample T-Test is used when the population standard deviation i s not know n. On the basis of statistics from two samples, each sample from a different population, this test measures the strength of the evidence for a selected hypothesis against the null hypothesis. The null hypothesis is that the two populations means are equal H 0 : μ 1 = μ 2 . You select one of the following alternative hypothese s against which to test the null hypothesis Inputs The inputs are: H 1 : μ 1 μ 2 < H 1 : μ 1 μ 2 > H 1 : μ 1 μ 2 â Field name Definition Sample 1 mean. Sample 2 mean. S1 Sample 1 standard dev iation. S2 Sample 2 standard dev iation. n1 Sample 1 si ze. n2 Sample 2 si ze. α Si gnificance level. _Pooled? Check this option to pool samples based on their standard d eviations. x1 x2 HP 3 9gs Engl ish. book Pa ge 14 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Inference aplet 11-15 Results The results are: Confidence intervals The confidence interval calculations that the HP 39gs can perform are based on the Normal Z-distribution or Studentâs t-distribution. One-Sample Z-Interval Menu name Z-INT: μ 1 This option uses the Normal Z-distributio n to calculate a confidence interval for m, the true mean of a population, when the true population standard deviation, s, is known. Inputs The inputs are: Result De scription Test T T-Test statistic. Prob Probability associated with the T-T est statistic. Critical T Boundary values of T assoc iated with the α level that you supplied. Field name Definition Sample mean. Ï Population stand ard deviation. n Sample size. C Confidence level. x HP 3 9gs Engl ish. book Pa ge 15 We dnes day, Dec embe r 7, 2005 11 : 24 PM
11-16 Inference a plet Results The results are: Two-Sample Z-Interval Menu name Z-IN T: μ1 â μ2 This option uses the Normal Z- distribution to calculate a confidence interval for the difference between the means of two populations, μ 1 â μ 2 , when the population st andard deviations, Ï 1 and Ï 2 , are known. Inputs The inputs are: Results The results are: Result Description Critical Z Critical value for Z. μ min Lower bound for μ . μ max Upper bound for μ . Field name Definition Sample 1 mean. Sample 2 mean. n1 Sample 1 si ze. n2 Sample 2 si ze. Ï 1 Population 1 s tandard deviation. Ï 2 Population 2 s tandard deviation. C Confidence level. x1 x2 Result Description Critical Z Critical value for Z. μ Min Lower bound for μ 1 â μ 2 . μ Max Upper bound for μ 1 â μ 2 . Î Î HP 3 9gs Engl ish. book Pa ge 16 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Inference aplet 11-17 One-Proportion Z-Interval Menu name Z-INT: 1 Ï This option uses the Normal Z-distributio n to calculate a confidence interval for the proportion of successes in a population for the case in wh ich a sample of size, n , has a number of successes, x . Inputs The inputs are: Results The results are: Two-Proportion Z-Interval Menu name Z-I NT: Ï 1 â Ï 2 This option uses the Normal Z-distributio n to calculate a confidence interval for the difference between the proportions of successes in two populations. Inputs The inputs are: Field name Definition x Sample success count. n Sample size. C Confidence level. Result Description Critical Z Critic al value for Z. Ï Min Lower bound for Ï . Ï Max Upper bound for Ï . Field name Definition Sample 1 success count. Sample 2 success count. x 1 x2 HP 3 9gs Engl ish. book Pa ge 17 We dnes day, Dec embe r 7, 2005 11 : 24 PM
11-18 Inference a plet Results The results are: One-Sample T-Interval Menu name T-INT: 1 μ This option uses the Studentâs t-distribution to ca lculate a confidence interval for m, the true mean of a population, for the case in which the true population standard deviation, s, is unknown. Inputs The inputs are: n1 Sample 1 si ze. n2 Sample 2 si ze. C Confidence level. Field name Definition (Continued) Result Description Critical Z Critical value for Z. Ï Min Lower bound for the difference between the proportions of succes ses. Ï Max Upper bound for the difference between the proportions of succes ses. Î Î Field name Definition Sample mean. Sx Sample standard deviatio n. n Sample size. C Confidence level. x 1 HP 3 9gs Engl ish. book Pa ge 18 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Inference aplet 11-19 Results The results are: Two-Sample T-Interval Menu name T-INT: μ 1 â μ 2 This option uses the Studentâs t-distribution to calculate a confidence interval for the difference between the means of two populations, μ 1 â μ 2, when the population standard deviations, s1 and s2, are unknown. Inputs The inputs are: Result Description Critical T C ritical value for T. μ Min Lo wer bound for μ . μ Max Upper bound for μ . Field name Definition Sample 1 mean. Sample 2 mean. s1 Sample 1 standard deviation. s2 Sample 2 standard deviation. n1 Sample 1 size. n2 Sample 2 size. C Confidence level. _Pooled Whether or not to pool the samples based on their stand ard deviations. x1 x2 HP 3 9gs Engl ish. book Pa ge 19 We dnes day, Dec embe r 7, 2005 11 : 24 PM
11-20 Inference a plet Results The results are: Result Description Critical T Critical value for T. μ Min Lower bound for μ 1 â μ 2 . μ Max Upper bound for μ 1 â μ 2 . Î Î HP 3 9gs Engl ish. book Pa ge 20 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Using th e Finance So lver 12-1 12 Using the Finance Solver The Finance Solver, or Fin ance aplet , is available by using the APLET key in your calculator. Use the up and down arrow keys to select the Finance aplet. Your screen should look as follows: Press the key or the soft m enu key to activate the aplet. The result ing screen shows the different elements involved in the soluti on of financial problems with your HP 39gs c alculator. Background information on and applications of financial calculations are provided next. Background The Finance Solver applicatio n provides you with the ability of solving time-value-of-money (TVM) and amortization problems. Th ese problems can be used for calculations involving compound interest applications as well as amortization tables. Compound interest is the process by which earned interest on a given princip al amount is added to the principal at specified compounding perio ds, and then the HP 3 9gs Engl ish. book Pa ge 1 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
12-2 Using the Fina nce Solver combined amount earns interest at a certain rate. Financial calculations involvin g compound interest include savings accounts, mo rtgages, pension funds, leases, and annuities. Time Value of Money (TVM) calculations, as the name implies, make use of the notion that a dollar today will be worth more than a dollar sometime in the future. A dollar today can be inv ested at a certain interest rate and generate a return that the same dollar in the future cannot. This TVM pri nciple under lies the not ion of interest rat es, compound interest and rates of return. TVM transactions can be represented by using cash flow diagrams . A cash flow diagram is a time line divided into equal segments re presenting the compounding periods. Arrows represent the cash flow s, which could be positive (upward arrows) or negati ve (downward arrows), depending on the poin t of view of the lender or borrower. The following cash flow diagram sho ws a loan from a borrower's point of view: On the other hand, the following cash flow diagram shows a load from the lender's point o f view: In addition, cash flow diagrams specify when payments occur relative to the compounding periods: at the beginning of each period or at the end . The Finance Solver application pr ovides both of these payment modes: Begin mode and End mode. The following cash Pres ent v alue (PV) (Loan) Money rece iv ed is a positi ve number Money paid out is a negati ve number E qual per iods 1 23 4 5 (P MT) F uture value (FV) E qual pa yments Pa y m e n t (P MT) Pa y m e n t (P MT) Pa y m e n t (P MT) Pa y m e n t (P MT) } } } } } FV E qual pa yments 1 23 4 5 } } } } PM T } PM T PM T PM T PM T E qual per iods PV Loan } HP 3 9gs Engl ish. book Pa ge 2 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Using th e Finance So lver 12-3 flow diagram shows lease payments at the beginning of each period. The following cash flow diagram shows deposits into an account at the end of each period. As these cash-flow diagrams imply, there are five TVM variables: PV 1 23 4 5 FV Capital i zed value of lease } PM T PM T PM T PM T PM T PV 1 23 4 5 FV PM T PM T PM T PM T PM T N The total number of compounding periods or payments. I%YR The nominal annual interest rate (or investment rate). This rate is divided by the number of paymen ts per year (P/YR) to compute the nominal interest rate per compounding period -- which is the interest rate actually used in TVM calculations. PV The present value of the initial cash flow. To a lender or borrower, PV is the amount of the loan; to an investor, PV is the initial investment. PV always occurs at the beginning of the first period. HP 3 9gs Engl ish. book Pa ge 3 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
12-4 Using the Fina nce Solver Performing TVM calculations 1. La unch the F inanc ial S olv er as indicated at the beginning of this secti on . 2 . Use the arr o w k e ys to hi ghlight the diff ere nt f ields and enter the kno wn var iables in the T VM calc ulations , pr essing the soft -menu k ey after enter ing each kno wn value . Be sure that values ar e enter ed for at least f our of the f iv e TVM var ia bles (namel y , N , I%YR , PV , P MT , and FV) . 3 . If necessar y , enter a differ ent v alue for P/YR (def ault value is 12 , i .e., monthl y pa ymen ts) . 4. Pr es s the k e y to change the P ay ment mode (Beg or End) as re quired . 5 . Us e the arr ow k ey s to highlight the TVM var i able y ou w ish to sol v e fo r and pres s the soft -men u k ey . PMT The periodic payment amount. The payments are the same amount each period and the TV M calculation assumes that no payments are sk ipped. Payments can occur at the beginning or the end of each compounding period -- an option you control by se tting the Payment mode to Beg or End. FV The future value of the transaction: the amount of the final cash flow or the compounded value of the series of previous cash flows. For a loan, this is the size of the final balloon payment (beyond any regular payment due). For an investment this is the cash value of an investment at the end of the investment period. HP 3 9gs Engl ish. book Pa ge 4 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Using th e Finance So lver 12-5 Example 1 - Loan calculations Suppose you finance the purcha se of a car with a 5-year loan at 5.5% annual intere st, compounded monthly. The purchase price of the car is $19,500, and the down payment is $3,000. What are the r equired monthly payments? What is the largest loan you can afford if your maximum monthly payment is $300? Assume that the payments start at the end of the first period. Solution. The following cash flow diagram il lustrates the loan calculations: Start the Finance Solver, selec ting P/YR = 12 and End payment option. ⢠Enter the kn o w n TVM var ia bles as sh o wn in the diagr am abov e. Y our input form should look as fo llo w s: ⢠Hi ghlighting the P MT fi eld , pr ess the soft menu k ey to obtain a pa y ment of -315 .17 (i .e ., P MT = -$315 .17) . ⢠T o deter mine the max imum loan possible if the monthl y pay ments are onl y $3 00, t y pe the value â300 in the P MT f ie ld, highlight the PV fie ld, and pr ess the soft men u k e y . The r esulting v alue is PV = $15, 7 0 5 .85 . PV = $1 6,500 1 2 59 60 FV = 0 l%YR = 5 .5 N = 5 x 12 = 60 P/YR = 12 ; End mode PMT = ? HP 3 9gs Engl ish. book Pa ge 5 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
12-6 Using the Fina nce Solver Example 2 - Mortgage with balloon payment Suppose you have taken out a 30-year, $150,000 house mortgage at 6.5% annual interest. You expect to sell the house in 10 years, repaying the loan in a balloon payment. Find the size of the balloon payment, the value of the mortgage after 10 years of payment. Solution. The following cash flow diagram illustrates the case of the mortgage with balloon payment: ⢠St art the F inance Sol v er , selecting P/YR = 12 and End pa yment opti on. ⢠Enter the kno wn TV M v ari ables as sho w n in the diagr a m abo ve . Y our input f orm , f or calc ulating monthl y pa ymen ts fo r the 30 -y r mortgage , should look as fo llo w s: ⢠Highlighting the P MT field , pre ss the soft menu k ey to obtain a pa yment of -9 4 8.10 (i .e ., P MT = -$9 48.10) ⢠T o dete rmine the balloon pay ment or f utur e value (FV) for the mo rtgage a fter 10 years , use N = 120, highli ght the FV f ield , an d pr es s the soft menu k e y . The r esulting value is FV = -$12 7 ,164.19 . T he negativ e value indicates a p a y ment fr om the homeo wner . C heck that the r equir ed balloon pay ments at the end of 20 years (N=2 40) and 2 5 y ears (N = 300) ar e -$83, 4 9 7 .9 2 and -$48 , 4 5 6.2 4, r especti vel y . PV = $15 0,000 1 2 59 60 l%YR = 6 .5 N = 30 x 12 = 360 (for PMT) N = 10 x 12 = 120 (f or balloon pa yment) P/YR = 12 ; End mode PMT = ? Balloon pa yment , FV = ? HP 3 9gs Engl ish. book Pa ge 6 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Using th e Finance So lver 12-7 Calculating Amortizations Amortization calculations, which also use the TVM variables, determine the amounts applied towards principal and interest in a payment or series of payments. To calculate amortizations: 1. St art the F inance So lv er as indicated at the beginning of t hi s se ction. 2 . Se t the follo w ing T VM v ari ables: a Number of pa y ments per y ear (P/YR) b P a yment at beginning or end of per iods 3 . Stor e values f or the T VM var iable s I%YR , PV , P MT , and FV , w hic h def ine the pa y ment schedule . 4. Pr ess the soft men u k e y and enter the number o f pay ments to amorti z e in this batc h. 5 . Pr ess the soft menu k e y to amorti ze a batc h of pay m ents. T he calculator w ill pro v ide for y ou the amount applied to inter est , to pr inc ipal, and the r emaining balance after this set of pay ments hav e been amor ti z ed. Example 3 - Amortization for home mortgage For the data of Example 2 abov e, find the amortization of the loan after the first 10 years (12x10 = 120 payments). Pressing the soft menu key produces the screen to the left. Enter 120 in the PAYMENTS field, and press the soft menu key to produce the results shown to the right. To continue amortizing the loan: 1. Pr ess the soft menu ke y to stor e th e new balance after the pr ev ious amorti z ation a s PV . 2 . Ente r the number of pa y ments to amorti z e in the ne w batch . HP 3 9gs Engl ish. book Pa ge 7 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
12-8 Using the Fina nce Solver 3 . Pr ess the soft menu k ey to amorti z e the new batch o f pay ments . Repeat st eps 1 thr ough 3 as often as needed. Example 4 - Amortization for home mortgage For the results of Example 3, show the amortization of the next 10 years of the mortgage loan. First, press the soft menu key. Then, keeping 120 in the PAYMENTS field, press the soft menu key to produce the results shown below. To amortize a ser ies of future payments starting at payment p: 1. Calc ulate the balance of the loan at pay ment p-1 . 2 . Stor e the ne w balance in PV using the soft menu k ey . 3 . Amorti z e the ser ies of pa yments s tarting at the new PV . The amortization operation reads the v alues from the TVM variables, rounds the nu mbers it gets from PV and PMT to the current display mode, then calculates the amortization rounded to the same setti ng. The original variables are not c hanged, except for PV, whic h is updated after each amortization. HP 3 9gs Engl ish. book Pa ge 8 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Using mathemati cal functions 13-1 13 Using math ematical func tions Math functions The HP 39gs contains many math func tions. The functions are grouped in categories. For example, the Matrix category contains functions for manipulating matrices. The Probability category (shown as Prob. on the MATH menu) contains functions for working with probability. To use a math function, you enter the function onto the command line, and include the ar guments in parentheses after the function. You can also select a math function from the MATH menu. The MATH menu The MATH menu provides access to math functions, physical constants, and programming constants. The MATH menu is organized by category . For each category of functions on the left, there is a list of function names on the right. The hi ghlighted category is the current category . ⢠When y ou pr ess , you s ee the menu list o f Math categor ies in the left column and the cor r espo nding func tions o f the highli ghted cate gory in the ri ght column. T he menu ke y indi cates that the MA TH FUNCT IONS men u list is acti ve . To select a function 1. Pr ess to display the MA TH menu . The categori es appear in alphabetical or der . Pr ess or to sc ro ll thr ough the cat egor ies . T o skip dir ectl y to a category , pr ess the f irst le tter of the categoryâs name . Note: Y ou do not need to pr ess fir st . HP 3 9gs Engl ish. book Pa ge 1 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
13-2 Using math ematical functions 2 . The list o f func tions (on the r ight) applie s to the c urr ently hi ghlighted category (on the left) . U se and to sw itch bet w een the categor y list and th e func tion lis t . 3 . Hi ghlight the name of the func tion y ou wan t and pr ess . This copi es the fu nctio n name (and an initial par enthesis, if appr opr iate) to the edit line . Function categories Math functions by category Syntax Each functionâs definiti on incl udes its syntax, that is, the exact order and spelling of a functionâs name, its delimiters (punctuation), and its arguments. Note that the syntax for a function does not require spaces. Functions common to keyboard and menus These functions are common to the keyboard and MA TH menu. Ï F or a desc ripti on , see â Ï â on page 13-8. ARG F or a desc r ipti on , see â ARGâ on page 13- 7. F or a desc ripti on , see â â on page 11- 7 . AND F or a desc r iption , see â AND â on page 13-19. â ⢠Cal culus ⢠Comp l ex num be rs ⢠Const ant ⢠Conver t ⢠Hyperb olic trigonometr y (Hy perb .) ⢠Li st s ⢠Lo o p ⢠Matri x ⢠Po l y n o m i a l ⢠Probabil it y ⢠Real n umbers (Real) ⢠Tw o - v a r i a b l e stat istics (Stat-T wo) ⢠Sym b o l i c ⢠Te s t s ⢠T rigonometr y (T r ig) HP 3 9gs Engl ish. book Pa ge 2 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Using mathemati cal functions 13-3 Keyboard functions The most frequently used functions are available directly from the keyboard. Many of the keyboard functions also accept complex numbers as arguments. ,, , Add, Subtract, Multiply, Di vide. Also accepts complex numbers, lists and matrices. va lu e 1 va lu e 2 , etc. e x Natural exponential. Also accepts complex numbers. e^ val u e Example e^5 re t u r n s 148.41315910 3 Natural logarithm. Also accepts complex numbers. LN ( val u e) Example LN(1) ret u r ns 0 ! F or a d esc ription , see âCO MB(5,2) r eturns 10. T hat is, ther e ar e ten diff er ent w ay s that fi ve things can be combined tw o at a time.!â on page 13-12. â F or a d esc ription , see â Σ â on page 13-11. EEX F or a d esc ription , see âSc ientifi c notati on (po w ers of 10)â on page 1- 20. F or a d esc ription , see â â on page 11- 7 . The multiplicative inverse function finds the inverse of a square matrix, and the multiplicative inve rse of a real or complex number. Also works on a list containing only these object types. â« â« x 1 â HP 3 9gs Engl ish. book Pa ge 3 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
13-4 Using math ematical functions 10 x Exponential (antilogarithm). Also acc epts complex numbers. 10^ val u e Example 10^3 r etur ns 1000 Common logarithm. Also accepts co mplex numbers. LOG ( val u e) Example LOG(100) r eturns 2 ,, Sine, cosine, tangent. Inputs and outputs depend on the current angle format (Degrees, Radi ans, or Grads). SIN ( val u e) COS ( val u e) TAN ( val u e) Example TAN(45) r eturns 1 (Degrees mode) . ASIN Arc sine: sin â1 x. Output range is from â90° to 90°, â Ï /2 to Ï /2, or â100 to 100 grads. Inputs and outputs depend on the current angle format. Also accepts complex numbers. ASIN ( val u e) Example ASIN(1) r eturns 90 (Degrees mode) . ACOS Arc cosine: cos â1 x . Output range is from 0° to 180°, 0 to Ï , or 0 to 200 grads. Inp uts and outputs depend on the current angle format. Also accepts complex numbers. Output will be complex for values outside the normal COS domain of . ACOS ( val u e) Example ACOS(1) ret u r ns 0 (Degrees mode). 1 â x 1 â¤â¤ HP 3 9gs Engl ish. book Pa ge 4 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Using mathemati cal functions 13-5 ATAN Arc tangent: tan â1 x . Output range is from â90° to 90°, 2 Ï /2 to Ï /2, or â100 to 100 grad s. Inputs and outputs depend on the current an gle format. Also accept s complex numbers. ATAN ( valu e) Example ATAN(1) ret u rn s 45 (Degrees mode). Square. Also accept s complex numbers. va lu e 2 Example 18 2 r eturns 324 Square root. Also accepts complex numbers. val ue Example r etur ns 18 Negation. Also accepts complex numbers. â val u e Example -(1,2) r eturns (-1,-2) Power ( x raised to y ). Also accepts complex numbers. va lu e ^ po w er Example 2^8 r eturns 256 ABS Absolute value. For a c omplex number, this is . ABS ( val ue ) ABS (( x ,y)) Example ABS(â1 ) r eturns 1 ABS((1,2)) ret u rn s 2.2360679775 324 x 2 y 2 HP 3 9gs Engl ish. book Pa ge 5 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
13-6 Using math ematical functions Takes the n th root of x . ro ot NTHROOT val ue Example 3 NTHROOT 8 r eturns 2 Calculus functions The symbols for differentiation and integration are available directly form the k eyboardâ and S respectivelyâas well as from the MATH menu. Differentiates expr ession with respect to the vari able of differentiation. From the command line, use a formal name (S1, etc.) for a non-numeric result. See âFinding derivativesâ on p age 13-21. va riab l e ( exp re ss io n ) Example s1(s1 2 3*s1) re t u r n s 2*s1 3 Integrates expression from lower to upper limits with respect to the variable of integration. To find the definite integral, both limits must ha ve numeric values (that is, be numbers or real variables). To find the indefinite integral, one of the limits must be a formal variable (s1, etc). ( l o w e r, u p p e r, e x p r e s s i o n , v a r i a b l e ) See âUsing f or mal var iables â on page 13- 20 f or fur t her de ta il s. Example (0,s1,2*X 3,X) finds the indefinite result 3*s1 2*(s1^2/2) See âT o find the indef inite inte gr al using f ormal v ari ables â on page 13- 2 3 f or mor e i nf or mation on finding inde f inite integr als. n â â â â« â« â« HP 3 9gs Engl ish. book Pa ge 6 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Using mathemati cal functions 13-7 TAYLOR Calculates the n th order Taylor polynomial of expression at the point where the given variab le = 0. TAYLOR ( e xpr ession , var iable , n ) Example TAYLOR(1 sin(s1) 2 ,s1,5) w ith Radians angle measur e and F rac tion n umber f ormat (s et in MODE S) r etur ns 1 s1^2-1/3*s1^4 . Complex number functions These functions are for com plex numbers only. You can also use complex numbers with all trigonometric and hyperbolic functions, and with some real-number and keyboard functions. Enter co mplex numbers in the form ( x,y ), where x is the real part and y is the imaginary part. ARG Argument. Finds the angle de fined by a complex number. Inputs and outputs use the current angle format set in Modes. ARG (( x, y)) Example ARG((3,3)) r eturns 45 (Degr ees mode) CONJ Complex conjugate. Conjugation is the negation (sign reversal) of the imaginary part of a complex number. CONJ (( x, y)) Example CONJ((3,4)) r eturns (3,-4) IM Imaginary pa rt, y, of a c omplex number, ( x, y ). IM (( x, y)) Example IM((3,4)) r eturns 4 RE Real part x , of a complex number, ( x, y ). RE (( x, y)) Example RE((3,4)) r eturns 3 HP 3 9gs Engl ish. book Pa ge 7 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
13-8 Using math ematical functions Constants The constants available from the MATH FUNCTIONS menu are mathematical constants. These are described in this section. The hp 39gs has two other menus of constants: program constant s and physical constants. These are described in âProgram constants and physical constantsâ on page 13-24. e Natural logarithm base. Internally represented as 2.71828182846. e i Imaginary value for , the complex number (0,1). i MAXREAL Maximum real number. Internally represented as 9.99999999999 x 10 499 . MAXREAL MINREAL Minimum real number. In ternally re presented as 1 x 10 -499 . MINREAL Ï Internally represented as 3.14159265359. Ï Conversions The conversion functions ar e found on th e Convert menu. They enable you to make the following conversions. â C Convert from Fahrenheit to Celcius. Example â C(212) r eturns 100 â F Convert from Celcius to Fahrenheit. Example â F(0) r eturns 32 â CM Convert from inches to centimeters. 1 â HP 3 9gs Engl ish. book Pa ge 8 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Using mathemati cal functions 13-9 â IN Convert from centimeters to inches. â L Convert from US gallons to liters. â LGAL Convert from liters to US gallons. â KG Convert from pounds to kilograms. â LBS Convert from kilograms to pounds. â KM Convert from miles to kilometers. â MILE Convert from kilometers to miles. â DEG Convert from radians to degrees. â RAD Conve rt from degrees to radians. Hyperbolic trigonometry The hyperbolic trigonometry functions can also take complex numbers as arguments. ACOSH Inverse hyperbolic cosine : cosh â1 x . ACOSH ( valu e) ASINH Inverse hyperbolic sine : sinh â1 x . ASINH ( valu e) ATANH Inverse hyperbolic tangent : tanh â1 x . ATANH ( valu e) COSH Hyperbolic cosine COSH ( valu e) SINH Hyperbolic sine. SINH ( valu e) TANH Hyperbolic tangent. TANH ( valu e) ALOG Antilogarithm (exponential). Th is is more accurate than 10^x due to limitations of the power function. ALOG ( valu e) HP 3 9gs Engl ish. book Pa ge 9 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
13-10 Using mathe matical functions EXP Natural exponential. This is mor e accurate than due to limitations of the power function. EXP ( val u e) EXPM1 Exponent minus 1 : . This is more accurate than EXP when x is close to zero. EXPM1 ( val ue ) LNP1 Natural log plus 1 : ln( x 1 ). This is more accurate than the natural logarithm function when x is close to zero. LNP1 ( val u e) List functions These functions work on list da ta. See âList fu nctionsâ on page 16-6. Loop functions The loop functions display a result after evaluating an expression a given number of times. ITERATE Repeatedly for #times evaluates an expression in terms of variable . The value for variable is updated each time, starting with initialvalue. ITERATE( e xpre ssion , va riab l e , initial value , #times ) Example ITERATE(X 2 ,X,2,3) r eturns 256 RECURSE Provides a method of defini ng a sequence without using the Symbolic view of the Seque nce aplet. I f used with | (âwhereâ), RECURSE will step through the evaluation. RECURSE( seq uencename , ter m n , term 1 , term 2 ) Example RECURSE(U,U(N-1)*N,1,2) U1(N) St or es a f actor ia l-calculating f unction named U1. When y ou enter U1(5) , f or e xam ple , the functi on calc ulates 5! ( 120 ). e x e x 1 â HP 3 9gs Engl ish. book Pa ge 10 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Using mathemati cal functions 13-11 Σ Summation. Finds the sum of expression with respect to variable from initialvalue to finalvalue. Σ ( v ar iable = initial v alue , fin a lval u e, e xp ression ) Example Σ (C=1,5,C 2 ) r etur ns 5 5 . Matrix functions These functions are for matr ix data stored in matrix variables. See âMatrix func tions and commandsâ on page 15-10. Polynomial functions Polynomials are products of constants ( coefficien ts ) and variables raised to powers ( terms ). POLYCOEF Polynomial coefficients. Returns the coefficients of the polynomial with the specified roots . POLYCOEF ([ roo t s ]) Example T o f ind the pol y nomial w ith roots 2 , â3, 4, â5: POLYCOEF([2,-3,4,-5]) r eturns [1,2,-25, -26,120] , r epr esenting x 4 2x 3 â25x 2 â26x 120 . POLYEVAL Polynomial evaluation. Evaluates a polynomial with the specified coefficients for the value of x . POLYEVAL([ coeff ic ients ] , va lu e ) Example Fo r x 4 2x 3 â25x 2 â26x 120 : POLYEVAL([1,2,-25,-26,120], 8) re t ur n s 3432 . POLYFORM Polynomial form. Creates a polynomial in variable1 from expression. POLYFORM ( expression , var iable1 ) Example POLYFORM((X 1)^2 1,X) ret u rn s X^2 2*X 2 . HP 3 9gs Engl ish. book Pa ge 11 We dnes day, Dec embe r 7, 2005 11 : 24 PM
13-12 Using mathe matical functions POLYROOT Polynomial roots. Return s the roots for the n th-order polynomial with the specified n 1 coeffici ents . POLYROOT ([ coe ff ic ien ts ]) Example Fo r x 4 2x 3 â25x 2 â26x 120 : POLYROOT([1,2,-25,-26,120]) r eturns [2,-3,4,-5] . HINT The results of POLYROOT will often not be easily seen in HOME due to the number of decimal places, especially if they are complex numbers. I t is better to store the results of POLYROOT to a matrix. For example, POLYROOT([1,0,0,-8] M1 will store the three complex cube roots of 8 to matri x M1 as a complex vector. Then you can see them easily by g oing to the Matrix Catalog. and access them individually in calculations by referring to M1(1), M1(2) etc. Probability functions COMB Number of combination s (without regard to order ) of n things taken r at a time: n!/(r!(n-r)) . COMB (n, r ) Example COMB(5,2) r eturns 10 . T hat is, ther e ar e ten differ ent wa y s that fi ve things can be combined tw o at a time .! Factorial of a positive integer. For non-integers, ! = Î (x 1) . This calculates the gamma function. value! PERM Number of permutations (w ith regard to order) of n things taken r at a time: n!/(r!(n-r)! PERM ( n, r ) Example PERM(5,2) r eturns 20 . T hat is, ther e ar e 20 differ ent permutati ons of f i v e things tak en t w o at a time . HP 3 9gs Engl ish. book Pa ge 12 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Using mathemati cal functions 13-13 RANDOM Random number (between zero and 1). Produced by a pseudo-random number sequence. The algorithm used in the RANDOM function uses a seed number to begin its sequence. To ensure that two calculators must produce different results for the RANDOM function, use the RANDSEED function to seed different starting values before using RANDOM to produce the numbers. RANDOM HINT The setting of Time will be different for each c alculator, so using RANDSEED(Time) is guar anteed to produce a set of numbers which are as close to random as possible. You can set the seed using the command RANDSEED. UTPC Upper-Tail Chi-Squared Probability given degrees of freedom, evaluated at value . Returns the probability that a Ï 2 random variable is greater than value. UTPC ( degr ees , val u e ) UTPF Upper-Tail Snedecorâs F Probability given numerator degrees of freedom and denominator degrees of freedom (of the F distribution), evaluated at value . Returns the probability that a Snedecor 's F random variable is greater than value. UTPF ( numerator , denominat or , va lu e ) UTPN Upper-Tail Normal Probability given mean and variance , evaluated at value. Returns the probability that a normal random variable is greater than value for a normal distribution. Note: The variance is the square of the standard deviation . UTPN ( mean , va ria nc e, valu e) UTPT Upper-Tail Studentâs t-Probability given degrees of freedom, evaluated at value. Returns the probability that the Student's t- random variable is greater than value. UTPT ( degr ees , val u e ) Real-number functions Some real-number functions can also take complex arguments. CEILING Smallest integer greater than or equal to value . CEILING ( val ue ) HP 3 9gs Engl ish. book Pa ge 13 We dnes day, Dec embe r 7, 2005 11 : 24 PM
13-14 Using mathe matical functions Examples CEILING(3.2) r eturns 4 CEILING(-3.2) r eturns -3 DEG â RAD Degrees to radians. Converts value from Degrees angle format to Radians angle format. DEG â RAD ( val ue ) Example DEG âRAD( 180) r eturns 3.14159265 359 , the va lu e of Ï . FLOOR Greatest integer less than or equal to value . FLOOR ( val ue ) Example FLOOR(-3.2) r eturns -4 FNROOT Function root-finder (lik e the Solve aplet). Finds the valu e for the given variable at which expression most nearly evaluates to zero. Uses guess as initial estimate. FNROOT ( e xpr essi on , var iable , gues s ) Example FNROOT(M*9.8/600-1,M,1) r eturns 61.2244897959 . FRAC Fractional part. FRAC ( val u e) Example FRAC (23.2) r eturns .2 HMS â Hours-minutes-seconds to deci mal. Converts a number or expression in H.MMSSs format (time or angle that can include fractions of a second) to x.x format (number of hours or degrees with a decimal fraction). HMS â ( H.M MSSs ) Example HMS â (8.30) r etur ns 8.5 â HMS Decimal to hours-minutes-seco nds. Converts a number or expression in x.x format (number of hours or degrees HP 3 9gs Engl ish. book Pa ge 14 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Using mathemati cal functions 13-15 with a decimal fraction) to H.MMSSs forma t (tim e or angle up to fractions of a second). â HMS ( x.x) Example â HMS(8.5) r eturns 8.3 INT Integer part. INT ( val ue ) Example INT(23.2) r eturns 23 MANT Mantissa (significant digits) of value . MANT ( valu e) Example MANT(21.2E34) r eturns 2.12 MAX Maximum. The greater of two values. MAX ( val ue 1 , va lu e2) Example MAX(210,25) r eturns 210 MIN Minimum. The lesser of two values. MIN ( val ue 1 , va lu e2) Example MIN(210,25) re t u rn s 25 MOD Modulo. The remai nder of value1 / value2. va lu e 1 MOD va l ue 2 Example 9 MOD 4 r eturns 1 % x percent of y ; that is, x /100* y . % ( x , y) Example % (20,50) r eturns 10 %CHANGE Percent change from x to y , that is, 100( yâx )/ x . % CHANGE( x , y) HP 3 9gs Engl ish. book Pa ge 15 We dnes day, Dec embe r 7, 2005 11 : 24 PM
13-16 Using mathe matical functions Example % CHANGE(20,50) r eturns 150 %TOTAL Percent total : (100) y/ x . What percentage of x , is y . % TOTAL( x , y) Example % TOTAL(20,50) r eturns 250 RAD â DEG Radians to degrees . Converts value from radians to degrees. RAD â DEG ( va lu e ) Example RAD âDEG( Ï) r eturns 180 ROUND Rounds value to decimal places . Accepts complex numbers. ROUND ( val ue , places) Round can also round to a number of significant digits as showed in example 2. Examples ROUND(7.8676,2) r eturns 7.87 ROUND (0.0036757,-3) r eturns 0. 00368 SIGN Sign of value . If positive, the result is 1. If negative, â1. If zero, result is zero. For a complex number, this is the unit vector in the direction of the number. SIGN ( val u e) SIGN (( x, y)) Examples SIGN (â2) re tu r n s â1 SIGN((3,4)) r eturns (.6,.8) TRUNCATE Truncates value to dec imal places . Accepts complex numbers. TRUNCATE ( valu e , places ) Example TRUNCATE(2.3678,2) r eturns 2.36 HP 3 9gs Engl ish. book Pa ge 16 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Using mathemati cal functions 13-17 XPON Exponent of value . XPON ( valu e) Example XPON(123.4) r eturns 2 Two-variable statistics These are functions for use with two-variable statistics. See âTwo-variableâ on pa ge 10-15. Symbolic functions The symbolic functions are used for symbolic manipulations of expression s. The variables can be formal or numeric, but the re sult is usually in symbolic form (not a number). You will find the symbols for the symbolic functions = and | ( where ) in the CHARS menu ( CHARS ) as well as the MATH menu. = ( equals ) Sets an equality for an equatio n. This is not a logical operator and does not store values. (See âTest functionsâ on page 13-18.) exp re ss io n 1 = e xpre ssion2 ISOLATE Isola tes the first occurrence of va riable in expression= 0 and returns a new expression, where variable=newexpression. The result is a general solution that represents multiple solutions by including the (formal) variables S1 to represent any sign and n1 to represent any integer. ISOLATE( expression , var iable ) Examples ISOLATE(2*X 8,X) ret u rn s -4 ISOLATE(A B*X/C,X) r eturns - (A*C/B) LINEAR? Tests whether expression is linear for the specified variable . Retur ns 0 (false) or 1 (true). LINEAR?( expression , var iable ) Example LINEAR?((X^2-1)/(X 1),X) r eturns 0 HP 3 9gs Engl ish. book Pa ge 17 We dnes day, Dec embe r 7, 2005 11 : 24 PM
13-18 Using mathe matical functions QUAD Solves quadratic expression= 0 for variab le and returns a new expression, where variable = newexpression. The result is a general solution th at represents both positive and negative solutions by in cluding the formal variable S1 to represent any sign: or â . QUAD( ex pre ss i on , variab l e ) Example QUAD((X -1) 2 -7,X) r eturns (2 s1*5.29150262213)/2 QUOTE Encloses an expression that should not be evaluated numerically. QUOTE( ex pre ss io n ) Examples QUOTE(SIN(45)) F1(X) stor es the e xpre ssion S IN(4 5) r ather than the value of SIN( 45 ) . Another meth od is to enclo se the e xpr essi on in single quotes. Fo r ex a m p l e, X^3 2*X F1(X) puts the e xpressi on X^3 2*X into F1(X) in the F uncti on apl et . | ( where ) Evaluates expression where each given variable is set to the given value . Defines numeric evaluation of a symbolic expression. e xpressi on |( var iable1=v alue1, var iable2=v alue2 ,... ) Example 3*(X 1)|(X=3) r eturns 12 . Test functions The test functions are logical operators that always return either a 1 ( true ) or a 0 ( false ). < Less than. Returns 1 if true, 0 if false. va lu e 1 < va lu e2 ⤠Less than or equal to. Returns 1 if true, 0 if false. va lu e 1 ⤠va lu e2 HP 3 9gs Engl ish. book Pa ge 18 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Using mathemati cal functions 13-19 = = Equals (logical test). Returns 1 if true, 0 if false. va lu e 1 ==va l ue 2 â Not equal to. Returns 1 if true, 0 if false. va lu e 1 â va l ue 2 > Greater than. Returns 1 if true, 0 i f false. va lu e 1 > va l ue 2 ⥠Greater than or equal to. Returns 1 if true, 0 if false. va lu e 1 ⥠va l ue 2 AND Compares value1 and value2 . Returns 1 if they are both non-zero, otherwise returns 0. va lu e 1 AND va l ue 2 IFTE If expression is true, do the trueclause ; if no t, do the falseclause. IFTE( e xpre ssion , true cla use , fals ecla use ) Example IFTE(X>0,X 2 ,X 3 ) NOT Returns 1 if value is zero , otherwise returns 0. NOT val ue OR Returns 1 if either value1 or value2 is n on-zero, otherwise returns 0. va lu e 1 OR va l ue 2 XOR Exclusive OR. Returns 1 if ei ther value1 or value2 âbut not both of themâis non-zero, otherwise r eturns 0. va lu e 1 XOR va l ue 2 Trigonometry functions The trigonometry functions can also take complex numbers as arguments. For SIN, COS, TAN, ASIN, ACOS, and ATAN, see the Keyboard category . ACOT Arc cotangent. ACOT ( valu e ) HP 3 9gs Engl ish. book Pa ge 19 We dnes day, Dec embe r 7, 2005 11 : 24 PM
13-20 Using mathe matical functions ACSC Arc cosecant. ACSC ( val u e) ASEC Arc secant. ASEC ( val u e) COT Cotangent: cos x /sinx . COT ( val u e) CSC Cosecant: 1/sin x CSC ( val u e) SEC Secant: 1/cos x . SEC ( val u e) Symbolic calculations The HP 39gs has the ability to perform symbo lic calculations, for example, symbolic integration and differentiation. You can perform symbolic calculations in HOME and in the Function aplet. In HOME When you perform calculation s that contain normal variables, the calcul ator substitutes values for any variables. For example, if you enter A B on the c ommand line and press , the calculator retrieves the values for A and B from memory and substitutes them in the calculation. Using formal variables To perform symbolic calculati ons, for example symbolic differentiations and integrations, you need to use formal names. The HP 39gs has six formal names available for use in symbolic calculations. Th ese are S0 to S5. When you perform a calculation that contai ns a formal name, the HP 39gs does not carry out any substitutions. You can mix formal names an d real variables. Evaluati ng (A B S1) 2 will evaluate A B , but not S1 . If you need to evaluate an expression that contains formal names numerically, you use the | ( where ) command, listed in the Math menu under the Symbolic categor y. For example to evaluate (S1*S2) 2 when S1=2 and S2=4 , you would enter the calculation as follows: HP 3 9gs Engl ish. book Pa ge 20 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Using mathemati cal functions 13-21 (The | symbol is in the CHARS menu: press CHARS . The = sign is listed in the MATH menu under Symbolic functions.) Symbolic calculations in the Function aplet You can perform symbolic operations i n the Function apletâs Symbolic view. For example, to find the derivative of a function in the Function apletâs Symbolic view, you define two functions and define the second function as a derivative of the first function. You then evaluate the second function. See âTo find derivatives in the Function apletâs Symbolic viewâ on p age 13-22 for an example. Finding derivatives The HP 39gs can perform symbo lic differentiation on some functions. There are two ways of using the HP 39gs to find derivatives. ⢠Y ou can perfor m differ entiatio ns in HOME b y using the fo rmal v ari ables , S1 to S5 . ⢠Y ou can perfor m differ entiati ons of f unctio ns of X in the F unction aplet . To find derivatives in HOME To find the derivative of the function in HO ME, use a formal variable in place of X. If you use X, the differentiation function substi tutes the value that X holds, and returns a numeric result. For example, consider the function: 1. Enter the diff er entiati on func tion o nto the command line , subs tituting S1 in place of X . S1 S1 2 dx x ( 2 ) sin ( 2 x () ) cos HP 3 9gs Engl ish. book Pa ge 21 We dnes day, Dec embe r 7, 2005 11 : 24 PM
13-22 Using mathe matical functions S1 2 . E valuate the f uncti on . 3 . Show the r esult . To find derivatives in the Function apletâs Symbolic view To find the derivative of the fu nction in the Function apletâs Symbolic view, you define two functions and define the second function as a derivati ve of the first function. For example, to differentiate : 1. Access the F unction a pletâs S y mbolic v ie w and def ine F1. 2 2. D e f i n e F 2 ( X ) as the der i vati ve of F(1). F1 3 . Select F 2( X ) and eva l ua t e it. x 2 () sin 2 x cos HP 3 9gs Engl ish. book Pa ge 22 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Using mathemati cal functions 13-23 4. Pr ess to display the r esult . Note: Us e the arr ow k ey s to v ie w the entir e functi on . | Y ou coul d also j us t def ine . To find the indefinite integral using formal variables F or ex ample, to f ind t he indefinite integral of use: 1. Enter the f uncti on . 0 S1 3 X 5 X 2 . Show the r esult f orm at . 3 . Pr ess to close the sho w w indo w . 4. Cop y the result and eva lu a te. Th us , substit uting X f or S1, it can be seen that: F 1 x () xx 2 () 2 x () co s sin () d = 3 x 2 5 â x d â« ( ) â« â X X S , 5 3 , 1 , 0 2 3 x 2 5 â x 5 x â3 x 3 3 ---- - X â â X () -------------- - ââ ââ ââ ââ ââ = d â« HP 3 9gs Engl ish. book Pa ge 23 We dnes day, Dec embe r 7, 2005 11 : 24 PM
13-24 Using mathe matical functions This result is de rived from substituting X = S1 and X = 0 into the original expression found in step 1. However, substituting X = 0 will not always evaluate to zero and may result in an unwanted constant. To see this, consider: The âextraâ constant of 6.4 results from the substitution of into ( x â2 ) 5 /5 , and should be disregarded if an indefinite integral is required. Program constants and physical constants When y ou pr ess , thr ee menus of func tions and constants become a vailable: ⢠the math functi ons menu (w hic h appears b y def ault) ⢠the pr ogr am constants menu , and ⢠the ph ysi cal constants menu . The math functions menu is described extensively earlier in this chapter. Program constants The program constants are numbers that have been assigned to various calculator settings to enable you to test for or specify such a setting in a program. For example, the various display formats are assigned the following numbers: 1 Standar d 2 F ix ed 3 Sc ientif ic 4 Engineering 5 Fraction 6 Mixed fraction In a program, you could store the constant number of a particular format into a variable and then subseque ntly test for that particular format. x 2 â () 4 x x ( 2 ) 5 â 5 ------------------- = d â« x 0 = HP 3 9gs Engl ish. book Pa ge 24 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Using mathemati cal functions 13-25 To access the menu of program constants: 1. Pr ess . 2. P r e s s . 3 . Use the ar r o w k e y s to na v igate thr ough the options . 4. Clic k and then to di spla y the number assigned to th e option you selected in th e pr ev ious step. The use of program constants i s illustrated in more detail in âProgrammingâ on page 18-1 Physical constants There are 29 physical cons tantsâfrom the fields of chemistry, physics and q uantum mechanicsâthat y ou can use in calculations. A list of all these constants can be found in âPh ysical Constantsâ on page R-16. To access the menu of physical constants: 1. Pr ess . 2. P r e s s . 3 . Use the ar r o w k e y s to na v igate thr ough the options . 4. T o see the s y mbol and va lue of a selected constan t , pr ess . (Clic k to close the infor mation w indo w that appears .) T he follo w ing e x ample sho ws the inf ormatio n av ailable about the spee d of li ght (one of the ph y sics constants) . 5 . T o us e the selected constant in a calculati on , pres s . The consta nt appears at the positio n of the c urso r on the edit line . HP 3 9gs Engl ish. book Pa ge 25 We dnes day, Dec embe r 7, 2005 11 : 24 PM
13-26 Using mathe matical functions Example Suppose you want to know the potential energy of a mass of 5 units according to the equation . 1. Enter 5 2 . Pr ess and then p r ess . 3 . Select light s... f r om the Phy sic s menu . 4. Pr ess . The menu c lose s and the v alue of the selec ted constant is cop ied to the edit line . 5 . Complete the equat ion as y ou w ould normally and pr ess to get the r esult . Em c 2 = HP 3 9gs Engl ish. book Pa ge 26 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Variables an d memory manageme nt 14-1 14 V ariables and memory manag ement Introduction The HP 39gs has approximately 200K of user memory. The calculator uses this memory to store variables, perform computations, and store history. A v a r i a b l e i s a n o b j e c t t h a t y o u c r e a t e i n m e m o r y t o h o l d data. The hp 39gs has two types of variables, home variables and aplet variables. ⢠Home variables are avai lable in all aplets. For example, you can store real numbers in variables A to Z and complex numbers in variables Z0 to Z9. These can be numbers you have entered, or the results of calculations. Th ese variables are available within all aplets and within any programs. ⢠Aplet variables apply only to a single aplet. Aplets have specific vari ables allocated to them which vary from aplet to aplet. You use the calculatorâs memory to store the following objects: ⢠copies of aplets with specific configurations ⢠new aplets that you download ⢠aplet variables ⢠home variables ⢠variables created thr ough a catalog or edito r, for example a matrix or a text note ⢠programs that you create. You can use the Memory Manager ( MEMORY ) to view the amount of memory av ailable. The catalog views, which are accessible via the Memory Manager, can be used to transfer variables such as lists or matrices between calculators. HP 3 9gs Engl ish. book Pa ge 1 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
14-2 Variables and m emory management Storing and recalling variables You can store numbers or expressi ons from a previous input or result into variables. Numeric Precision A number stored in a variable is always stored as a 12- digit mantissa with a 3-digit exponent. Numeric precision in the display, however, de pends on the display mode (Standard, Fixed, Scientific, Engineering, or Fraction). A displayed number has only the precision that is displayed. If you copy it from the HOME view display history, you obtain only the precision displayed, not the full internal precision. On the other hand, the variable Ans always contains the most recent result to full precis ion. To store a value 1. On the command line, enter the value or the calc ulation for the r esult yo u wi s h to s t ore . 2. P r e s s 3 . Ente r a name fo r the va riab l e. 4. Pr ess . To store the result s of a calculation If the value you want to s tore is in the HOME view display history, for example the results of a previous calculation, you need to copy it to the co mmand line, then store it. 1. P er f or m the calc ulation f or the r esult y ou want t o st or e . 3 86 3 2 . Mov e the highli ght to the r esult y ou w ish to st or e . 3 . Pr ess to copy the r esult to the command line . 4. Pr ess . HP 3 9gs Engl ish. book Pa ge 2 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Variables an d memory manageme nt 14-3 5 . Enter a name for the v ari able . A 6 . Pres s to stor e the re sult . The results of a calculation can also be stored directly to a variable. For example: 2 5 3 B To recall a value To recall a var iableâs value , type the name of the variable and press . A To use variables in calculations You can use variables in calculations. The calculator substitutes the variableâs value in the calculation: 65 A To clear a variable You can use the CLRVAR command to clear a specified variable. Fo r example, if you have stored {1 ,2,3,4} in variabl e L1, entering CLRVAR L1 w ill clear L1. (Y ou can find the CLRVAR command b y pr essing and c hoosing the PROMPT category of commands.) HP 3 9gs Engl ish. book Pa ge 3 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
14-4 Variables and m emory management The VARS menu You use the VARS menu to access all variables in the calculator. The VARS menu is organi sed by category. For each variable category in the left column, there is a list of variables in the right colu mn. You select a variable category and then select a variable in the category. 1. Open the V ARS menu . 2 . Use the arr o w k e y s or pr ess the alpha k ey o f the f irst letter in the category to select a v ari able category . Fo r ex a m p l e, t o s e l e c t the Matr i x category , pr ess . Note: In this instance , ther e is no need to pr ess the ALP HA ke y . 3 . Mo v e the highli ght to the v ar iable s column. 4. Use the arr ow k ey s to selec t the var iable that y ou w ant . F or ex ample , to select M2 , pr ess . HP 3 9gs Engl ish. book Pa ge 4 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Variables an d memory manageme nt 14-5 5 . Ch oose w h ether to place the var ia ble name or the v ari able v alue on the command line . â Pres s to indicate that y ou w a nt the v ari able âs contents t o appear on the command line . â Pr ess to indicate that y ou w ant the v ari able âs name to a ppear on the command line . 6 . Pr ess to place the va lue or name on the command line . The s elected ob jec t appears on the command line . Note: T he V AR S menu can also be used to en ter the names or va lues of var iables into pr ogr ams. Example This example demonstrates how to use the VARS menu to add the contents of two list variables, and to store the result in another list vari able. 1. Display the L ist Catalog . LIST to select L1 2 . Enter the data f or L1. 88 90 89 65 70 3 . R etur n to the L ist Cat alog to c r eate L2 . LIST to select L2 HP 3 9gs Engl ish. book Pa ge 5 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
14-6 Variables and m emory management 4. Enter data for L2 . 55 48 86 90 77 5 . Pr ess to ac cess HO ME . 6 . Open the v ar iable men u and selec t L1. 7 . Cop y it to th e command line . Note: Because the option is hi ghlighted , the var iable âs name , r ather than its contents , is copied to the command line . 8. Insert the oper ator and s elect the L2 v ar ia ble fr om t h e Li s t va ri ab l e s. 9 . Stor e the answ er in the List cat alog L3 var iable . L3 Note: Y ou can also type list name s dir ectl y fr om the k ey board . HP 3 9gs Engl ish. book Pa ge 6 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Variables an d memory manageme nt 14-7 Home variables It is not possible to store data of one type in a variable of another type. For example, yo u use the Matrix catalog to create matrices. You can crea te up to ten matrices, and you can store these in variables M0 to M9. You cannot store matr ices in variab les other than M0 to M9. Cate- gory A v ai lable name s Complex Z0 to Z9 Fo r ex a m p l e, (1,2) Z0 or 2 3 i Z1. Y ou can enter a complex number by ty ping (r ,i) , wher e r repr esents the r eal par t , and i r e pr esents the imaginar y part. Graphic G0 to G9 SeeâGraphic commandsâ on page 18-21 for more information on storing graphi c objects via programming commands. See âTo store into a graphics variableâ on page 17-5 for more information on storing graphic object via the sketch view. Library Aplet library va riables can store aplets that you have created, either by saving a copy of a standard aplet, or downloading an aplet from another source. List L0 to L9 For example, {1,2,3} L1. Matrix M0 to M9 can store matri ces or vectors. For example, [[1,2],[3,4] ] M0. Modes Modes variables store the modes settings that you can configure using MODES . Notepad Notepad variables store notes. Program P rogram variables store programs. Real A to Z and θ. Fo r ex a m p l e, 7 . 45 A . HP 3 9gs Engl ish. book Pa ge 7 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
14-8 Variables and m emory management Aplet variables Most aplet variables stor e values t hat are uniqu e to a particular aplet. These includ e symbolic expressions and equations (see below), settings for the Plot and Numeric views, and the results of some calculations such as roots and intersections. See the Reference Information chapter for more information about aplet variables. To access an aplet variable 1. Open the a plet that contains the v ar iab le y ou w ant to re c al l. 2 . Pr ess to display the V ARS menu . 3 . Use the arr o w k e y s to s elect a v ari able category in the left column, then pre ss to access the vari ables in the ri ght column . 4. Use the arr o w k e y s to se lect a v ar ia ble in the ri ght column. 5 . T o cop y the name of the v ar iable o nto the edit line , pr ess . ( is the defau lt setting .) Category Av ailable names Function F0 to F9 (Symbolic view). See âFunction aplet variablesâ on page R-7. Parametric X0, Y0 to X9, Y9 (Symbolic view). See âParametric a plet variablesâ on page R-8. Polar R0 to R9 (Symbolic view). See âPolar aplet variablesâ on page R-9. Sequence U0 to U9 (Symbolic view). See âSequence aplet variablesâ on page R-10. Solve E0 to E9 (Symbolic view). See âSolve aplet variablesâ on page R-11. Statistics C0 to C9 (Numeric view). See âStatistics aplet v ariablesâ on page R-12. HP 3 9gs Engl ish. book Pa ge 8 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Variables an d memory manageme nt 14-9 6 . T o cop y the v alue of the v ar iable in to the edit line , pr es s and pr ess . Memory Manager You can use the Memory Manager to determine the amount of available memory on the calculator. You can also use Memory Manager to organize memory. For example, if the available memory is low, you can use the Memory Manager to determine which aplets or variables consume large amounts of memo ry. You can make deletions to free up memory. Example 1. St art the Memory Manager . A list of var ia ble categor ies is displa yed . MEMORY F ree memory is display ed in the to p r ight cor ner and the body o f the scr een lists each catego r y , the memory it uses , and the per centage of the total memory it uses . 2 . Select the category w ith whi c h y ou w ant to w or k and pr ess . Memory Manager display s memory details of v aria bles w ithin the category . 3 . T o delet e var iables in a category: â Pr ess to delete the s elect ed v ari able . â Pres s CLEA R to dele te all var iables in the selec ted category . HP 3 9gs Engl ish. book Pa ge 9 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
HP 3 9gs Engl ish. book Pa ge 10 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Matrices 15-1 15 M atr ices Introduction You can perform matrix calc ulation s in HOME and in programs. The matrix and each row of a matrix appear in brackets, and the elements and rows are separated by commas. For example, the following matrix: is displayed in the history as: [[1,2,3],[4,5,6]] (If the Decimal Mark mode is set to Comma , then separate each element and each row with a period.) You can enter matrices directly in the command line, or create them in the matrix editor. Vectors Vectors are one-dimensional arrays. They are composed of just one row. A vector is represented with single brackets; for example, [1,2,3]. A vector c an be a real number vector or a complex number vector, for example [(1,2), (7,3)]. Matrices Matrices are two-dimensi onal arrays. They are composed of more than one row and more than one column. Two-dimensional matrices ar e represente d with nested brackets; for example, [[1,2,3],[4,5,6]]. You can create complex matrices, for example, [[(1,2), (3,4 )], [(4,5), (6,7)]]. Matrix Variables There are ten matrix variables available, named M0 to M9. You can use them in ca lculations in HOME or in a program. You can retrieve th e matrix names from the VARS menu, or just type th eir names from the keyboard. 123 456 HP 3 9gs Engl ish. book Pa ge 1 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
15-2 Matr ices Creating and storing matrices You can create, edit, delete, send, and receiv e matrices in the Matrix catalog. To open the Matrix catalog, press MATRIX . You can also create and store matricesânamed or unnamedâ-in HOME. For example, the command: POLYROOT([1,0,â1,0]) îM1 stores the root of the c omplex vector of length 3 into the M1 variable. M1 now contai ns the three roots of Matrix Catalog keys The table below lists the operations of the menu key s in the Matrix Catalog, as well as the use of Delete ( ) and Clear ( CLEAR ). x 3 x â0 = Key M e a n i n g Opens the highlighted matrix for editing. Prompts for a matrix type, then opens an empty matrix with the highlighted name. Transmits the highlighted matrix to another hp 39gs or a disk drive. See âSending and receiving apletsâ on page 19-4. Receiv es a matrix from anoth er hp 39gs or a disk drive. See âSending and receiving apletsâ on page 19-4. Clears the highlighted matrix. CLEAR Clears all matrices. or Moves to the end or the beginning of the catalog. HP 3 9gs Engl ish. book Pa ge 2 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Matrices 15-3 To create a ma trix in the Matrix Catalog 1. Pr ess MATRIX to open the Matr i x Ca talog . The Matri x catalog lists the 10 av ailable matr ix v ar iable s, M0 to M9 . 2 . Hi ghlight the matr ix v a r iable name you w ant to use and pres s . 3 . Select the type o f matr i x to c r eate. â For a v ec tor (one -dim ensional array) , sele ct Real vector or Complex vector . Certain oper atio ns ( , â , CROSS ) do n ot r eco gni z e a one -d ime nsi onal matr i x as a v ect or , so t his sele ction i s im por tant. â For a matrix (t w o -dimension al array) , sele ct Real matrix or Complex matrix . 4. F or each element in the matr i x , type a number or an e xpr ession , and pr es s . (The e xpr essi on ma y not cont ain sy mbolic v ar iable names .) For c om p l ex n u mb e rs , ente r eac h n umbe r in comple x fo rm; that is , (a, b) , wher e a is the real part and b is the imaginar y part . Y ou must inc lude the par entheses and the comma . 5 . Us e the c urs or k e y s to mo v e to a differ ent r ow or column . Y ou can change the dir ection o f the highli ght bar by pre ssing . The menu ke y toggles betw een the f ollo w ing thr ee options: â spec if ies that the c ursor mo ves t o the cell belo w the c u r r ent cell w hen y ou pre ss . â s pec if ies that the c ursor mo ves t o the cell to the ri ght of the c urr ent cell w hen y ou pr ess . â s pec ifi es that the c ursor st a y s in the c urr ent cell when y ou pr ess . 6 . When done , pr ess MATRIX to see the Matri x catalog , or pr ess to r eturn to HO ME . The matri x entr ie s ar e automati cally stor ed. HP 3 9gs Engl ish. book Pa ge 3 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
15-4 Matr ices A matrix is listed with two dimensions, even if it is 3Ã1. A vector is listed with the number of elements, such as 3. To transmit a matrix You can send matrices between c alculators just as you can send aplets, programs, lists, and notes. 1. Align the HP 3 9gs calculator s â infr ared ports (or connect the calc ulators using an appr opr iate cable) . 2 . Open the Matr ix catalogs on bo th calc ulator s. 3 . Hi ghlight the matri x to send . 4. Pr ess and ch oose the method of sending (infr ar ed or cable) . 5 . Pr ess on th e r ecei v ing cal c ulator and c hoose the method of r ecei v ing (infr ar ed or cable) . F or more infor matio n on sending and r ecei v ing file s, see âSending and rece i ving a plets â on page 19- 4. Working with matrices To edit a matrix In the Matrix catalog, highli ght the name of the matrix you want to edit and press . Matrix e dit keys The follow ing table lists the matrix edit key operations. Key M e a n i n g Copies the highlighted element to the edit line. Inserts a row of zeros above, or a column of zeros to the left, of the highlighted cell. (You are prompted to choose row or column.) A three-way toggle for cursor advancement in the Matrix editor. advances to the right, ¸ advances downward, and does not advance at all. Switches between larger and smaller font sizes. HP 3 9gs Engl ish. book Pa ge 4 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Matrices 15-5 To display a matrix ⢠In the Matri x catalog ( MATRIX ) , highlight the matri x name and pres s . ⢠In HOME , ente r the name of the matr i x v ari able and pr ess . To display one element In HOME, enter matrixname ( row,column ). For example, if M2 is [[3,4],[5,6]] , then M2(1,2) returns 4 . To create a ma trix in HOME 1. Ente r the matr i x in the edit line . Start and end the matri x and each r ow w i th square br ack ets (the s hifted and k e y s) . 2 . Separate each element and each r o w w ith a comma. Ex ample: [[1,2],[3,4]] . 3 . Pr ess to enter and displa y the matr i x . The left screen below shows the matrix [[2.5,729],[16,2]] being stored into M5. The screen on the right shows the vector [66,3 3,11] being stored into M6. Note that you can enter an expression (like 5/2) for an element of the matrix, and it will be evaluated. Deletes the highlighted cells, row, or column (you are prompted to make a choice). CLEAR Clears all elements from the matrix. Moves to the first row, last row, first column, or last column respectively. K ey Meaning (Conti nued) HP 3 9gs Engl ish. book Pa ge 5 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
15-6 Matr ices To store one element In HOME, enter, value matrixname ( row, column ). For example, to change the element in the first row and second column of M5 to 728, then display the resulting matrix: 728 M 512 M5 . An attempt to store an element to a row or column beyond the size of the matrix results in an error message. Matrix arithmetic You can use the arithmetic functions ( , â, Ã , / and powers) with matrix arguments. Division left-multiplies by the inverse of the divisor. You can enter the matrices themselv es or enter t he names of sto red matrix va riables. The matrices can be real or complex. For the next examples, store [[1,2],[3,4]] into M1 and [[5,6],[7,8]] into M2. Example 1. Cr eate the fi rst matr ix . MATRIX 1 2 3 4 2 . Create the se cond matr i x . MATRIX 5 6 7 8 HP 3 9gs Engl ish. book Pa ge 6 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Matrices 15-7 3 . Add the matr ices that yo u cre a t e d. M1 M2 To multiply and divide by a scalar For division by a scalar, enter the matrix first, then the operator, then the scalar. For multiplication, the order of the operands does not matter. The matrix and the scalar can be real or complex. For example, to divide the result of the previous example by 2, press the following keys: 2 To multiply two matrices To multiply the two matrices M1 and M2 that you created for the previous example, press the following keys: M1 M 2 To multiply a matrix by a vector, enter the matrix first, then the vector. The number of elements in the vector must equal the nu mber of columns in the matrix. To raise a matrix to a power You can raise a ma trix to any power as long as the power is an integer. The following example shows the re sult of raising matrix M1, created earlier, to the power of 5. M1 5 Note: You can also raise a matrix to a power without first storing it as a variable. Matrices can be raised to ne gative powers . In this case, the result is equivalent to 1/[matrix]^ABS(power). In the following example, M1 is raised to the power of â2. HP 3 9gs Engl ish. book Pa ge 7 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
15-8 Matr ices M1 2 To divide by a square matrix For division of a matrix or a vector by a square matrix, the number of rows of the dividend (or th e number of elements, if it is a vector) must equal the number of rows in the divisor. This operation is not a mathematical di vision: it is a left- multiplication by the inverse of th e divisor. M1/M2 is equivalent to M2 â1 * M1. To divide the two matrices M1 and M2 that you created for the previous example, press the following keys: M1 M2 To invert a matrix You can invert a square matrix in HOME by typing the matrix (or its variable name) and pressing x â1 . Or you can use the matri x INVERSE command. Enter INVERSE ( ma trixn ame ) in HOME and press . To negate each element You can change the sign of each element in a matrix by pressing before the matrix name. Solving systems of linear equations Example Solve the following linear system: 1. Open the Matr i x catalog a nd cr ea te a ve cto r . MATRIX 2 x 3 y 4 z 5 xy z â 7 4 xy â2 z 1 = = = HP 3 9gs Engl ish. book Pa ge 8 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Matrices 15-9 2 . Cr eate the vec tor of the constants in the linear sys t em . 5 7 1 3 . R etur n to the Matri x Cat al og. MATRIX In this e x ample , the ve ctor y ou cr eated is listed a s M1. 4. Cr eate a ne w matr i x . Sele ct Real matrix 5 . Enter the equati on coeff ic ients . 23 4 11 1 4 12 In this e x ample , the matri x y ou c r eated is listed as M2 . 6 . R etur n to HOME and ent er the calc ulatio n to left-multipl y the constants v ector b y the inv erse o f the coeff ic ien ts matr i x. M2 x â1 M1 The result is a vector of the solutio ns x = 2, y = 3 and z = â2. An alternative method, is to use the RREF function. See âRREFâ on page 15-12. HP 3 9gs Engl ish. book Pa ge 9 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
15-10 Matri ces Matrix functions and commands About functions ⢠Fu n c t i o n s c a n b e u s e d i n a ny a p l e t o r i n H O M E. T h e y ar e listed in the MA TH menu unde r the Matr i x categor y . T h e y can be used in mathematical e xpr essi ons âpr imar ily in HOMEâa s w ell as in pr ogr ams. ⢠F unctions al wa ys pr oduce and displa y a r esult . The y do not c hange any st or ed var iables , such as a matri x va riab l e. ⢠F unctions ha ve ar guments that ar e enclo sed in pare ntheses and separ ated b y commas; f or e x ample , CROSS ( vect or 1 , ve cto r 2 ) . The matr i x input can be either a matr i x v ari able name (such a s M1 ) or the actual matr i x data inside br ack ets. F or ex ample, CROSS(M1,[1,2]) . About commands Matrix commands are listed in the CMDS menu ( CMDS ), in the matrix category. See âMatrix commandsâ on page 18-24 for details of the matrix commands available for use in programming. Functions differ from co mmands in that a function can be used in an expression. Commands cannot be used in an expression. Argument conventions ⢠Fo r row # or column# , supply the n umber of the r ow (counting fr om the top, s tarting with 1) or the number of the column (counting fr om the left , starting w ith 1) . ⢠T he ar gument matr ix can r efer to either a v ector or a matr i x . Matrix functions COLNORM Column Norm. Finds the maxi mum value (over all columns) of the sums of the absolute values of all elements in a column. COLNORM ( matr ix ) HP 3 9gs Engl ish. book Pa ge 10 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Matrices 15-11 COND Condition Number. Finds the 1-norm (column norm) of a square matrix . COND ( matr i x ) CROSS Cross Product of vector1 with vector2 . CROSS ( vec to r 1 , ve ct or 2 ) DET Determinant of a square matrix . DET ( matr i x ) DOT Dot Product of two arrays, matrix1 matrix2 . DOT ( matr i x1, matr i x2 ) EIGENVAL Displays the eigenvalue s in vector form for matrix . EIGENVAL ( matri x ) EIGENVV Eigenvectors and Eige nvalues for a square matri x . Displays a list of two arra ys. The first contains the eigenvectors and the second contains the ei genvalues. EIGENVV ( matri x ) IDENMAT Identity matrix. Creates a square matrix of dimension size à size whose diagonal elements a re 1 and off- diagonal elements are zero. IDENMAT ( siz e ) INVERSE Inverts a square matrix (real or complex). INVERSE ( matri x ) LQ LQ Factor ization. Factors an m à n matrix into three matrices: {[[ m à n lowertrapezoidal ]],[[ n à n orthogona l ]], [[ m à m permutation ]]}. LQ ( matr i x ) LSQ Least Squares. Displays the minimum norm least squares matrix (or vector ). LSQ ( matr i x1, matr i x2 ) HP 3 9gs Engl ish. book Pa ge 11 We dnes day, Dec embe r 7, 2005 11 : 24 PM
15-12 Matri ces LU LU Decomposition. Factors a square matr ix into three matrices: {[[ lowertriangular ]],[[ uppertriangular]],[[ permutation ]]} The uppertriangular has ones on its diagonal. LU ( matr ix ) MAKEMAT Mak e Matrix. Creates a matrix of dimension rows à columns , using expression to calculate each ele ment. If expression contains the variables I and J, then the calculation for each element substitutes the current row number for I and the current column number for J. MAKEMAT ( ex p res s i on , rows, columns) Example MAKEMAT(0,3,3) r eturns a 3Ã3 z ero matr i x , [[0,0,0],[0,0,0],[0,0,0]] . QR QR Factorization. Factors an m à n matri x into three matrices: {[[ m Ãm orthogonal ]],[[m Ãn uppertrapezoidal ]],[[ n à n permutation ]]}. QR ( matr ix ) RANK Rank of a rectangular matrix . RANK ( matr i x ) ROWNORM Row Norm. Finds the maximum value (over all rows) for the sums of the absolute values of all elements in a row. ROWNORM ( matr i x ) RREF Reduced-Row Echelon Form. Changes a rectangular matrix to its reduced row-echelon for m. RREF ( matr i x ) SCHUR Schur Decomposition. Factors a square matrix into two matrices. If matrix is real, then the resu lt is {[[ orthogonal ]],[[ up per-quasi triangular ]]}. If matrix is complex, then the result is {[[ unitary ]],[[ upper-triangular ]]}. SCHUR ( matr i x ) SIZE Dimensions of matrix . Returned as a list: {rows,columns}. SIZE ( matr i x ) HP 3 9gs Engl ish. book Pa ge 12 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Matrices 15-13 SPECNORM Spectral Norm of matrix . SPECNORM ( matri x ) SPECRAD Spectral Radi us of a squa re matrix . SPECRAD ( matri x ) SVD Singular Value Decomp osition. Factors an m à n matrix into two matrices and a vector: {[[ m à m square orthogonal ]],[[ n à n square orthogonal ]], [ real ]}. SVD ( matr i x ) SVL Si ngular Values. Returns a vector containing the singular values of matrix. SVL ( matr i x ) TRACE Finds the trace of a square matrix. The trace is equal to the sum of the diagonal elements. (It is also equal to the sum of the eigenvalues.) TRACE ( matr i x ) TRN Transposes matr ix . For a complex matrix, TRN finds the conjugate transpose. TRN ( matr i x ) Examples Identity Matrix You can create an identity matrix with the IDENMAT function. For example, IDENMAT(2) creates the 2Ã2 identity matrix [[1,0],[0, 1]]. You can also create an identity matrix using the MAKEMAT ( make matrix ) function. For example, entering MAKEMAT(I¼J,4,4) creates a 4 à 4 matrix showing the numeral 1 for all elements except zeros on the diagonal. The logical operator ¼ returns 0 wh en I (the row number) and J (the column number) are equal, and returns 1 when they ar e not equal . HP 3 9gs Engl ish. book Pa ge 13 We dnes day, Dec embe r 7, 2005 11 : 24 PM
15-14 Matri ces Trans posi ng a Matrix The TRN function swaps the row-column and column-row elements of a matrix. For instance, e lement 1,2 (row 1, column 2) is swapped with element 2,1; element 2,3 is swapped with element 3,2; and so on. For examp le, TRN([[1,2],[3,4]]) creates the matrix [[1,3],[2,4]] . Reduced-Row Echelon Form The following set of equations can be written as the augmented matrix which can then stored as a real matrix in any matrix variable. M1 is used in this example. You can use the RREF function to change this to reduced row echelon form, storing it in any matrix variable. M2 is used in this example. The reduced row echelon matrix gives the solution to the linear equation in the fourth column. An advantage of using the RREF function is that it will also work with inconsistent matrices resulting from syst ems of equations which have no solution or infinite solutions. For example, the following set of equations has an infinite number of solutions: x 2 y â3 z 1 4 2 xy z â 3 4 x â 2 y â2 z 1 4 = = = 12 â3 1 4 21 1 â3 â 42 â2 1 4 34 Ã xy z â 5 2 xy â7 x 2 y â z 2 = = = HP 3 9gs Engl ish. book Pa ge 14 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Matrices 15-15 The final row of zeros in the reduced-row echelon form of the augmented matrix indicates an inconsistent system with infinite solutio ns. HP 3 9gs Engl ish. book Pa ge 15 We dnes day, Dec embe r 7, 2005 11 : 24 PM
HP 3 9gs Engl ish. book Pa ge 16 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Lists 16-1 16 L ists You can do list operations in HOME and in programs. A list consists of comma-separated real or complex numbers, expressions, or matr ices, all enclosed in braces . A list may, for example, contain a sequence of real numbers such as {1,2,3} . (If the Decimal Mark mode is set to Comma , then the separators are periods.) Lists represent a convenient way to group related objects. There are ten list variables available, named L0 to L9. You can use them in calculations or expressions in HOME or in a program. Retrieve the li st names from the VARS menu, or just type their names fro m the keyboard. You can create, edit, delete , send, and re ceive named lists in the List catalog ( LIST ). You can also create and store listsânamed or unnnamedâin HOME lists List variables are identical in behavio ur to the columns C1.C0 in the Statistics aplet. You can store a statistics column to a list (or vice versa) a nd use any of the list functions on the statistics columns, or the statistics functions, on the list variables. Create a list in the List Catalog 1. Open the List catalog. LIST . 2 . Highligh t the list name y ou want to assig n to the ne w list (L1, etc .) and pres s to display the List editor . HP 3 9gs Engl ish. book Pa ge 1 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
16-2 Lists 3 . E nter the values you want i n th e l ist, pressi ng after each one. V alue s can be r eal or comple x numbers (o r an expr ession) . If you enter a calc ulation , it is e valuated and the r esult is inserted in the list . 4. When done , pr ess LIST to see the List catalog, or pr ess to re turn to HO ME . List catalog ke ys The list catalog keys are: Key M e a n i n g Opens the highlighted list for editing. Transmits the highlighted list to another hp 39gs or a PC. See âSending and receiving apletsâ on page 19-4 for further information. Receives a list from another hp 39gs or a PC. See âSending and receiving apletsâ on page 19-4 for further information. Clears the highlighted list. CLEAR Clears all lists. or Moves to the end or the beginning of the catalog. HP 3 9gs Engl ish. book Pa ge 2 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Lists 16-3 List edit keys When you press to create or change a list, the following keys are available to you: Create a list in HOME 1. Enter the list on the edit line . Start and end the list w ith br aces (the shifted and ke ys) and separ ate each element with a comma. 2 . Pr ess to ev a luate and display the list. Immediatel y after typing in the list , y ou can sto r e it in a var iable by pr essing lis tname . The list v ar iable name s ar e L0 thr ough L9 . This example stores the list {2 5,14 7 , 8} in L1. Note: Y ou can omit the final br ace when enter ing a list . Key M e a n i n g Copies the highlighted list ite m into the edit line. Inserts a new value before the highlighted item. Deletes the highlighted item from the list. CLEAR Clears all elements from the list. or Moves to the end or the beginning of the list. HP 3 9gs Engl ish. book Pa ge 3 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
16-4 Lists Displaying and editing lists To display a list ⢠In the List cata log, hi ghlight the list name and pr ess . ⢠In HOME , ente r the name of the list and pr ess . To display one element In HOME, enter listname ( element# ). For example, if L2 is {3,4,5,6}, then L2(2) returns 4 . To edit a list 1. Open th e L ist catalog. LIST . 2 . Pr ess or to highlight the name of the list y ou w ant to edit (L1, etc.) and press to display the list contents. 3 . Pres s or to hig hlight the el ement yo u want to edit . In this e x ample , edit the third e lement s o that it has a value of 5 . 5 4. Pr ess . HP 3 9gs Engl ish. book Pa ge 4 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Lists 16-5 To insert an element in a list 1. Open the List catalog. LIST . 2. P r e s s o r t o highli ght the name of the list y ou wan t to edit (L1, etc .) and pre ss to displa y the list conten ts. New elements are inserted abov e the highlighted positi on . In this example, an element, with the value of 9, is inserted between the first and second elements in the list. 3 . Pr ess to the insertion position, then pr ess , and press 9. 4. Pr ess . To stor e one element In HOME, enter value listname ( element ) . For example, to store 148 as the second element in L1, type 148 L1(2) . HP 3 9gs Engl ish. book Pa ge 5 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
16-6 Lists Deleting lists To delete a list In the List catalog, highli ght the list name and press . You are prompted to confirm that you want to delete the contents of the highlighted list variable. Press to delete the contents. To delete all lists In the List catalog, press CLEAR . Transmitting lists You can send lists to calculators or PCs just as you c an aplets, programs, matrices, and notes. 1. Align the HP 3 9gs calculator s â infr ared ports (or connect the calc ulators using an appr opr iate cable) . 2 . Open the L ist catalogs on both calc ulator s. 3 . Hi ghlight the list to send . 4. Pr ess and ch oose the method of sending (infr ar ed or cable) . 5 . Pr ess on th e r ecei v ing cal c ulator and c hoose the method of r ecei v ing (infr ar ed or cable) . F or more infor matio n on sending and r ecei v ing file s, see âSending and rece i ving a plets â on page 19- 4. List functions List functions are found in the MATH menu. You c an use them in HOME, as well as in programs. You can type in the name of the function, or you can copy the name of the function from the List category of the MA TH menu. Press (the alpha L character key). This highlights the List category in the left column. Press to move the cursor to the right column which contain the List functions, select a function, and press . List functions have the following syntax: ⢠F unctions ha ve ar guments that ar e enclo sed in pare ntheses and separated b y commas. Example: HP 3 9gs Engl ish. book Pa ge 6 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Lists 16-7 CONCAT(L1,L2) . An ar gument can be either a list v ari able name (su ch as L1) or the actual list . F or e xample , REVERSE({1 ,2,3}) . ⢠If Dec i mal Mark in Modes is set to C omma, u se peri ods to separat e ar guments. F or e x ample , CONCAT(L1.L2) . Common operators like , â, Ã, and / c an take lists as arguments. I f there are t wo ar guments and both are lists, then the lists must have the same length, since the calculation pairs the elements . If there are two arguments and one is a real number, then the calculation pairs the number with each element of the list. Example 5 * {1,2,3} re t u rn s {5,10,15} . Besides the common operator s that can take numbers, matrices, or lists as arguments, ther e are commands that can only operate on lists. CONCAT Concatenates two lists into a new list. CONCAT( list1 , list2 ) Example CONCAT({1,2,3},{4}) ret u rn s {1,2,3,4} . Î LIST Creates a new list composed of the first differences, that is, the differences between the se quential elements in list1. The new list has one fewer elements than list1 . The first differences for {x 1 x 2 ... x n } are {x 2 âx 1 ... x n âx nâ1 } . Î LIST( list1 ) HP 3 9gs Engl ish. book Pa ge 7 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
16-8 Lists Example In HOME, store {3,5,8,12,17 ,23} in L5 and find the first differences for the list. { 3,5, 8,12 ,1 7 ,2 3 } L 5 L Select Î LIST L5 MAKELIST Calculates a sequence of elements for a new lis t. Evaluates expression with variable from begin to end values, taken at increment steps. MAKELIST( expression , va riab l e , begin , end , incr ement ) The MAKELIST function generates a series by automatically producing a list from the repeated evaluation of an expression. Example In HOME, generate a series of squares from 23 to 27. L Sele ct MAKELIST A A 2 3 27 1 Î LIST Calculates the product of all elements in list. Î LIST( list ) Example Î LIST({2,3,4}) re t u rn s 24 . POS Returns the position of an element within a list. The element can be a value, a variable, or an expression. If there is more than one instance of the element, the HP 3 9gs Engl ish. book Pa ge 8 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Lists 16-9 position of the first occurrence is retu rned. A value of 0 is returned if there is no occurrence of the specified element. POS( list , element ) Example POS ({3, 7, 12, 19},12) returns 3 REVERSE Creates a list by reversing the order of the elements in a list. REVERSE( list ) SIZE Calculates the number of elements in a list. SIZE( list ) Also works with matrices. Σ LIST Calculates the sum of all elements in list. Σ LIST( list ) Example Σ LIST({2,3,4}) ret u rn s 9 . SORT Sort s elements in a scending order. SORT( list ) Finding statistical values for list elements T o f i n d v a l u e s s u c h a s t h e mean, median, maximum, an d minimum values of the elements in a list, use the Statistics aplet. Example In this example, use the Statistics aplet to find the mean, median, maximum, and minimum values of the elements in the list, L1. 1. Cr eate L1 w ith values 8 8, 9 0, 8 9 , 6 5, 7 0, and 8 9 . { 8 8 90 89 65 7 0 89 } L1 HP 3 9gs Engl ish. book Pa ge 9 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
16-10 Lists 2 . In HOME , st or e L1 into C1. Y ou w ill then be able to see the list data in the Numer ic vi e w of the Statis tics aplet . L1 C1 3 . S tart the Statis tic s aplet , and select 1-v ar ia ble mode (pr ess , i f necess ary , to displa y ) . Sele ct Statistics Note: Y our list values ar e no w in column 1 (C1) . 4. In the S ymboli c v ie w , def ine H1 (fo r ex ample) as C1 (sample ) and 1 (fr equency). 5 . Go to the Numer ic v ie w to displa y calc ulated statisti cs . See âOne -v ar iable â on page 10 -14 for the mea ning of each com puted statis tic . HP 3 9gs Engl ish. book Pa ge 10 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Notes and sketches 17-1 17 Notes and sk etc hes Introduction The HP 39gs has text and pi cture editors for entering notes and sketche s. ⢠E ach a plet has its o wn independent Note v iew and Sk etch vi e w . Not es and sk etc hes that y ou cr eate in these vi e ws ar e assoc iated w ith t he aplet. When y ou sa v e the aplet , or send it to another calc ulator , the notes and sketc hes are sa ved or sent as well . ⢠Th e Notepad is a collection o f notes independent of all aplets. T hese notes can also be sent to another calc ulato r v ia the No tepad C atalog . Aplet note view You can attach text to an aplet in its Note view. To write a note in Note view 1. In an aplet , pr ess NOTE f or the Note v ie w . 2 . Use the not e editing k e y s sho wn in the ta ble in the fo llo w i ng sec tion . 3 . Set A lpha lock ( ) for quic k entry of letters. F or lo wer case Alpha lock , pr ess . 4. While Alpha loc k is on: â T o type a single letter of the opposit e case , pre ss letter . â T o type a single n on-alpha ch ar acte r (suc h as 5 or [ ) , pr es s f i r st . (This turns off A lpha lo ck fo r o ne cha ract er .) Y our w or k is automati call y sav e d . Pr ess an y vi e w ke y ( , , , ) or to e xi t the Notes v ie w . HP 3 9gs Engl ish. book Pa ge 1 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
17-2 Notes and sketches Note edit keys Key M e a n i n g Space key for text entry. Displays next page of a multi-pa ge note. Alpha-lock for letter entry. Lower-case alpha-loc k for letter entry. Backspaces cursor and deletes character. Deletes current character. Starts a new line. CLEAR Erases the entire note. Menu for entering variable names, and contents of variab les. Menu for entering math operations, and constants. CMDS Menu for entering program commands. CHARS Displays special characters. To type one, highlight it and press . To copy a chara cter without closing the CHARS screen, press . HP 3 9gs Engl ish. book Pa ge 2 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Notes and sketches 17-3 Aplet sketch view You can attach pictures to an aplet in its Sketch view ( SKETCH ). Y our wor k is aut omaticall y sa v ed w ith the aplet . Press an y other vi e w ke y or to e x it the Sk etch v ie w Sketch keys To dr aw a li ne 1. In an aplet , pr ess SKETCH f or the Sketc h v ie w . 2 . In Sk etch v iew , pr ess and mo ve the c ursor to w her e y ou w ant to start the line 3 . Pr ess . This turns on line- dr aw ing . 4. Mo v e the c urso r in any dir ectio n to the end poin t of the line b y pr essing the , , , k ey s. 5 . Pr ess to finish th e line . Key M e a n i n g Stores the specified portion of the current sketch to a graphics variable (G1 through G0). Adds a new, blank page to the current sketch set. Displays next sketch in the sketch set. Animates if held down. Opens the edit line to type a text label. Displays the menu-key labels for drawing. Deletes the current sketch. CLEAR Erases the entire sketch set. Toggles menu key labels on and off. If menu key labels are hidden, or any menu key, redisplays the menu key labels. H P 3 9 gs E n gl i s h . bo o k P a ge 3 W ed n es d a y , D ec e m b e r 7, 2 005 11: 24 P M
17-4 Notes and sketches To draw a box 1. In Sk etch v ie w , pres s and mov e the c ursor t o wher e you w ant any corner of the bo x to be. 2. P r e s s . 3 . Mo v e the cur sor to mar k the opposite cor ner for the bo x . Y ou can adj ust the si ze of the bo x by mo v ing the cu rs o r . 4. Pr ess to f inish the bo x . To draw a circle 1. In Sket ch v ie w , press and mo v e the c ursor t o wher e you want the center of the c i r cle to be . 2 . Pres s . This tur ns on c irc le dr aw ing. 3 . Mo v e the curs or the distance of the radius . 4. Pr ess to dr aw the c irc le . DRAW keys Key M e a n i n g Dot on. Turns pixels o n as the cursor moves. Dot off. Turns pixels o ff as the cursor moves. Draws a line from the cursorâs starting position to the cursorâs current position. Press when you have finished. You can draw a line at any angle. Draws a box from the cursorâs starting position to the cursorâs current position. Press when you have finished. Draws a circle with the cursorâs starting position as the center. The radius is the distance between the cursorâs starting and ending position. Press to draw the circle. HP 3 9gs Engl ish. book Pa ge 4 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Notes and sketches 17-5 To label parts of a sketch 1. Pr ess and type the te xt on the edit line . T o lock the Alpha shift on , pre ss (for upper case) or (for lo w er cas e) . T o mak e the label a smalle r c har acte r si z e , turn o ff befo r e pres sing . ( is a toggle betw een small and lar ge f ont si z e) . The smaller c har acter si z e cannot displa y lo w er case letters . 2. P r e s s . 3 . P osition the label w here y ou want it b y pr essing the , , , ke ys . 4. Pr ess again to affi x the label. 5. P re s s to c o n t i n u e dr aw ing, or pre ss to e xit the Sk etch v ie w . To crea te a set of sketches You can create a set of up to ten sketches. This allows for simple animatio n. ⢠After making a sk etc h , pre ss to add a ne w , blank page. Y ou can no w mak e a new sk etch , whic h becomes part of the c urr ent se t of sk etches . ⢠T o v ie w the next sk etch in an e x isting set , pr ess . Hold do wn f or ani mati on . ⢠T o r emov e t he c urr ent pag e in the c urr ent sk etch ser ies , pre ss . To store into a graphics variable You can define a portion of a s ketch inside a box, and then store that graphic into a graphics variable. 1. In the Sk etch v ie w , display the sk etc h y ou want t o copy (stor e i nto a v ariable). 2. P r e s s . 3 . Highligh t the var iable name yo u w ant to us e and pr ess . 4. Dr aw a bo x ar ound the por ti on y ou w ant to cop y : mo ve the c ursor to one cor ner , press , then mov e the curs or to the opp osite corner , a nd pre ss . HP 3 9gs Engl ish. book Pa ge 5 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
17-6 Notes and sketches To import a graphics variable You can copy the contents of a graphics variable into the Sketch view of an aplet. 1. Open the Sketch v iew of the aplet ( SKETCH ). T he graphi c w ill be copied her e. 2 . Pr ess , . 3 . Highlight Graphic , then pr ess and highligh t the name of the v ari able ( G1 , etc .) . 4. Pr es s to r ecall the co ntents of the gr aphics va riab l e. 5 . Mov e t he box to w here y o u w ould like to copy the gr aphi c, the n pr es s . The notepad Subject to available memory , you can store as many notes as you want in the Notepad ( NOTEPAD ). These notes are independent of any aplet. The Notepad catalog lists the existing entries by name. It does not include notes that were created in apletsâ Note view s , but these can be imported. See âTo import a noteâ on page 17-8 . To create a note in the Notepad 1. Displa y the Notepad catalog. NOTEPAD 2 . Cr eate a new not e . 3 . Ente r a name fo r y our note. MYNO TE HP 3 9gs Engl ish. book Pa ge 6 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Notes and sketches 17-7 4. W r ite y our note . See âNote e dit ke ys â on page 17 - 2 for mor e infor mation on the entry and editing of notes. 5 . When yo u are f inis hed , press or an aplet ke y to e x it Notepad . Y our wor k is automaticall y sav ed. Notepad Catalog keys Key M e a n i n g Opens the selected note for editing. Begins a new note, and asks for a name. Transmits the selected note to another HP 39 gs or PC. Receives a note being transmitted from another HP 39gs or PC. Deletes the selected note . CLEAR Deletes all notes in the catalog. HP 3 9gs Engl ish. book Pa ge 7 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
17-8 Notes and sketches To import a note You can import a no te from the Notepad into an apletâs Note view, and vice versa. Supp ose you want to copy a note named âAssignmentsâ fr om the Notepad into the Function Note view: 1. In the F unction aplet , display the Not e v ie w ( NOTE ). 2 . Pr ess , highlight Notepad in the left column, then hi ghlight the name â Assi gnments â in the r ight co lumn . 3 . Pr ess to copy the cont ents of â Assignments â to the F unction Not e v ie w . Note: T o r ecall the name in st ead of the contents , pr ess inst ead of . Suppose you want to copy the Note view from the current aplet into the note, Assignments, in the Notepad. 1. In the Notepad ( NOTEPAD ), open the note , â Assignments â . 2 . Pr ess , hig hlight Note in the left column , then pr ess and highligh t NoteText in the ri ght column. 3 . Pres s to r ecall the conte nts of the Not e v ie w into the note â Assignments â . HP 3 9gs Engl ish. book Pa ge 8 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Programming 18-1 18 Pr ogr amming Introduction This chapter describes how to pro gram using the hp 39gs. In this chapter youâll learn about: ⢠using the Pr ogram catalog to c r eate and edit pr ogr ams ⢠pr ogr amming commands ⢠stor ing and retr ie v ing var iables in pr ograms ⢠pr ogr amming var iables. HINT More information on programming, including examples and special tools, ca n be found at HPâs calculators web site: http://www.hp.com /calculators The Contents of a Program An HP 39gs program contains a sequence of numbers, mathematical expressions, and commands that execute automatically to perform a task. These items are separated by a colon ( : ). Commands that take multiple arguments have those arguments separated by a semicolon ( ; ). For example, PIXON xposition ; yposition: Structured Programming Inside a program you can use branching structures to control the execution flow. You can take advantage of structured programming by creating building-bloc k programs. Each building -block program stands aloneâand it can be c alled from other programs. Note: If a program has a space in it s name then you have to put quotes around it when you want to run it . HP 3 9gs Engl ish. book Pa ge 1 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
18-2 Programming Example RUN GETVALUE: RUN CALCULATE: RUN " SHOW ANSWER" : This program is separated into three main tasks, each an individual program. Within each progr am, the task can be simpleâor it can be di vided further into other programs that perform smaller tasks. Program catalog The Program catalog is wher e you create, edit, delete, send, receive, or run progra ms. This section describes how to ⢠open the Pr ogr am catalog ⢠cr eate a ne w pr ogr am ⢠enter commands f r om the pr o gr am commands menu ⢠enter f uncti ons fr om the MA TH men u ⢠edit a pr ogram ⢠run and debug a pr ogram ⢠stop a pr ogram ⢠copy a pr ogram ⢠send and r ecei ve a pr ogram ⢠delete a pr ogr am or its contents ⢠c ustomi z e an aplet . Open Program Catalog 1. Pr ess PROGR M . T he Pr ogram C atalog displa y s a list of pr ogram names . The Pr ogr am Catalog contains a built-in entr y called Editline . Editline cont ains the last e xpr essio n that yo u enter ed fr om the edit line in HOME , or the last data y ou ent er ed in an inpu t fo rm . (If you pr ess fr om HOME w ithout enter ing any dat a , the HP 3 9gs runs the cont ents of Editline .) Bef or e starting to w ork w ith progr ams, y ou should tak e a fe w minutes to become f a miliar w ith the Pr ogr am catalog menu k e y s. Y ou can use an y of the follo wing k ey s (both menu and k ey board), to per for m tasks in the Pr ogram catalog . HP 3 9gs Engl ish. book Pa ge 2 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Programming 18-3 Program catalog k eys The program catalog keys are: Key M e a n i n g Opens the highlighted program for editing. Prompts for a new program name, then opens an empty program. Transmits the highlighted program to another HP 39gs or to a disk drive. Receives the highlighted program from another HP 39gs or from a disk drive. Runs the highlighted program. or Moves to the beginning or end of the Program catalog. Deletes the highlighted program. CLEAR Deletes all programs in the program catalog. HP 3 9gs Engl ish. book Pa ge 3 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
18-4 Programming Creating and editing programs Create a new program 1. Pr ess PROGR M to open the Pr ogr am catalog . 2. P r e s s . The HP 3 9gs pr ompts yo u fo r a n a m e. A pr ogr am name can contain spec ial char acters , such as a space . Ho we ve r , if y ou use spec ial char acters and then run the pr ogr am b y typing it in HOME , y ou must enc lose the pr ogr am name in double quotes ( " " ) . Don't use the " s ymbol w ithin y our pr ogr am name. 3 . T ype y our progr am name , then pr ess . When y ou pr ess , the Pr ogr am E ditor opens. 4. Enter y our pr ogr am. W hen done , star t an y other acti vity . Y our wor k is sa ve d auto maticall y . Enter commands Un til you become familiar with the HP 39gs commands, the easiest way to enter comma nds is to select them from the Commands menu from the Program editor. You can also type in commands using alpha c haracters. 1. F r om the Pr ogra m edito r , pr es s CMDS to open the Pr ogr am Commands men u . CMDS HP 3 9gs Engl ish. book Pa ge 4 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Programming 18-5 2 . On the left, u se or to highligh t a command category , then pr ess to ac cess the commands in the category . Select the command that y ou w ant . 3 . Pr ess to paste the command into the pr ogram editor . Edit a program 1. Pres s PR OGRM to open the Pr ogram catalog. 2 . Use the arr o w k e y s to hi ghlight the pr ogram y ou wa nt to edit, and pr ess . T he HP 39gs opens the Pr ogr am E ditor . The name of y our progr am appears in the title bar of the displa y . Y ou can us e the fo llo w i ng k ey s to edit yo ur pr ogr am . HP 3 9gs Engl ish. book Pa ge 5 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
18-6 Programming Editing keys The editing keys are: Key M e a n i n g Inserts the character at the editing point. Inserts space into text. Display s previous page of the program. Displays next page of the program. Moves up or down one line. Moves right or left one character. Alpha-lock for letter entry. Press A...Z to lock lower case. Backspaces cursor and deletes character. Deletes current character. Starts a new line. CLEAR Erases the entire program. Displays menus for selecting variable names, contents of variables, math functions, and program constants. CMDS Displays menus for selecting program conmmands. CHARS Displays all char acters. To type one, highlight it and press . To enter several characters in a row, use the menu key while in the CHARS menu. HP 3 9gs Engl ish. book Pa ge 6 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Programming 18-7 Using programs Run a program From HOME, type RUN program_name. or From the Program catalog, highlight the program you want to run and press Regardless of where you star t the program, all programs run in HOME. What you see will differ slightly depending on where you started the program. If you start the program from HOME, the HP 39gs displays the contents of Ans (Home variable containing the last result), when the program has finished. If you start the program from the Program catalog, the hp39gs returns you to the Program catalog when the program ends. Debug a program If you run a program that contains errors, the program will stop and you will see an error message. To debug the program: 1. Pr ess to edit the pr ogr am. T he insert c ursor a ppears in the pr ogra m at the poin t w her e the err or occ urr ed. 2 . Edit the pr ogram t o fi x the err or . 3 . R u n the pr ogram . 4. R epeat the pr ocess un til y ou corr ect all er r ors . Stop a program You c an stop the running of a program at any time by pressing CANCEL (the key). Note: You may have to press it a couple of times. HP 3 9gs Engl ish. book Pa ge 7 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
18-8 Programming Copy a program You can use the following procedure if you want to make a copy of y our work before editingâor if you want to use one program as a template for another. 1. Pr ess PROGR M to open the Pr ogr am catalog . 2. P r e s s . 3 . T ype a ne w f ile name, then c hoose . T he Progr am Edito r opens with a ne w pr ogr am . 4. Pr ess to open the var iables menu . 5 . Pr ess to quickly sc r oll to Pr ogram . 6 . Pr ess , then highlight the pr ogr am y ou w ant to copy . 7 . Pres s , then pr ess . T he conte nts of the hi ghligh ted pr ogr am ar e copi ed into the c u r r ent pr ogram at the c urs or location . HINT If you use a programming routine often, save the routine under a different program name, then use the above method to copy it into your programs. Transmit a program You can send programs to, and rec eive programs from, other calculators just as you can send and receive aplets, matrices, lists, and notes. After aligning the calculatorsâ infrared port s, open the Program catalogs on both calculators. Highlight the program to send, then press on the sending calculator and on the receiving calculator. You can also send programs to, and receive programs from, a remote storage devi ce (aplet di sk drive or computer). This takes pla ce via a cable connection and requires an aplet disk driv e or specialized software running on a PC (such as a connectivi ty kit). HP 3 9gs Engl ish. book Pa ge 8 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Programming 18-9 Delete a program To delete a program: 1. Pr ess PROGRM to open the Progr am catalog. 2 . Highligh t a pr ogr am to delet e , then pr ess . Delete all programs You can delete all programs at once. 1. In the Pr ogr am catalog , pres s CLEAR . 2. P r e s s . Delete the contents of a program You can clear t he contents of a program withou t deleting the program name. 1. Pr ess PROGRM to open the Progr am catalog. 2 . Hi ghligh t a pr ogr am, then pr ess . 3. P re s s CLEAR , then pr ess . 4. T he conten ts of the pr ogr am ar e deleted , but the pr ogr am name r emai ns . Customizing an aplet You can customize a n aplet and develop a set of programs to work with the aplet. Use the SETVIEWS command to create a custom VI EWS menu which links specially wr itten programs to the new aplet. A useful method for customizing an aplet is illu strated below: 1. Dec ide on the built-in aplet that y ou want to c ustomi ze . Fo r ex a mple y ou coul d c ustomi ze the F unction aplet or the S tatistic s aplet . T he c us tomi z ed aplet inher its all the prope rties of the built-in aplet . Sa v e the cu stomi z ed aplet w ith a unique name . 2 . C ust omi z e the new a plet if y ou need to , for e x ample b y pr esetting ax es or angle mea sur es . 3 . De v elop the pr ogr ams to w or k w ith y our c us tomi z ed aplet . When yo u dev elop the apletâs pr ograms , use the standar d aplet naming conv ention . This allo ws y ou to k eep trac k of the pr ograms in the Pr ogr am catalog th at belong to ea c h aplet. See â Aplet naming con ven tion â on page 18-10. HP 3 9gs Engl ish. book Pa ge 9 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
18-10 Programming 4. Dev elop a progr am that uses the SE T VIEW S command to modify the apletâs VIEW S menu . The menu opti ons pr o v ide links to ass oc iated pr ograms . Y ou can spec i fy an y other progr ams that you w ant tr ansfe rr ed with the aplet . See âSETVIEW Sâ on page 18-14 for inf ormati on on the command . 5 . Ensur e that the cu stomi z ed aplet is selec ted , then run the menu conf igur atio n pr ogr am to conf igur e the apletâs VIEW S menu . 6 . T es t the cu st omi z ed aplet and debug the ass oc iat ed pr ogr ams. (R efer to âDebug a pr ogr am â on page 16 - 7) . Aplet naming convention To assist users in kee ping tr ack of a plets and associated programs, use the following naming co nvention when setting up an apletâs programs: ⢠St art all pr ogram name s w ith an abbr e v iati on of the aplet name . W e will u se AP L in this ex ample. ⢠Name pr o gr ams called b y menu entr ies in the VIEW S menu number , after the entry , fo r ex ample: â APL .ME1 f or the pr o gr am called by menu opti on 1 â APL .ME2 f or the pr o gr am called by menu opti on 2 ⢠Name the pr ogram that conf igur es the new VIE W S menu option APL .S V where S V stands for SETVIEWS . For example, a customized aplet called âDifferentiationâ might call programs called DIFF.ME1, DIFF.ME2, and DIFF. SV. Example This example aplet is designed to demonstr ate the process of customizing an aplet. The new aplet is based on the Function aplet. Note: This aplet is not intended to serve a serious use, merely to illu strate the process. HP 3 9gs Engl ish. book Pa ge 10 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Programming 18-11 Save the aplet 1. Open the F uncti on aplet and sa ve it as âEXP ERIMENT â . The ne w aplet appear s in the Aplet library . Select Function EXP ERIMENT 2 . Cr eate a pr ogr am called EXP .ME1 with contents as show n. T his pr ogr am conf igur es the plot r anges, then r uns a pr ogr am that allo ws y ou to s et the angle f ormat . 3 . Cr eate a pr ogr am called EXP .ME2 with contents as show n. T his pr ogr am sets the numer ic v iew opti ons fo r the aplet , and r uns the pr ogr am that y ou can us e to conf igur e the angle mode . 4. Cr eate a progr am called EXP .ANG wh ic h the pr e v io us tw o pr ogr ams call . 5 . Cr eate a pr ogr am called EXP .S w hich r uns w hen you start th e aplet , as show n. T his pr ogr am sets the angle mode to degrees , and sets u p the initial f uncti on that the aplet plots . Configuring the Setviews menu option programs In this secti on w e will begin b y confi gur ing the VIEW S menu b y using the SETVI EW S command. W e w ill then c r eate the âhelper â pr ogr ams called b y the VIEW S menu whi ch w ill do the actual w ork . HP 3 9gs Engl ish. book Pa ge 11 We dnes day, Dec embe r 7, 2005 11 : 24 PM
18-12 Programming 6 . Open the Pr ogram cat alog and cr eate a progr am named âEXP .S Vâ . Include the f ollo w ing code in the pr ogr am. E a c h entry line after the command SE T VIEW S is a tri o that consists of a VIEW S menu te xt li ne (a space indicate s none), a progr am name , and a number that def ines the v ie w to go to afte r the pr ogr am has r un its course . All pr ogr ams listed her e will tr ansfer w ith an aplet w hen the a plet is tr ansfer r ed . SETVIEWS â â â â ; â â â â ; 18; Sets the f i r st menu opti on to be â Auto scale â . This is the fo urth standar d F uncti on aplet v ie w menu opti on and the 18 â Auto scale â , spec ifi es that it is to be inc luded in the ne w menu . The empty quotes w ill ensur e that the old name of â A uto scale â appears on the ne w menu . See âSETVIEWSâ o n page 18-14. â â My Entry1â â ;â â EXP.ME1â â ;1; Sets the seco nd menu option . This optio n runs pr ogram EXP .ME1, then r eturns to view 1 , Pl ot vi ew . â â My Entry2â â ;â â EXP.ME2â â ;3; Sets the third men u option . This option runs the pr ogra m EXP .ME2 , then r eturns to v ie w 3, the NUM v ie w . â â â â ;â â EXP.SVâ â ;0; This line spec ifi es that the pr ogram to s et the V ie w menu (this pr ogr am) is tr ansfe rr ed with the a plet . T he space char acter between the f irst set of quotes i n the tr io sp ec if ie s that no men u option appears f or the entry . Y ou do not ne ed to tr ansfe r this progr am w ith the aplet , but it allo ws user s to modif y the apletâs men u if the y wan t to . HP 3 9gs Engl ish. book Pa ge 12 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Programming 18-13 â â â â ;â â EXP.ANGâ â ;0 ; The pr o gr am EXP .ANG is a small routine that is called by other pr ogr ams that the aplet us es . This e ntry spec ifi es that the pr ogr am EXP.ANG is transfer r ed w hen the aplet is tr ansfer r ed, bu t the space in the fir st quotes en sur es that no entry appears on the menu . â â Startâ â ;â â EXP.Sâ â ;7: T his spec ifi es the S tart menu option . The pr ogr am that is ass oc iated w ith this entry , EXP.S, runs a utomati call y when y ou start the aple t . Beca use this menu opti on spec ifi es v ie w 7 , the VIEW S menu opens when y ou star t the apl et . Y ou onl y need to run this pr ogr am once to conf igur e y our apletâs V IEW S menu . Onc e the apletâ s VIEW S menu is conf igured , it remains that w a y until y ou run SETVIEW S again. Y ou do not need to inc lude this pr ogr a m f or y our aplet to w ork , but it is use ful to spec ify that the pr ogr am is atta c hed to the aplet , and transmitted w hen the aplet is transmitted . 7 . Re turn to the pr ogram catalog. T he progr ams that y ou c r eated sh ould appear as f ollow s: 8. Y ou must now th e pr ogr am EXP . S V to ex ecute t he SETVIEW S command and cr eate th e modified VIEW S menu . Check that the name of the ne w aplet is hig hlighted in the A plet vi ew . 9 . Y ou can no w r etur n to the Aplet libr ary and pre ss to run y our new a plet . Programming commands This section describes th e commands for programming with hp 39GS. You can enter these commands in your program by typing them or by accessing them from the Commands menu. HP 3 9gs Engl ish. book Pa ge 13 We dnes day, Dec embe r 7, 2005 11 : 24 PM
18-14 Programming Aplet commands CHECK Checks (selects) the correspon ding function in the current aplet. For example, Check 3 would check F3 if the current aplet is Function. T hen a checkmark would appear next to F3 in Symbolic view, F3 would be plotted in Plot view, and evaluated in Numeric view. CHECK n : SELECT Selects the named aplet and ma kes it the current aplet. Note: Quotes are needed if th e name contains spaces or other special characters. SELECT apletname : SETVIEWS The SETVIEWS command is used to define entries in the VIEWS menu for aplets that you customize. See âCustomizing an ap letâ on page 18-9 for an example of using the SETVIEWS command. When you use the SETVIEWS command, the apletâs standard VIEWS menu is deleted and the customized menu is used in its place. You only need to apply the command to an aplet once. The VIEWS menu changes remain unless you apply the command again. Typically, you develop a program that uses the SETVIEWS command only. The command contains a trio of arguments for each menu option to create, or program to attach. Keep the following points in mind when using this command: ⢠The SE T VIEW S command deletes an apletâs standar d V ie w s menu opti ons . If y ou wan t to us e an y of the standar d opti ons on y our r econf igur ed VI EW S menu , y ou must inc lude th em in the confi guratio n. ⢠When y ou in v ok e the SETVIEW S command, the changes to an apletâs VIEW S menu remain w ith the aplet . Y ou need to in vok e the comman d on the a plet again to change the VIEW S menu . ⢠All the pr ograms that ar e called fr om the VI EW S menu ar e tr ansfe rr ed when the a plet is tr ansferr ed, f or ex amp le to anot her cal c ulator or to a PC. ⢠As part of the VIEW S menu conf igur ation , y ou can spec i fy pr ogr ams that you w ant tr ansfer r ed w ith the aplet , but ar e not called as menu optio ns. F or e xam ple , these can be su b-pr ogr ams that menu HP 3 9gs Engl ish. book Pa ge 14 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Programming 18-15 options u se , or the pr ogr am that def ines the a pletâs VIEW S menu . ⢠Y ou can inclu de a âStart â optio n in the VIEW S men u to spec if y a pr ogr am that y ou w ant to run auto maticall y when the aplet s tarts. This pr ogram typically sets up the apletâ s initial confi guration . T he S T AR T option on the men u is also usef ul for r esetting the aplet . Command syntax The syntax for the command is as follows: SETVIEWS " Pr ompt1 " ;" Pr ogr amName1 " ; ViewN um be r1 ; " Pr ompt2 " ;" Pr ogr amName2 " ; ViewN um be r2 : (Y ou can repeat as man y Prompt/ProgramName/ ViewNumber tri os of ar guments as y ou lik e .) Within each Prompt/ProgramName/ViewNumber trio, you separate each item with a semi-colon. Prompt Prompt is the text that is displayed for the corresponding entry in the Views menu. Enclose the prompt text in double quotes. Associating programs with your aplet If Prompt consists of a single space, then no entry appears in the view menu. The program specified in the ProgramName item is associated with the aplet and transferred whenever the aplet is transmitted. Typically, you do this if you want to transfer the Setviews program with the aplet, or you want to transfer a sub-program that other menu programs use. Auto-run programs If the Prompt item is âStartâ, then the ProgramName program runs whenever y ou start the aplet. This is useful for setting up a program to co nfigure the aplet. Users can select the Start item from the VIEWS menu to reset the aplet if they change conf igurations. You can also define a menu item called âResetâ which is auto-run if the user choo ses the button in the APLET view. HP 3 9gs Engl ish. book Pa ge 15 We dnes day, Dec embe r 7, 2005 11 : 24 PM
18-16 Programming ProgramName ProgramName is the name of the program that runs when the corresponding menu entry is selected. All pr ograms that are identified in the apletâs SETV IEWS command are transferred when the aplet is transmitted. ViewNumber V iewNumber is the number of a view to start after the program finishes runn ing. For example, if you want the menu option to display the Pl ot view when the associated program finishes, you would spec ify 1 as the ViewNumber value. Including standard menu options To include one of an apletâs standard VIEWS menu options in your customized menu, set up the arguments trio as follows: ⢠T he firs t ar gument spec ifi es the menu item name: â Leav e the argument empt y to use the stand ar d V ie w s menu name fo r the item, or â Enter a menu item name to r eplace the standar d name . ⢠The second argument spec ifi es the pr ogr am to run: â Lea v e the ar gument em pty to r un the standar d menu option . â Insert a progr am name to run the pr ogram be for e the standar d menu optio n is e xec uted. ⢠T he thir d ar gument s pec if ies the v ie w and the menu number f or the item . Deter mine the menu number fr om the Vi ew n umbers ta ble belo w . Note: SE TVIEW S w ith no ar guments r esets the v ie w s to def ault of the base aplet . HP 3 9gs Engl ish. book Pa ge 16 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Programming 18-17 View numbers The Function aplet views are numbered as follows: View numbers from 15 on will vary according to the parent aplet. The list shown above is for the Function aplet. Whatever the normal VIEWS menu for the parent aplet, the first entry will become number 1 5, the second number 16 and so on. UNCHECK Unchecks (unselects) the corresponding functio n in the current aplet. For example, Uncheck 3 would unc heck F3 if the current aplet is Function. UNCHECK n : Branch commands Branch commands let a program make a deci sion based on the result of one or more tests. Unlike the ot her programming commands, the branch commands work in logical groups. Therefore, the commands are described together rather than each independently. IF...THEN...END Executes a sequence of commands in the true-clause only if the test-clause evaluate s to true. Its syntax is: IF test-clause THEN true-clause END 0 1 2 3 4 5 6 7 8 9 10 HOME Plot Symbolic Numeric Plot-Setup Symbolic-Setup Numeric-Setup Views Note Sketch view Aplet Catalog 11 12 13 14 15 16 17 18 19 20 21 List Catalog Matrix Catalog Notepad Catalog Program Catalog Plot-Detail Plot-Table Overlay Plot Auto scale Decimal Integer Trig HP 3 9gs Engl ish. book Pa ge 17 We dnes day, Dec embe r 7, 2005 11 : 24 PM
18-18 Programming Example 1 î A : IF A==1 THEN MSGBOX " A EQUALS 1" : END: IF... THEN... ELSE... END Executes the true-clause sequence of commands if the test- clause is true, or the false-clause se quence of commands if the test-clause is false. IF test-clause THEN true-clause ELSE fals e-clause END Example 1 î A : IF A==1 THEN MSGBOX "A EQUALS 1" : ELSE MSGBOX "A IS NOT EQUAL TO 1" : END: CASE...END Executes a series of test-clause commands that execute the appropriate true-c lause sequence of c ommands. Its syntax is: CASE IF test-clause 1 THEN true -c laus e 1 END IF test-clause 2 THEN true -c laus e 2 END . . . IF test-clause n THEN tr ue -clau se n END END: When CASE is execute d, test-clause 1 is evaluated. If the test is true, true-clause 1 is executed, and execution skips to END. If test-clause 1 if false, execution proceeds to test- clause 2 . Execution with the CASE structur e continues until a true-clause is executed (o r until all the tes t-clauses evaluate to false). IFERR... THEN... ELSE⦠END... Many conditions are automati cally recognized by the HP 39gs as error conditions and are automatically treated as errors in programs. HP 3 9gs Engl ish. book Pa ge 18 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Programming 18-19 IFERR...THEN...ELSEâ¦END allows a program to intercept error conditions that otherwise would cause the program to abort. Its syntax is: IFERR tr ap-cla us e THEN clause _1 ELSE clause _2 END : Example IFERR 60/X î Y: THEN MSGBOX "Error: X is zero.": ELSE MSGBOX "Value is "Y: END: RUN Runs the named program. If your program name c ontains special characters, such as a space, then you must enclose the fi le name in double quotes (" "). RUN " pr ogram name " : or RUN pr ogr amname : STOP Stops the current pr ogram. STOP : Drawing commands The drawing commands act on the display. The scale of the display depends on the current aplet's Xmin, Xmax, Ymin, and Ymax values. The following examples assume the hp 39gs default settings with t he Function aplet as the current aplet. ARC Draws a circular arc, of give n radius, whose centre is at (x,y) The arc is drawn from start_angle_measurement , to end_angle_measurement . ARC x;y; radius ; start_angle_measurement ; end_angle_measurement : HP 3 9gs Engl ish. book Pa ge 19 We dnes day, Dec embe r 7, 2005 11 : 24 PM
18-20 Programming Example ARC 0;0;2;0;2 Ï : FREEZE: Dr a w s a c irc le center ed at (0, 0) of r adius 2 . T he FREEZE command causes the c ir cle to r emain di spla ye d on t he sc reen until y ou pr ess a k ey . BOX Draws a box with diagonally opposite corners ( x1,y1 ) and ( x2,y2 ). BOX x1 ; y1; x2; y2: Example BOX -1;-1;1;1: FREEZE: Dr a w s a bo x , lo w er corner at (â1,â1) , upper corner at (1,1) ERASE Clears the display ERASE: FREEZE Halts the program, freezing the cu rrent display. Execution resumes when any key is pressed. LINE Dr aws a line from (x1, y1) to ( x2, y2 ) . LINE x1; y1; x2 ; y2: PIXOFF Turns off the pixel at the specified coordinates (x,y) . PIXOFF x;y : PIXON Turns on the pixel at the specified coordinates (x,y) . PIXON x;y : TLINE Toggles the pixels along the line from (x1, y1) to ( x2, y2) on and off. Any pixel that was turned off, is turned on; any pixel that was turned on, is turned off. TLINE can be used to erase a line. TLINE x1 ; y1 ; x2 ; y2: HP 3 9gs Engl ish. book Pa ge 20 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Programming 18-21 Example TLINE 0;0;3;3: Er ase s pr e v iou sly dr a wn 4 5 degr ee line fr om (0, 0) to (3, 3) , or dr aw s that line if it doesnât alr eady e xist . Graphic commands The graphic commands use th e graphics variables G0 through G9âor the Page variable from Sketchâas graphicname arguments. The position argument takes the form ( x,y ). Position coordi nates depend on the current apletâs scale, which is specified by Xmin, Xmax, Ymin, and Ymax. The upp er left corn er of the target graphic ( graphic2 ) is at (Xmin,Ymax). You can capture the current display and store it in G0 by simultaneously pressing . DISPLAY â Stores the curr ent display in graphicname . DISPLAY â gr aphi cname : â DISPLAY Displays graph ic from graphicname in the display. â DISPLAY gr aphi cname : â GROB Creates a graphic from ex pression , using font_size , and stores the resulting graphic in graphicname . Font sizes are 1, 2, or 3. If the fontsize argument is 0, the HP 39gs creates a graphic display li ke that created by the SHOW operation. â GROB gr aphicname ; ex p ress io n ; fon ts iz e : GROBNOT Replaces graphic in graphicname with bitwise-inverted graphic. GROBNOT gr aphicname : GROBOR Using the logical OR, superimposes graphicname2 onto graphicname1 . The upper left corner of graphicname2 is placed at position . GROBOR gr aphic name1 ; ( po sition) ; gr aphi cname2 : Example GROBOR G0; (1,1); G1 : HP 3 9gs Engl ish. book Pa ge 21 We dnes day, Dec embe r 7, 2005 11 : 24 PM
18-22 Programming will superimpose G1 onto G0 starting a position (1,1), where the position is given in terms of the current axes settings, not as a pixel position. GROBXOR Using the logical XOR, su perimposes graphicname2 onto graphicname1 . The upper left corner of graphicname2 is placed at position . GROBXOR gr aphi cname1 ; ( position) ; gr aphicname2 : MAKEGROB Creates graphic with given width, heig ht, and hexadecimal data, and stores it in graphicname . MAKEGROB gr aphicname ; wi dt h ; he ight ; he xdata : PLOT â Stores the Plot view display as a graphic in graphicname . PLOT â graphi cnam e : PLOT â and DISPLAY â can be used to transfer a copy of the current PLOT view into the sketch view of the aplet for later use and editing. Example 1 î PageNum: PLOT â Page: â DISPLAY Page: FREEZE: This program stores the current PLOT view to the first page in the sketch view of the current aplet and then displays the sketch as a gr aphi c object u ntil any key is pressed. â PLOT Puts graph from graphicname into the Plot view display. â PLOT graphi cnam e : REPLACE Replaces portion of graphic in graphicname1 with graphicname2 , s tarting at position . REPLACE also works for lists and matrices. REPLACE gr aphi cname1 ; ( posi tion ) ; gr aphicname2 : SUB Extracts a portion of the named graphic (or list or matrix), and stores it in a new variable, name . The portion is specified by position and positions. SUB name ; graphi cname ; ( positi on ) ; ( positions ) : HP 3 9gs Engl ish. book Pa ge 22 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Programming 18-23 ZEROGROB Creates a blank graphic with given width and height , and stores i t in graphicname . ZEROGROB gr aphicname ; wi dt h ; hei ght : Loop commands Loop hp allow a program to execute a routine repeatedly. The HP 39gs has three loop structures. The example programs below illustrate each of these structures incrementing the variable A from 1 to 12. DOâ¦UNTIL â¦END Do ... Until ... End is a loop command that executes the loop-clause repeatedly until test-clause returns a true (nonzero) result. Because the test is executed after the loop-clause, the loop-clause is always executed at least once. Its syntax is: DO loop-cla use UNTIL test-clause END 1 î A: DO A 1 î A DISP 3;A: UNTIL A = = 12 END: WHILE⦠REPEAT⦠END While ... Repeat ... End is a loop command that repeatedly evaluates test-clause and exe cutes loop-clause sequence if the test is true. Because the test-clause is executed before the loop-clause, the lo op-clause is not executed if the test is initially false. Its syntax is: WHILE test-clause REPEAT loop-c lause END 1 î A: WHILE A < 12 REPEAT A 1 î A DISP 3;A: END: FORâ¦TOâ¦STEP ...END FOR name = start -expr essi on TO end-expr ession [STEP incr ement ]; loop-cla use END FOR A=1 TO 12 STEP 1; DISP 3;A: END: HP 3 9gs Engl ish. book Pa ge 23 We dnes day, Dec embe r 7, 2005 11 : 24 PM
18-24 Programming Note that the STEP parameter is optional. If it is omitted, a step value of 1 is assumed. BREAK Terminates loop. BREAK: Matrix commands The matrix commands take variables M0âM9 as arguments. ADDCOL Add Column. Inserts values into a column before column_number in the specified matrix . You enter the values as a vector. The values must be separated by commas and the number of valu es must be the same as the number of rows in the matrix name . ADDCOL name ;[ val u e 1 ,...,value n ]; column_number : ADDROW Add Row. Inserts values into a row before row_number in the specified matrix. You enter the values as a vector. The values mu st be sepa rated by commas and the number of values must be the same as the number of columns in the matrix name . ADDROW name ;[ va l u e 1 ,..., va lu e n ]; r o w_nu mber : DELCOL Delete Column. Deletes the specified column from the specified matrix . DELCOL name ; column_number : DELROW Delete Row. Deletes the spe cified row from the specified matrix. DELROW name ; row _ n u m b e r : EDITMAT Starts the Matrix Editor and displays the s pecified matrix. If used in programming, return s to the program when user presses . EDITMAT name : HP 3 9gs Engl ish. book Pa ge 24 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Programming 18-25 RANDMAT Creates random matrix with a specified number of rows and columns and stores the result in name ( name must be M0...M9 ). The entries will be integers ranging from â9 to 9. RANDMAT name ; rows ; c olumns : REDIM Redimensions the specified matrix or vector to si ze . For a matrix, size is a list of two integers {n1,n2} . For a vector, size is a list co ntaining one integer {n} . REDIM name ; si z e : REPLACE Replaces portion of a matrix or vector stored in name with an object starting at position start . start for a matr ix is a list containing two numbers; for a vector, it is a single number. Replace also works with lists and graphics. REPLACE name ; star t ; objec t : SCALE Multiplies the specified row_number of the specified matrix by value . SCALE name ; val ue ; rown u m b er : SCALEADD Multiplies the row of the matrix nam e by value , then adds this result to the second specified row. SCALEADD name ; val u e ; row 1 ; row 2 : SUB Extracts a sub-objectâ a portion of a list, matrix, or graphic fro m object âand stores it into name . start and end are each specified using a list with two numbers for a matrix, a number for vector or lists, or an ordered pair, ( X,Y ), for graphic s. SUB name ; object ; sta rt ; end : SWAPCOL Swaps Columns. Exch anges column1 and column2 of the specified matrix . SWAPCOL name ; column1 ; column2 : SWAPROW Swap Rows. Exc hanges row1 and row2 in the specified matrix . SWAPROW name ; row 1 ; row2 : HP 3 9gs Engl ish. book Pa ge 25 We dnes day, Dec embe r 7, 2005 11 : 24 PM
18-26 Programming Print commands These commands print to an HP infrared printer, for example the HP 82240B printer. PRDISPLAY Prints the contents of the display. PRDISPLAY: PRHISTORY Prints all objects in the history. PRHISTORY: PRVAR Prints name and co ntents of variablename . PRVAR va ri ablename : You can also use the PRVAR comman d to print the contents of a program or a note. PRVAR pr ogr amname ;PROG: PRVAR not ename ; NOTE: Prompt commands BEEP Beeps at the frequency and for the time you specify. BEEP frequen cy ; seconds : CHOOSE Creates a choose box, which is a bo x containing a list of options from which the user chooses one. Each option is numbered, 1 through n . The result of the choose command is to store the number of the option chosen in a variable. The syntax is CHOOSE variable_name ; t itle ; option 1 ; option 2 ; ... optio n n : where variable_name is the number of the option that will be highlighted by default whenever the choose box is displayed, title is the text displayed in the title bar of the choose box, an d option 1 ...option n are the options listed in the choose box. HP 3 9gs Engl ish. book Pa ge 26 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Programming 18-27 Example 3 î A:CHOOSE A; "COMIC STRIPS"; "DILBERT"; "CALVIN&HOBBES"; "BLONDIE": CLRVAR Clears the specified va riable. The syntax is: CLR V AR v ari able : Example If you have stored {1,2,3,4} in variable L1, entering CLVAR L1 w ill clear L1. DISP Displays textitem in a row of the display at the line_number . A text item consists of any number of expressions and quoted strings of text. The expressions are evaluated and turned into strings. Lines are numbered from the top of the screen, 1 being the top and 7 being the bottom. DISP line_nu mber ; te x titem : Example DISP 3;"A is" 2 2 Res u lt : A is 4 (display ed on line 3) DISPXY Dis plays object at position ( x_pos , y_pos ) in size font . The syntax is: DISPXY x_po s ; y_po s ; fo nt ; object : The value of object can be a text string, a variable, o r a combination of both. x_pos and y_pos are r elati ve to the c urr ent settings of Xmin, Xmax , Ymin and Ymax (whi c h y ou set in th e PL O T SETUP vie w) . T he value of fo nt is either 1 (small) or 2 (lar ge). HP 3 9gs Engl ish. book Pa ge 27 We dnes day, Dec embe r 7, 2005 11 : 24 PM
18-28 Programming Example DISPXY â3.5;1.5;2;"HELLO WORLD": DISPTIME Displays the current date and time. DISPTIME To set the date and time, simply store the correct settings in the date and time variables. Use the following formats: M.DDYYYY for the date and H.MMSS for the time. Examples 5.152000 î DATE( sets the date to May 15, 2000) . 10.1500 î TIME (sets the time to 10:15 am). EDITMAT Matrix Editor. Opens the Matr ix editor for the specified matrix. Returns to the program when user presses EDITMAT matr ixname : The EDITMAT command can also be used to create matrices. 1. Pr ess CMDS 2. P r e s s M 1, and the n pr ess . T he Matri x catalog opens w ith M1 a vailable f or editing . EDITMAT matrixname is an alternative to opening the matrix editor with matrixname . FREEZE This command prevents the display from being updated after the program runs. This allows you to view the graphics created by the program. Cancel FREEZE by pressing any key. FREEZE: HP 3 9gs Engl ish. book Pa ge 28 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Programming 18-29 GETKEY Waits for a key, then st ores the key code rc.p in name, where r is row number, c is column number, and p is key- plane number. The key-planes numbers are: 1 for unshifted; 2 for shifted; 4 for alpha-shifted; and 5 for both alpha-shifted and shifted . GETKEY name : INPUT Creates an input form with a title bar and one field. The field has a label and a default value. There is text help at the bottom of the form. The user enters a value and presses the menu key. The value that the user enters is stored in the vari able name . The title , label , and help items are text strings and need to be enclosed in double quotes. Use CHARS to type the quote marks " ". INPUT name ; title , label ; help ; de fa ult : Example INPUT R; "Circular Area"; "Radius"; "Enter Number";1: MSGBOX Displays a message box cont aining textitem. A text item consists of any number of expressions and quoted strings of text. The expressions are evaluated and turned into strings of text. For examp le, "AREA IS:" 2 2 becomes ARE A IS: 4 . Use CHARS to type the quote marks " ". MSGBOX te xtitem : Example 1 î A: MSGBOX "AREA IS: " Ï*A^2: You can also use the NoteText variable to provide text arguments. This can be used to insert line breaks. For example, press NOTE and ty pe AREA IS . The position line MSGBOX NoteText " " Ï*A^ 2: will display the same message box as the previous example . HP 3 9gs Engl ish. book Pa ge 29 We dnes day, Dec embe r 7, 2005 11 : 24 PM
18-30 Programming PROMPT Displays an input box with name as the title, and prompts for a value for name . name can be a variable such as Aâ¦Z, θ , L1â¦l9, C1â¦C9 or Z1â¦Z9. PROMPT name : WAIT Halts program execution for the specified number of seconds. WAIT sec onds : Stat-One and Stat-Two commands The following commands are used for analyzing one- variable and two-variable statistic al data. Stat-One commands DO1VSTATS Calculates STATS using dat asetname and stores the results in the corresponding variables: N Σ , Tot Σ , Mean Σ , PVar Σ , SVar Σ , PSDev, SSDev, Min Σ , Q1, Median, Q3, and Max Σ . Datasetname can be H1, H2, ..., or H5. Datasetname must include at least two data points. DO1VSTATS datas etname : SETFREQ Sets datasetname frequency a ccording to column or value. Datasetname can be H1, H2,..., or H5, column can be C0âC9 and value can be any positive integer. SETFREQ data setname ; colum n : or SETFREQ def inition ; va l u e : SETSAMPLE Sets datasetname sample according to column. Datasetname can be H1âH5, and column can be COâC9. SETSAMPLE datas etname ; column : Stat-Two commands DO2VSTATS Calculates STATS using dat asetname and stores the results in corresponding variables: MeanX, Σ X, Σ X2, MeanY, Σ Y, ΣY2, Σ XY, Corr, PCov, SCo v, and RELERR. HP 3 9gs Engl ish. book Pa ge 30 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Programming 18-31 Datasetname can be SI, S2,..., or S5 . Datasetname must include at least two pairs of data points. DO2VSTATS datasetname : SETDEPEND Sets datasetname dependent column . Datasetname can be S1, S2, â¦, or S5 and column can be C0âC9. SETDEPEND datasetname ; column : SETINDEP Sets datasetname independent column . Datasetname can be S1, S2,â¦, or S5 and co lumn can be C0âC9. SETINDEP datasetname ; column : Storing and retrieving variables in programs The hp 39gs has both Home variables and Aplet variables. Home variables ar e used for real numbers, complex numbers, graphics, lists, and matrices. Home variables keep the same values in HOME and in aplets. Aplet variables are those whose values depend on the current aplet. The aplet variab les are used in programming to emulate the definitions and settings you make when working with aplets interactively. You use the Variable menu ( ) to retrieve either Home variables or aplet vari ables. Se e âThe VARS menuâ on page 14-4. Not all variables are availa ble in every aplet. S1fitâS5fit, for example, are only available in the St at is tic s a pl et . U nde r e ac h va ri ab le nam e i s a li st of th e aplets where the variable can be used. HP 3 9gs Engl ish. book Pa ge 31 We dnes day, Dec embe r 7, 2005 11 : 24 PM
18-32 Programming Plot-view variables Area Function Contains the last value found by the Area function in Plot- FCN menu. Axes All Aplets Turns axes on or off. From Plot Setup, check (o r uncheck) AXES . or In a program, type: 1 î Axes âto turn axes on (def ault) . 0 î Axes âto turn ax es off . Connect Function Parametric Polar Solve Statistics Draws lines between successively plotted points. From Plot Setup, check (o r uncheck) CONNECT . or In a program, type 1 î Connect â to connect plotted points (def ault , e x cept in St atistic s w her e the def ault is off). 0 î Connect â not to connect plotted po ints . Coord Function Parametric Polar Sequence Solve Statistics Turns the coordinate-display mode in Plo t view on or off. From Plot view, use the Menu mean key to toggle coordinate display on an off. In a program, type 1 î Coord âto tur n coor dinate displa y on (def ault). 0 î Coord âto turn coor din ate displa y off . Extremum Function Contains the last value foun d by the Extremum operation in the Plot-FCN menu. FastRes Function Solve Toggles resolution between plotting in every other column (faster), or plotting in every column (more detail). From Plot Setup, choose Faster or More Detail. or In a program, type 1 î FastRes âfor f aster . 0 î FastRes âfor mor e detail (def ault) . HP 3 9gs Engl ish. book Pa ge 32 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Programming 18-33 Grid All Aplets Turns the background grid in Plot view o n or off. From Plot setup, check (or uncheck) GRID . or In a program, type 1 î Grid to tur n the gr id on . 0 î Grid to tur n the gri d off (def ault). Hmin/Hmax Statistics Defines minimum and maximum values for histogram bars. From Plot Setup for one-variable statistics, set values for HRNG . or In a program, type î Hmin î Hmax wh ere Hwidth Statistics Sets the width of histogram bars. From Plot Setup in 1VAR stats set a value for Hwidth or In a program, type n î Hwidth Indep All Aplets Defines the value of the independent variable used in tracing mode. In a program, type n î Indep InvCross All Aplets Toggles between solid crosshai rs or inverted crosshairs. (Inverted is useful if the background is solid). From Plot Setup, check (or uncheck) InvCross or In a program, type: 1 î InvCross âto in v ert the cr osshair s. 0 î InvCross âf or soli d cr osshair s (default). n 1 n 2 n 2 n 1 > HP 3 9gs Engl ish. book Pa ge 33 We dnes day, Dec embe r 7, 2005 11 : 24 PM
18-34 Programming Isect Function Contains the last value found by the Intersection function in the Plot-FCN menu. Labels All Aplets Draws labels in Plot view showing X and Y ranges. From Plot Setup, check (o r uncheck) Labels or In a program, type 1 î Labels âto turn labels on . 0 î Labels âto turn labels o ff (def ault) . Nmin / Nmax Sequence Defines the minimum and maxi mum independent variable values. Appears as the NRNG fi elds in the Plot Setup input form. From Plot Setup, enter values for NRNG . or In a program, type î Nmin î Nmax whe re Recenter All Aplets Recenters at the crosshairs locations when zooming. From Plot-Zoom-Set Factors, check (or un check) Recenter or In a program, type 1 î Recenter â to tur n r ecent er on (def ault). 0 î Recenter âto tur n r ecenter o ff . Root Function Contains the last value found by the Root function in the Plot-FCN menu. n 1 n 2 n 2 n 1 > HP 3 9gs Engl ish. book Pa ge 34 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Programming 18-35 S1markâS5mark Statistics Sets the mark to use for scatter plots. From Plot Setup for two-variable statistics, S1mark- S5mark , then choose a mark. or In a program, type n î S1mark wh ere n is 1,2,3,...5 SeqPlot Sequence Enables you to choose types of sequence plot: Stairstep or Cobweb. From Plot Setup, select SeqPlot , then choose Stairstep or Cobwe b . or In a program, type 1 î SeqPlot âfor Stairstep. 2 î SeqPlot âfor Cobweb. Simult Function Parametric Polar Sequence Enables you to choose between simultaneous and sequential graphing of all selected expressions . From Plot Setup, check (or uncheck) _ SIMULT or In a program, type 1 î Simult âf or simultaneou s gr aphing (def ault). 0 î Simult âf or seq uenti al gr aphing . Slope Function Contains the last value found by the Slope function in the Plot-FCN menu. StatPlot Statistics Enables you to choose types of 1-variable statistics plot between Histogram or Box-and-Whisker. From Plot Setup, select StatPlot , then choose Histogram or BoxWh isker . or In a program, type 1 î StatPlot âfor Histogram. 2 î StatPlot âfor Box-and-Whisker. HP 3 9gs Engl ish. book Pa ge 35 We dnes day, Dec embe r 7, 2005 11 : 24 PM
18-36 Programming Umin/Umax Polar Sets the minimum and maxi mum independent values. Appears as the URNG field in the Plot Setup input form. From the Plot Setup input form, enter values for URNG . or In a program, type î Umin î Umax wher e Ustep Polar Sets the step size for an independent v ariable. From the Plot Setup input form, enter values for USTEP . or In a program, type n î Ustep wher e Tmin / Tmax Parametric Sets the minimum and maxi mum independent variable values. Appears as the TRN G field in the Plot Setup input form. From Plot Setup, enter values for TRNG . or In a pr ogr am, type î Tmin î Tmax wher e Tracing All Aplets Turns the tracing mode on or off in Plot view. In a program, type 1 î Tracing âto tur n T r ac ing mode on (def ault) . 0 î Tracing âto tur n T r ac ing mode off . n 1 n 2 n 2 n 1 > n 0 > n 1 n 2 n 2 n 1 > HP 3 9gs Engl ish. book Pa ge 36 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Programming 18-37 Tstep Parametric Sets the step size for the independent variable. From the Plot Setup input form, enter values for TSTEP . or In a program, type n î Tstep wh ere Xcross All Aplets Sets the horizontal coordinate of the c rosshairs. Only works with TRACE off. In a program, type n î Xcross Ycross All Aplets Sets the vertical coordinate of the crosshairs. Only works with TRACE off. In a program, type n î Ycross Xtick All Aplets Sets the distance between tick marks for the horizontal axis. From the Plot Setup input form, enter a value for Xtick . or In a program, type n î Xtick wh ere Ytick All Aplets Sets the distance between tick marks for the vertical axis. From the Plot Setup input form, enter a value for Ytick . or In a program, type n î Ytick wh ere Xmin / Xmax All Aplets Sets the minimum and maximum horizontal values of the plot screen. Appears as the XRNG fields (horizontal range) in the Plot Setup input form. From Plot Setup, enter values for XR NG . or In a program, type n 0 > n 0 > n 0 > HP 3 9gs Engl ish. book Pa ge 37 We dnes day, Dec embe r 7, 2005 11 : 24 PM
18-38 Programming î Xmin î Xmax whe re Ymin / Ymax All Aplets Sets the minimum and maximum vertical values of the plot screen. Appears as the YRNG fields (vertical range) in the Plot Setup input form. From Plot Setup, enter the values for YRNG . or In a program, type î Ymin î Ymax whe re Xzoom All Aplets Sets the horizontal zoom factor. From Plot-ZOOM-Set Factors, enter the value for XZOOM . or In a program, type n î XZOOM wher e The default value is 4. Yzoom All Aplets Sets the vertical zoom factor. From Plot-ZOOM-Set Factors, enter the value for YZOOM . or In a program, type n î YZOOM The default value is 4. n 1 n 2 n 2 n 1 > n 1 n 2 n 2 n 1 > n 0 > HP 3 9gs Engl ish. book Pa ge 38 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Programming 18-39 Symbolic-view variables Angle All Aplets Sets the angle mode. From Symbolic Setup, choose Degrees , Radia ns , or Grads for angle measure. or In a program, type 1 î Angle âfor De grees. 2 î Angle âfor Radian s. 3 î Angle âfor Grads. F1...F9, F0 Function Can contain any expression. Independent variable is X . Example 'SIN( X)' î F1( X ) You must put single quotes around an expression to keep it from being evaluated before it is stored. Use CHARS to type the single quote mark. X1, Y1...X9,Y9 X0,Y0 Parametric Can contain any expression. Independent variable is T. Example 'SIN(4*T)' î Y1(T):'2*SIN(6*T)' î X1(T) R1...R9, R0 Polar Can contain any expression. Independent variable is θ . Example '2*SIN(2* θ)' î R1( θ ) U1...U9, U0 Sequence Can contain any expression. Independent variable is N. Example RECURSE (U,U(N-1)*N,1,2) î U1(N) E1...E9, E0 Solve Can contain any equa tion or expression. Independent variable is selected by high lighting it in Numeric View. Example 'X Y*X-2=Y' î E1 HP 3 9gs Engl ish. book Pa ge 39 We dnes day, Dec embe r 7, 2005 11 : 24 PM
18-40 Programming S1fit...S5fit Statistics Sets the type of fit to be used by the FIT operation in drawing the regression line. From Symbolic Setup view, specify the fit in the field for S1FIT, S2FIT, etc. or In a program, store one of the fo llowing constant numbers or names into a variable S1fit , S2fit , etc. 1 Linear 2 LogFit 3 ExpFit 4 Power 5 QuadFit 6 Cubic 7 Logist 8 ExpFit 9 TrigFit 10 User Defined Example Cubic î S2fit or 6 î S2fit HP 3 9gs Engl ish. book Pa ge 40 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Programming 18-41 Numeric-view variables The following aplet variabl es control the Numeric view . The value of the variable appl ies to the current aplet only. C1...C9, C0 Statistics C0 through C9 , for column s of data. Can contain lists. Enter da ta in the N umeric view or In a program, type LIST î C n wh ere n = 0, 1, 2, 3 ... 9 Digits All Aplets Number of decimal places to use for Number format in the HOME view and for labeling axes in the Plot view. From the Modes view, enter a value in the second field of Number Format . or In a program, type n î Digits wh ere Format All Aplets Defines the number display format to use for numeric format in the HOME view and for labeling axes in the Plot view. From the Modes view, choose Standard , Fixed , Scientific , Engineering, Fraction or Mixed Fraction in the Number Format field. or In a program, store the constant number (or its name) into the vari able Format . 1 Standard 2 Fixed 3 Sci 4 Eng 5 Fraction 6 MixFraction 0 n 11 << HP 3 9gs Engl ish. book Pa ge 41 We dnes day, Dec embe r 7, 2005 11 : 24 PM
18-42 Programming Note that if Fraction or M ixed Fraction is chosen, the setting will be ignored when labeling axes in Plot view. A setting of Scientific will be used instead. Example Scientific î Format or 3 î Format NumCol All Aplets except Statistics aplet Sets the column to be highlighted in Numeric view. In a program, type n î NumCol where n can be 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 . NumFont Function Parametric Polar Sequence Statistics Enables you to choose the font size in Numeric view. Does not appear in the Num Setup input form. Corresponds to the key in Numeric view. In a program, type 0 î NumFont fo r small (defa ult) . 1 î NumFont for big. NumIndep Function Parametric Polar Sequence Specifies the list of indepe ndent valu es to be used by Build Your Own Table. In a program, type LIST î NumIndep NumRow All Aplets except Statistics aplet Sets the row to be highlighted in Numeric view. In a program, type n î NumRow wher e NumStart Function Parametric Polar Sequence Sets the starting value for a table in Numeric view. From Num Setup, enter a value for NUMSTART . or In a program, type n î NumStart n 0 > HP 3 9gs Engl ish. book Pa ge 42 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Programming 18-43 NumStep Function Parametric Polar Sequence Sets the step size (increment value) for an independent varia ble in N umeri c view. From Num Setup, enter a value for NU MSTEP . or In a program, type n î NumStep wh ere NumType Function Parametric Polar Sequence Sets the table format. From Num Setup, choose Automatic or Build You r Own . or In a program, type 0 î NumType f or Build Y our Ow n . 1 î NumType for A utomatic (d ef ault ) . NumZoom Function Parametric Polar Sequence Sets the zoom factor in the Numeric view. From Num Setup, type in a value for NUMZOOM . or In a program, type n î NumZoom wh ere StatMode Statistics Enables you to choose between 1-variable and 2- variable statistics in the Statistics aplet. Does not appear in the Plot Setup input form. Corresponds to the and menu keys in Numeric View. In a program, store the constant name (or its number) into the variab le StatMode. 1VAR = 1 , 2VAR = 2. Example 1VAR î StatMode or 1 î StatMode n 0 > n 0 > HP 3 9gs Engl ish. book Pa ge 43 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Note variables The following aplet variable is available in Note view. NoteText All Aplets Use NoteText to recall text previously entered in Note view. Sketch variables The following aplet variables are available in Sk etch view. Page All Aplets Sets a page in a sketch set. The graphics can be viewed one at a time using the and keys. The Page var iable refers to the cu rrently displayed page of a sketch set. In a program, type gr aphi cname î Page PageNum All Aplets Sets a number for referring to a particular page of the sketch set (in Sketch view). In a program, type the page that is shown when SKETCH is pressed. n î PageNum HP 3 9gs Engl ish. book Pa ge 44 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Extending aplets 19-1 19 Extending aplets Aplets are the application environments where you explore different cla sses of mathematical operations. You can extend the capabili ty of the HP 39gs in the following ways: ⢠Cr eate ne w aplets , based on e x isting aplets , w ith spec ifi c conf igur ations suc h as angle measur e, gr aphical or tabular settings, and annotations. ⢠T r ansmit aplets between HP 3 9gs calculator s v ia an infr a re d link. ⢠Do wnload e-lessons (teac hing aplets ) fr om He wlett-P ac k ar dâs Calc ulator w eb site. ⢠Pr ogr am new aplets . See c hapter 18, âPr ogramming â, for further details. Creating new aplets based on existing aplets You can create a new aplet ba sed on an existing aplet. To create a new aplet, save an existing aplet under a new name, then modify the aplet to add the configurations and the functionality that you want. Information that defines an a plet is saved automatically as it is entered into the calculator. To keep as much memory available for storage as possible, delete any aplets you no longer need. Example This e xample demonstrates how to create a new aplet by saving a copy of the bu ilt-in Solve aplet. The new aplet is saved under the name âTRIANGLESâ contains the formulas commonly used in calculation s involving right-angled triangles. HP 3 9gs Engl ish. book Pa ge 1 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
19-2 Exten ding aplet s 1. Open the Solv e aplet and save it under the n e w name . Solve | T R I A N G L E S 2 . En te r t he fou r formu l as : θ O H θ A H θ OA AB C 3 . Dec ide whether y ou want the a plet to oper ate in Degr ees , R adians , or Gr ads. MODES Degrees 4. V ie w the Aplet L ibr ary . T he âT RIANGLE Sâ aplet is listed in t he Aplet L ibrary . T he Solv e aplet can no w be r eset and used f or other pr oblems. HP 3 9gs Engl ish. book Pa ge 2 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Extending aplets 19-3 Using a customized aplet To use the âT rianglesâ aplet, simply s elect the appropriate formula, change to the Numeric view and solve for the missing variable. Find the length of a ladder leaning against a vertical wall if it forms an angle of 35 o with the horizontal and extends 5 metres up the wall. 1. Selec t the aplet. TRIANGLES 2 . Ch oose the sine f or mula in E1. 3 . Change to the Numer ic vi ew a n d e n t e r t he kno w n values . 35 5 4. Sol ve f or the missing va lu e. T he length of the ladder is appr o x imately 8.7 2 metr es Resetting an aplet Resetting an aplet clears all data and resets all default settings. To reset an aplet, open the Library, select the aplet and press . You can only r eset an aplet that is based on a built-i n aplet if the programmer who created it has provided a Reset option. HP 3 9gs Engl ish. book Pa ge 3 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
19-4 Exten ding aplet s Annotating an aplet with notes The Note view ( NOTE ) attaches a note to the current aplet. See Chapter 17, âNotes and sketc hesâ. Annotating an aplet with sketches The Sketch view ( SKETCH ) attaches a picture to the current aplet. See chapter 17, âNotes and sketchesâ. HINT Notes and s k et c hes th at y ou atta c h to an aplet becom e part of the aplet. W hen yo u transfer the aplet to another calculator , the associ ated note a nd sketc h are tr ansferr e d as well. Downloading e-lessons from the web In addition to the standard aplets that come with the calculator, you can download aplets from the world wide web. For example, Hewlett-Packardâs Calculators web site contains aplets that de monstrate certain mathematical concepts. Note that you need the Graphing Calculator Connectivity Kit in order to load aplets from a PC. Hewlett-Packardâs Calculators web site can be found at: http://www.hp.com/calculators Sending and receiving aplets A convenient way to distribute or share problems in class and to turn in homework is to transmit (copy) aplets d i r e c t l y f r o m o n e H P 3 9 g s t o a n o t h e r . T h i s c a n t a k e p l a c e via the infrared port or via a suitable cable. (You can use a serial cable with a 4-pin mini-USB connector, which plugs into the RS232 port on the calculator. The serial cable is available as a separate accessory.) You can also send aplets to, and receive aplets from, a PC. This requires special softwa re running on the PC (such as the PC Connectivity Kit). A USB cable with a 5-pin mini- USB connector is provided with the hp39gs for connecting with a PC. It plugs into the USB port on the calculator. HP 3 9gs Engl ish. book Pa ge 4 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Extending aplets 19-5 To transmit an aplet 1. Co nnect the P C or a plet disk dr i v e to the calc ulator by cable or align the tw o calc ulators â infr ar ed ports by matc hing up the tr iangle marks on the r ims of the calc ulators . P lace the calculato rs no mor e than 4 inches (10 cm) apar t. 2 . Sending calc ulator : Open the L ibrary , highlight the aplet to s end, and pr ess . â Th e S END TO men u appears w ith th e f ollo w ing optio ns: HP39G (IRDA) = to send vi a high-speed infr ared HP39/40 (USB) = to send vi a the USB port HP39/40 (SER) = to send via the R S2 3 2 serial port USB DISK DRIVE = to send to a disk dri ve v ia the USB port SER. DISK DRIVE = to send to a disk dr iv e vi a the R S 232 s e r i a l p o r t Note : c hoos e a disk dri ve optio n if you ar e using the hp3 9gs connecti vity kit to tr ansfer the ap let . Hi ghlight y our selecti on and pres s . â If transmitting to a disk dr iv e , y ou ha ve the optio ns of se nding to the c ur r ent (de fault) directory or to anot her director y . 3 . R ecei ving calc ulator : Open the aplet library and pr ess . â Th e RECEIVE FROM menu appear s w ith the fo llo w i ng optio ns: HP39G (IRDA) = to r ecei v e v ia hi gh-speed infr ar ed HP39G = to r ecei ve v ia low-s peed infr ared HP39/40 (USB) = to r ecei v e v ia the U SB por t HP39/40 (SER) = to rece i ve v ia the R S2 3 2 seri al port USB DISK DRIVE = to recei ve fr om a disk dr i ve v ia the USB po r t SER. DISK DRIVE = to r ece i v e fr om a disk dri ve vi a the R S 232 s e r i a l p o r t HP 3 9gs Engl ish. book Pa ge 5 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
19-6 Exten ding aplet s Note : ch oose a disk dri ve option if y ou are using the hp3 9gs connecti vity kit to tr ansfer the a plet . Hi ghlight y our selec tion and pr ess . The T r ansmit annu nc iatorâ âi s display e d until tr ansmis sion is co mplet e . If you are using the PC Connectivity Kit to download aplets from a PC, you will see a list of aplets in the PCâs current directory. Chec k as ma ny item s as you wou ld like to receive. Sorting items in the aplet library menu list Once you have entered information into an aplet, you have defined a new version of an aplet. The information is automatically saved under the cur rent aplet name, such as âFunction.â To create additio nal aplets of the same type, you must give the current aplet a new name. The advantage of storing an ap let is to allow you to keep a copy of a working environment for later use. The aplet library is where you g o to manage your aplets. Press . Highlight (using the arrow keys) the name of the aplet you want to act on. To sort the aplet list In the aplet library, press . Select the sorting scheme and press . ⢠Chronologically pr od uces a c hr onological order based on the dat e an aplet w as last used . (The last- used aplet ap pears firs t, and so on .) ⢠Alphabetically pr o duces an alphabetical or der b y aplet name . To delete an aplet You cannot delete a built-in aplet. You can only clear its data and reset its default settings. To delete a customized aplet, open the aplet library, highlight the aplet to be deleted, and press . To delete all custom aplets, press CLEAR . HP 3 9gs Engl ish. book Pa ge 6 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
R-1 R Re fer ence inf ormation Glossary aplet A small application, limited to one topic. The built-in aplet types are Function, Parametric , Polar, Sequence, Solve, Statistics, Inference, Finance, Trig Explorer, Quad Explorer, Linear Solver and Triangle Solve. An aplet can be filled with the data and solutions for a specific problem. It is reusable (like a program, but easier to use) and it records all your settings and definitions. command An operation for use in programs. Commands can store results in variables, but do no t display results. Arguments are separated by semi- colons, such as DISP expression ; line# . expression A number, variable, or algebraic expression (numbers plus functions) that produces a value. function An operation, possibly with arguments, that returns a result. It does not store results in variables. The arguments must be enclosed in parentheses and separated with commas (or periods in Comma mode), such as CROSS ( matrix1,matrix2 ). HOME T he basic starting point of the calculator. Go to HOME to do calculatio ns. Library For aplet management: to start, save, reset, send and receive aplets. HP 3 9gs Engl ish. book Pa ge 1 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
R-2 list A set of values separated by commas (periods if the Decimal Mark mode is set to Comma ) and enclosed in braces. Lists are commonly used to enter statistical data and to evaluate a function with multiple values. Created and manipulate d by the List editor and catalog. matrix A two-dimensional ar ray of values separated by commas (periods if the Decimal Mark mode is set to Comma ) and enclosed in nested brackets. Created and manipulated by the Matrix catalog and editor. Vectors are also handled by the Matrix catalog and editor. menu A choice of options given in the display. It can appear as a list or as a set of menu-key labels across the bottom of the display. menu keys The top row of keys. Th eir operations depend on the current context. The labels along the bottom of the display show the current meanings. note Text that you write in the Notepad or in the Note view for a specific aplet. program A reusable set of instructions that you record using the Program editor. sketch A drawing that you make in the Sketch view for a specific aplet. variable The name of a number, list, matrix, note, or graphic that is stored in memory. Use to store and use to retrieve. vector A one-dimensional ar ray of values separated by commas (periods if the Decimal Mark mode is set to Comma ) and enclosed in single brackets. Created and manipulated by the Matrix catalog and editor. HP 3 9gs Engl ish. book Pa ge 2 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
R-3 Resetting the HP 39gs If the calculator âlocks upâ and seems to be stuc k, you must reset it. This is much like resetting a PC. It cancels certain operations, restores ce rtain conditio ns, and clears temporary memory locations. However, it does not clear stored data (variables, ap let databases, programs) unless you use the proced ure, âTo e rase all memor y and reset defaultsâ. To reset using the keyboard Press and hold the key and the thir d menu key simultaneously, then release them. If the c alculator does not respond t o the above key sequence, then: 1. T ur n the calc ulator o v er and locate the small hole in the bac k of the calc ulator . 2 . Insert the end of a straightened metal paper c lip into the hole as f a r as it w i ll go . Hold it ther e fo r 1 second , then r emo v e it . 3 . Pre ss If necessary , pr es s and the f irst and last men u k e y s simultaneou sly . (Note: This w ill era se y our calc ulator memory .) To erase all memory and reset defaults If the calculator does not respond to the above resetting procedures, you might need to re start it by erasing all of memory. You will lose everything you have stored. All factory-default settings are restored. 1. Pr ess and h old the k e y , the firs t menu k ey , and the last menu ke y simultaneously . 2 . R eleas e all k e y s in the re ver se or der . Note: T o cancel this pr ocess, r elease only the top-r ow k e ys , then pr ess the thir d menu k ey . views T he possible contexts for an aplet: Plot, Plot Setup, Numeric, Numeric Setup, Symbolic, Symbolic Setup, Sketch, Note, and special views like split screens. Refe renc eInf o.fm Pa ge 3 Fri day, Dec embe r 16 , 20 05 1 0:00 AM
R-4 If the calculator does not turn on If the HP 39gs does not turn on follow the steps below until the calculator turns on. You may find that the calculator turns on before you have completed the procedure. If the calculator still does not turn on, please contact Customer Support for further information. 1. Pr ess and hold the ke y for 10 seconds. 2 . Pr ess and hold the k e y and the thir d menu k ey simultaneou sl y . R elease the thir d menu k ey , then r elease t he ke y . 3 . Pr ess and h old the k ey , the first men u k e y , an d the si xth menu k ey simultaneo usly . Rele ase the si xth menu k ey , then r elease the fir st men u k e y , and then r elease t he ke y . 4. L ocate the small hole in the bac k of the calc ulator . Insert the end of a straightened metal paper clip into the hole as f ar as it w ill go . Hold it there f or 1 second , then r emov e it . Pre ss the k ey . 5 . Remo ve the batter ie s (see âBatter ies â on page R - 4) , pr ess and hold the ke y f or 10 seconds, and then put the bat ter ies back in. Pr ess the k e y . Operating details Operating temperature: 0 ° to 45 ° C (32 ° to 113 ° F). Storage temperature: â20 ° to 65 ° C (â 4 ° to 149 ° F). Operating and storage humidity: 90% relative humidity at 40 ° C (104 °F) maximum. Avoid getting the calculator wet. Battery operates at 6.0V dc, 80mA maximum. Batteries The calculator uses 4 AAA(LR03) batteries as main power and a CR2032 li thium battery for memory ba ckup. Before using the calculator , please install the batteries according to the following procedure. Refe renc eInf o.fm Pa ge 4 Fri day, Dec embe r 16 , 20 05 1 0:00 AM
R-5 To install the main batteries a. Slide up the battery compartment cove r as illustrated. b. Insert 4 new AAA (LR03) batteries into the main compartment. Make sure each battery is inserted in the indicated direction. To install the backup battery a. Press down the holder. Push the plate to the shown direction and lift it. b. Insert a new CR2032 lithium battery. Make sure its positive ( ) side is facing up. c. Replace the plate and push it to the origin al place. After installing the batteries, press to turn the power on. Warning: It is recommended that you replace this battery every 5 years. When the low battery ico n is disp layed, you need to replace the batte ries as soon as possible. However, avoid removing th e backup battery and ma in batteries at the same time to avoid data lost. Refe renc eInf o.fm Pa ge 5 Fri day, Dec embe r 16 , 20 05 1 0:00 AM
R-6 Variables Home variables The home variables are: Categor y Available name Complex Z1... Z9, Z0 Graphic G1 ... G9, G0 Library Function Parametric Polar Sequence Solve Statistics User-named List L1 ... L9 , L0 Matrix M1 ... M9 , M0 Modes Ans Date HAngle HDigits HFormat Ierr Time Notepad User-named Program Editline User-named Real A...Z, θ HP 3 9gs Engl ish. book Pa ge 6 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
R-7 Function aplet variables The function aplet variables a re: Category Av ailable name Plot Axes Connect Coord FastRes Grid Indep InvCross Labels Recenter Simult Tracing Xcross Ycross Xtick Ytick Xmin Xmax Ymin Ymax Xzoom Yxoom Plot-FCN Area Extremum Isect Root Slope Symbolic Angle F1 F2 F3 F4 F5 F6 F7 F8 F9 F0 Nume ric Digits Format NumCol NumFont NumIndep NumRow NumStart NumStep NumType NumZoom Note N oteText Sketc h Page PageNum HP 3 9gs Engl ish. book Pa ge 7 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
R-8 Parametric aplet variables The parametric aplet variables are: Categor y Available name Plot Axes Connect Coord Grid Indep InvCross Labels Recenter Simult Tmin Tmax Tracing Tstep Xcross Ycross Xtick Ytick Xmin Xmax Ymin Ymax Xzoom Yzoom Symbolic Angle X1 Y1 X2 Y2 X3 Y3 X4 Y4 X5 Y5 X6 Y6 X7 Y7 X8 Y8 X9 Y9 X0 Y0 Numeric Digits Format NumCol NumFont NumIndep NumRow NumStart NumStep NumType NumZoom Note NoteText Sketch Page PageNum HP 3 9gs Engl ish. book Pa ge 8 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
R-9 Polar aplet variables The polar aplet variables are: Category Av ailable names Plot Axes Connect Coord Grid Indep InvCross Labels Recenter Simult Umin Umax θ step Tracing Xcross Ycross Xtick Ytick Xmin Xmax Ymin Ymax Xzoom Yxoom Symbolic Angle R1 R2 R3 R4 R5 R6 R7 R8 R9 R0 Nume ric Digits Format NumCol NumFont NumIndep NumRow NumStart NumStep NumType NumZoom Note N oteText Sketc h Page PageNum HP 3 9gs Engl ish. book Pa ge 9 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
R-10 Sequence aplet variables The sequence aplet variables are: Categor y Available name Plot Axes Coord Grid Indep InvCross Labels Nmin Nmax Recenter SeqPlot Simult Tracing Xcross Ycross Xtick Ytick Xmin Xmax Ymin Ymax Xzoom Yzoom Symbolic Angle U1 U2 U3 U4 U5 U6 U7 U8 U9 U0 Numeric Digits Format NumCol NumFont NumIndep NumRow NumStart NumStep NumType NumZoom Note NoteText Sketch Page PageNum HP 3 9gs Engl ish. book Pa ge 10 We dnes day, Dec embe r 7, 2005 11 : 24 PM
R-11 Solve aplet variables The solve aplet variables are: Category Av ailable name Plot Axes Connect Coord FastRes Grid Indep InvCross Labels Recenter Tracing Xcross Ycross Xtick Ytick Xmin Xmax Ymin Ymax Xzoom Yxoom Symbolic Angle E1 E2 E3 E4 E5 E6 E7 E8 E9 E0 Nume ric Digits Format NumCol NumRow Note N oteText Sketc h Page PageNum HP 3 9gs Engl ish. book Pa ge 11 We dnes day, Dec embe r 7, 2005 11 : 24 PM
R-12 Statistics aplet variables The statistics aplet variables are: Categor y Available name Plot Axes Connect Coord Grid Hmin Hmax Hwidth Indep InvCross Labels Recenter S1mark S2mark S3mark S4mark S5mark StatPlot Tracing Xcross Ycross Xtick Ytick Xmin Xmax Ymin Ymax Xzoom Yxoom Symbolic Angle S1fit S2fit S3fit S4fit S5fit Numeric C0,...C9 Digits Format NumCol NumFont NumRow StatMode Stat-One Max Σ Mean Σ Median Min Σ N Σ Q1 Q3 PSDev SSDev PVar Σ SVar Σ Tot Σ Stat-Two Corr Cov Fit MeanX MeanY RelErr Σ X Σ X2 Σ XY Σ Y Σ Y2 Note NoteText Sketch Page PageNum HP 3 9gs Engl ish. book Pa ge 12 We dnes day, Dec embe r 7, 2005 11 : 24 PM
R-13 MATH menu categories Math functions The math functions are: Category Av ailable name Calculus TAYLOR Complex ARG CONJ IM RE Constant e i MAXREAL MINREAL Ï Hyper b. ACOSH ASINH ATANH COSH SINH TANH ALOG EXP EXPM1 LNP1 List CONCAT Î LIST MAKELIST Ï LIST POS REVERSE SIZE Σ LIST SORT Loop ITERATE RECURSE Σ â â« HP 3 9gs Engl ish. book Pa ge 13 We dnes day, Dec embe r 7, 2005 11 : 24 PM
R-14 Matrix COLNORM COND CROSS DET DOT EIGENVAL EIGENVV IDENMAT INVERSE LQ LSQ LU MAKEMAT QR RANK ROWNORM RREF SCHUR SIZE SPECNORM SPECRAD SVD SVL TRACE TRN Polynom. POLYCOEF POLYEVAL POLYFORM POLYROOT Prob. COMB ! PERM RANDOM UTPC UTPF UTPN UTPT Real CEILING DEG âRAD FLOOR FNROOT FRAC HMS â â HMS INT MANT MAX MIN MOD % %CHANGE %TOTAL RAD âDEG ROUND SIGN TRUNCATE XPON Stat-Two PREDX PREDY Symbolic = ISOLATE LINEAR? QUAD QUOTE | Category Av ailable name (Continued) HP 3 9gs Engl ish. book Pa ge 14 We dnes day, Dec embe r 7, 2005 11 : 24 PM
R-15 Program constants The program constants are: Tests < ⤠= = â > ⥠AND IFTE NOT OR XOR Trig ACOT ACSC ASEC COT CSC SEC Category Av ailabl e name (Continued) Category Av ailable name Angle Degrees Grads Radians Format Standard Fixed Sci Eng Fraction SeqPlot Cobweb Stairstep S1...5fit Linear LogFit ExpFit Power Trigonometric QuadFit Cubic Logist User Exponent StatMode Stat1Var Stat2Var StatPlot Hist BoxW HP 3 9gs Engl ish. book Pa ge 15 We dnes day, Dec embe r 7, 2005 11 : 24 PM
R-16 Physical Constants The physical constants are: Categor y Available Na me Chemist ⢠Avogadro (A vogadr o âs Number , NA) ⢠Boltz . (Boltmann, k) ⢠mol. vo... (molar v olume , Vm) ⢠univ gas (uni v ers al gas , R) ⢠std temp (standard temper ature , St d T ) ⢠std pres (standar d pr essur e, St d P ) Phyics ⢠StefBolt (S tef a n-Boltzmann, Ï ) â¢l ight s... (speed of ligh t , c) ⢠permitti (per mittiv it y , ε 0) ⢠permeab (permeab ilit y , μ 0) ⢠acce gr... (acceleration of gr av it y , g) ⢠gravita... (gr av itation , G) Quantum ⢠Plankâs (P lank âs constant , h) ⢠Diracâs (Dir acâs, hbar ) ⢠e charge (electr onic c har ge , q) ⢠e mass (electr on mass, me) ⢠q/me ra... (q/me r atio , qme) ⢠proton m (pr oton mass , mp) ⢠mp/me r... (mp/me r atio , mpme) ⢠fine str (f ine stru ctur e, α ) ⢠mag flux (magnetic f lu x , Ï ) ⢠Faraday (F arada y , F) ⢠Rydberg (Ry dberg , ) ⢠Bohr rad (Bohr r adius , a0) ⢠Bohr mag (Bohr magneton , μ B) ⢠nuc. mag (nuc lear magneton , μ N) ⢠photon... (photon w ave length, λ ) ⢠photon... (photon f r equenc y , f0) ⢠Compt w... (Compton w av elength, λ c) R â HP 3 9gs Engl ish. book Pa ge 16 We dnes day, Dec embe r 7, 2005 11 : 24 PM
R-17 Program commands The program commands are: Category Command Aplet CHECK SELECT SETVIEWS UNCHECK Branch IF THEN ELSE END CASE IFERR RUN STOP Drawing ARC BOX ERASE FREEZE LINE PIXOFF PIXON TLINE Graphic DISPLAY â â DISPLAY â GROB GROBNOT GROBOR GROBXOR MAKEGROB PLOT â â PLOT REPLACE SUB ZEROGROB Loop FOR = TO STEP END DO UNTIL END WHILE REPEAT END BREAK Matrix ADDCOL ADDROW DELCOL DELROW EDITMAT RANDMAT REDIM REPLACE SCALE SCALEADD SUB SWAPCOL SWAPROW Print PRDISPLAY PRHISTORY PRVAR Prompt BEEP CHOOSE CLRVAR DISP DISPXY DISPTIME EDITMAT FREEZE GETKEY INPUT MSGBOX PROMPT WAIT Stat-One D O1VSTATS RANDSEED SETFREQ SETSAMPLE HP 3 9gs Engl ish. book Pa ge 17 We dnes day, Dec embe r 7, 2005 11 : 24 PM
R-18 Status messages Stat-Two DO2VSTATS SETDEPEND SETINDEP Category Command (Continued) Messag e M eaning Bad Argument Type Incorrect input for this operation. Bad Argument Value The value is out of range for this operation. Infinite Result Math exception, such as 1/0. Insufficient Memory You must recover some memory to continue operation. Delete one or more matrices, lists, notes, or programs (using catalogs), or custom (not built- in) aplets (using MEMORY ). Insufficient Statistics Data Not enough data points for the calculation. For two-variable statistics there must be two columns of data, and each column must have at least four numbers. Invalid Dimension Array argumen t had wrong dimensions. Invalid Statistics Data Need two columns with equal numbers of data values. HP 3 9gs Engl ish. book Pa ge 18 We dnes day, Dec embe r 7, 2005 11 : 24 PM
R-19 Invalid Syntax The function or command you entered does not include the proper arguments or order of arguments. The delimiters (parentheses, commas, periods, and semi-colons) must also be correct. Look up the function name in the index to find its proper syntax. Name Conflict The | (where) function attempted to assign a value to the variable of integration or summation index. No Eq uati ons Checked You must e nter and chec k an equation (Symbolic view) before evaluating this function. (OFF SCREEN) Function value, root, extremum, or intersection is not visible in the current screen. Receive Error Pro blem with data reception from another calculator. Re- send the data. Too Few Arguments The command requires more arguments than you supplied . Undefined Name The global variable named does not exist. Undefined Result The calculation has a mathematically undefined result (such as 0/0). Out of Memory You must recover a lot of memory to continue operation. Delete one or more matrices, lists, notes, or programs (using catalogs), or custom (not built- in) aplets (using MEMORY ). Message Meaning (Continued) HP 3 9gs Engl ish. book Pa ge 19 We dnes day, Dec embe r 7, 2005 11 : 24 PM
HP 3 9gs Engl ish. book Pa ge 20 We dnes day, Dec embe r 7, 2005 11 : 24 PM
W-1 L imited W arr anty HP 39gs Graphing Calculator; Warranty peri od: 12 months 1. HP war r ants to you , the end- us er cu stomer , t hat HP har dw are , acc es sor ies and su pplies w i ll be fr ee fr om def ects in mater ials and w ork manship after the date of pur chase , for the peri od spec if ied abo v e . If HP r ecei ves notice of such defects during t he war r ant y peri od, HP w ill, at its option , e ither re pair or re place pr oducts w hic h pr o v e to be defecti v e . R eplacement pr oducts ma y be either ne w or like -ne w . 2 . HP w arr ants to y ou that HP softwar e will no t fail to e x ecu te its pr ogramming ins truc tio ns after the date o f pur chase , for the per iod spec ifi ed abo v e , due to def ects in mater ial and w orkmanship w hen pr operl y installed and used . If HP recei ves noti ce of suc h def ects dur ing the w arr anty per iod , HP will r eplace softwar e media whic h does not ex ecute its pr ogr amming instruc tions due to suc h defe cts. 3 . HP does no t war r ant that the oper ation of HP pr oducts w ill be uninter rupted or er r or fr ee. If HP is unable , w ithi n a r easonable time , to r epair or r eplace an y produc t to a condition as w a r r anted, y ou will be entitled to a r ef und of the pur c hase pr ice upon pr om pt r etur n of the pr oduct w ith proo f of pur chas e . 4. HP pr oducts may con tain r emanuf a ctur ed par ts equi v alent to ne w in perfor mance or ma y hav e been sub jec t to inc iden tal us e . 5 . W arr ant y does not apply to def ects r esulting from (a) impr oper or inadequate maintenance or calibr ation, (b) soft w are , inter f acing , par ts or suppl ies not suppli ed by HP , (c) unauthori z ed modificati on or mi suse, ( d) op eratio n out sid e of t he pub lis he d en vir onmental spec ificati ons f or the pr oduct , or (e) impr oper site pr eparation o r maintenance . HP 3 9gs Engl ish. book Pa ge 1 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
W-2 6 . HP MAKE S NO O THER E XPRE S S W ARRANTY OR CONDI T ION WHET HER WRI TTEN OR OR AL . T O THE EXTENT ALL O WED B Y L OCAL LA W , ANY IMP LIED W ARRANTY OR CONDI TION OF MERCHANT ABILITY , S A T ISF A CT OR Y QU ALITY , OR FI TNE SS F OR A P AR TICUL AR P URP OSE I S LIMITED T O THE DUR A TION OF THE EXP RE S S W A RRANTY SET F OR TH ABO VE . Some countr ies , st ates or pr o v inces do not allo w limitations o n the dur ation o f an implied warr ant y , so th e abo v e limitation or e x clu sio n might n ot appl y to y ou . T his w ar r anty gi ve s y ou spec if ic legal r ights and y ou might also hav e other r igh ts that vary fr om country to country , st ate to state , or pro vince to pr ov ince . 7 . T O THE EXTENT ALL O WED B Y L OCAL L A W , THE REMEDIE S IN THIS W ARRANTY S T A TEMENT ARE Y OUR S OLE AND EX CL USIVE REMEDIE S. EX CEPT AS INDICA TED ABO VE , IN NO EVENT WILL HP OR I T S S UPP LI ER S BE LIABLE FOR L O S S OF DA T A OR F OR DIRE CT , SPE CIAL , INCIDENT AL, C ONSE QUENT IAL (INCL UDING L OS T PR OFIT OR D A T A) , OR O THER D AMA GE , WHETHER B ASED IN CONTRA CT , T OR T , OR O THERWI SE . Some countr ies , States or pro vinces do not allo w the ex clusi on or limitati on of inc idental or conseq uenti al damages, so the abo ve limit ation or e x clu sion ma y not appl y to y ou . 8. The onl y war r anties for HP pr oducts and serv ices ar e set forth in the e x pr ess w arr anty statements accompany ing such pr oducts and serv ices . HP shall not be lia ble for t echni cal or editor ial err ors or omissions contain ed herein . FOR CONSUMER TRANSACTIONS IN AUSTRALIA AND NEW ZEALAND: THE WARRANTY TERMS CONTAINED IN THIS STATEMENT, EXCEPT TO THE EXTENT LAWFULLY PERMITTED, DO NOT EXCLUDE, RESTRICT OR MODIFY AND ARE IN ADDI TION TO THE MANDATORY STATUTORY RIGHTS A PPLICABLE TO THE SALE OF THIS PRODUCT T O YOU. HP 3 9gs Engl ish. book Pa ge 2 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
W-3 Service Europe Countr y : T elephone numbers Au str ia 43-1-3 60 2 77120 3 Belgium 3 2 - 2 - 712 6 219 D e n m a r k 45 - 8 - 2 332 84 4 Ea s te r n Eu ro p e countr ies 4 20-5- 414 2 2 5 2 3 Fi n l a n d 35 - 896 40 0 09 F r ance 3 3-1- 4 99 39 006 German y 4 9-6 9-9 5 30 7103 Gr eece 4 20 -5-414 2 2 5 2 3 Holland 3 1- 2 -06 54 5 301 Italy 3 9-0 2 - 7 5419 7 8 2 No r wa y 4 7 - 63 84 9 309 P ortugal 3 51- 2 29 5 7 0 200 Spain 34 -915-64 20 9 5 S weden 4 6 -8519 9 206 5 Sw i t ze r l a n d 4 1 - 1 - 43953 58 (German) 41- 2 2 -8 2 7 8 7 80 (F renc h) 3 9-02 - 7 5419 7 8 2 (Italian) T ur ke y 4 20 -5-414 2 2 5 2 3 UK 44 - 20 7 - 4 5 80161 Cz ech R epubli c 4 20 -5- 414 2 2 5 2 3 South A fr ica 2 7 -11- 2 3 7 6 200 Lu xembour g 3 2 - 2 - 712 6 219 Other Eur opean countr ies 4 20-5- 414 2 2 5 2 3 Asia P ac ific Country : T elephone numbers A ust r alia 61-3-9 8 41-5 211 Singapor e 61-3-9 841-5 211 HP 3 9gs Engl ish. book Pa ge 3 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
W-4 P lease logon to http://www .hp.com f or t he lat est se r v ice and supp ort info rmati on .h L.Ame r ic a Country: Telephone numbers Ar gentina 0 - 810 -5 5 5-5 5 20 Bra zil Sao P aulo 3 7 4 7 - 7 7 9 9; RO T C 0 -800 -15 77 51 M e xi c o M x C i t y 5258 - 9 922; RO T C 01-800 - 4 7 2 -66 84 Ven e z u e l a 0 80 0 - 4 7 46 - 8368 Chi le 800 - 3 609 99 C o l u m b i a 9 - 8 0 0 - 1 1 4726 P eru 0 - 800 -10111 Central Ame rica & Caribb ean 1-800 - 71 1- 2 88 4 Guatemala 1-800 -99 9-51 0 5 Pu e r t o R i c o 1 - 877- 232- 0 5 89 Cos ta R ica 0 -800 -011 -0 5 2 4 N.Americ a Country : T elephon e numbers U . S. 1800-HP INVENT Ca n ad a (9 05) 20 6 - 4663 o r 800 - HP INVENT RO TC = Rest of th e co unt r y HP 3 9gs Engl ish. book Pa ge 4 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
W-5 Regulatory infor mation Federal Communications Commission Noti ce This equipment has been tested and found to comply with the limits for a Class B digital dev ice, pursuant to Part 15 of the FCC Rules. These limi ts are designed to provide reasonable protection agains t harmful interference in a residential installation. This equipment generates, uses, and can radiate ra dio frequency energy and, if not installed and used in accord ance with the instructions, may cause harmful interferenc e to radio communications. However, there is no guarante e that interference will not occur in a particula r installa tion. If this equipment does cause harmful interference to radio or television reception, which can be determined by turning the equipment off and on, the user is encouraged to try to correct the inter ference by one or more of the follo wing measures: ⢠Reorient or relocate the receiving antenna. ⢠Increase the separation be tween the equipment and the receiver. ⢠Connect the equipment into an outlet on a circuit different from that to which the receiver is connected. ⢠Consult the dealer or an exp erienced radio or television technician for help. Modifications The FCC requires the user to be notified that any changes or modifications made to this device that are not expressly approved by Hewlett-Packard Company may void the user's authority to operate the equipment. Cables Connecti ons to this device mu st be made with shielded cables with metallic RFI/EMI connector hoods to maintain compliance with FCC rules and regulations. Declaration of Conformity for Products Marked with FCC Logo, United States Only This device complies with Pa rt 15 of the FCC Rules. Operation is subject to the following two condi tions: (1) this device may not cause harmful interference, and (2) this device must accept any interference received, including interference that may cause undesired operation. For questions regarding your product, contact: Hewlett-Packard Company P. O. Box 692000, Mail Stop 530113 HP 3 9gs Engl ish. book Pa ge 5 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
W-6 Houston, Texas 77269-2000 Or, call 1-800-474-6836 For questions regarding this FCC declarati on, contact: Hewlett-Packard Company P. O. Box 692000, Mai l Stop 510101 Houston, Texas 77269-2000 Or, call 1-281-514-3333 To identify this produc t, refer to the part, series, or model number found on the product. Canadian Notice This Class B digital apparatus meets all requ irements of the Canadian Interference-Causing Equipment Regulations. Avis Canadien Cet ap pareil numé ri que de la classe B r especte toutes l es e x igences du Règlement sur le matériel br ouil leur du Can ad a . European Union Regulatory Notice This product complies with the following EU Directives: ⢠Low Voltage Directive 73/23/EEC ⢠EMC Directive 89/336/EEC Compliance with these direct ives implies conformity to applicable h armonized European standa rds (European Norms) which are listed on the EU Declaration of Conformity issued by Hewlett- Packard for this product or product family. This compliance is indicated by the following conformity marking placed on the product: Japanese Notice ã ã®è£ ç½®ã¯ã æ å ±å¦çè£ ç½®çé»æ³¢é害èªä¸»è¦å¶å è°ä¼ ï¼VCCIï¼ ã®åº æºã« åº ã¥ ã 㯠㩠㹠B æ å ±æè¡è£ ç½® 㧠ã ã ã ã®è£ ç½®ã¯ã 家åºç°å¢ 㧠使ç¨ã ã ã 㨠ã ç®ç 㨠ã 㦠ã ã¾ ã ãã ã ã® è£ ç½®ã 㩠㸠㪠ã ã 㬠ã 㸠㧠㳠å ä¿¡æ© ã« è¿æ¥ ã ã¦ ä½¿ç¨ ã ã ã 㨠ã å ä¿¡ é 害ãå¼ãèµ· ã ã ã 㨠ã ã ã ã¾ã ã å ã æ± ã 説ææ¸ ã« å¾ ã£ ã¦ æ£ ã ã å ã æ± ã ã ã 㦠ã ã ã ãã Th is markin g is v alid f or non- T ele- com prodcts and E U harmoniz ed T elecom product s (e.g . Bluetooth). xxxx* Th is mark ing is v alid f or E U non- harmoni zed T elecom pr oducts. *Notified body number (used only if applicable - r efer to the product label) HP 3 9gs Engl ish. book Pa ge 6 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
W-7 Korean Notice Disposal of Waste Equipment by Users in Private Household in the European Union This symbol on the product or on its packaging indicates that this product must not be disposed of with your other household waste. Instead, it is your responsibility to dispose of your waste equipment by handing it over to a designated collection point for the recycling of waste electrical and electronic equipment. The separate collection and recycling of your waste equipment at the time of disposal will help to conserve natural resources and ensure that it is recycled in a manner that protects human health and the environment. For more information about where you can drop off your waste equi pment for recycling, please contact your local city office, yo ur household waste disposal service or the sh op where you purchased the product. HP 3 9gs Engl ish. book Pa ge 7 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
HP 3 9gs Engl ish. book Pa ge 8 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
I-1 Index A absolute value 13-5 add 13-3 algebraic entry 1-19 alpha characters typing 1-6 alphabetical so rting 19-6 angle measure 1-10 in statistics 10-12 setting 1-11 animation 17-5 creating 17 -5 annunciators 1-3 Ans (last answer) 1-24 antilogarithm 13-4, 13-9 aplet attaching notes 19-4 clearing 19-3 copying 19-4 definition of R-1 deleting 19-6 Function 13-21 Inference 11-1 key 1-4 library 19-6 Linear Solver 8-1 opening 1-16 Parametric 4-1 Polar 5-1 receiving 19-5 resetting 19-3 sending 19-4 , 19-5 Sketch view 17-1 Solve 7-1 sorting 19-6 statistics 10-1 transmitting 19-5 Triangle Solver 9-1 aplet commands CHECK 18-14 SELECT 18-14 SETVIEWS 18-17 UNCHECK 18-17 aplet variables definition 14 -1 , 14-8 in Plot view 18-32 new 14-1 aplet views canceling operations in 1-1 changing 1-19 note 1-18 Numeric view 1-17 Plot view 1-16 sketch 1-18 split-screen 1-17 Symbolic view 1-16 arc cosecant 13-20 arc cosine 13-4 arc cotangent 13-19 arc secant 13-20 arc sine 13-4 arc tangent 13-5 area graphical 3-10 interactive 3-10 variable 18-32 arguments with matrices 15-10 attaching a note to an aplet 17-1 a sketch to an aplet 17-3 auto scale 2-14 axes plotting 2-7 variable 18-32 B bad argument R-18 bad guesses error message 7-7 batteries R-4 box-and-whisker plot 10-16 branch commands CASE...END 18-18 IF...THEN...ELSE...END 18-18 IFERR...THEN...ELSE 18-18 branch structures 18-1 7 build your own table 2-19 HP 3 9gs Engl ish. book Pa ge 1 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
I-2 C calculus operat ions 13-7 catalogs 1-30 chronological sorting 19-6 circle dra wing 17-4 clearing aplet 19-3 character s 1-22 display 1-22 display history 1-25 edit line 1-22 lists 16-6 plot 2-7 cobweb graph 6-1 coeffi cients polynomial 13-11 columns changing position 18-25 combinations 13-12 commands aplet 18-14 branch 18-17 definition of R-1 drawing 18-19 graphic 18-21 loop 18-23 print 18-26 program 18-4, R-17 stat-one 18-30 stat-two 18-30 with matrices 15-1 0 complex number functions 13-5, 13-16 conjugate 13-7 imaginary pa rt 13-7 real p art 13-7 complex numbers 1-29 entering 1-29 math functions 13-7 storing 1-29 confide nce in tervals 11-15 conjugate 13-7 connecting data points 10-1 9 variable 18-32 via infrar ed 19-5 via serial cable 19-5 via USB cable 19-5 connectivity kit 19-4 constant? error message 7-7 constants e 13-8 i 13-8 maximum real number 13-8 minimum real number 13-8 physical 1-8, 13-25, R-16 program R-15, R-16 contrast decreasing disp lay 1-2 increasing display 1-2 conversi ons 13-8 coordinate display 2-9 copying display 1-22 graphics 17-6 notes 17-8 programs 18-8 correlation coefficient 10-17 CORR 10-17 statistical 10-15 cosecant 13-20 cosine 13-4 inverse hyperbolic 13-9 cotangent 13-2 0 covariance statistical 10-15 creating aplet 19-1 lists 16-1 matrices 15-3 notes in Notepad 17-6 programs 18-4 sketches 17-3 critical value(s) displayed 11-4 cross product vector 15-11 curve fitting 10-12, 10-17 D data set definition 10-8 date, setting 18-28 debugging programs 18-7 decimal changing format 1-10 scaling 2-14, 2-15 decreasing display contrast 1-2 HP 3 9gs Engl ish. book Pa ge 2 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
I-3 definite integral 13-6 deleting aplet 19-6 lists 16-6 matrices 15-5 programs 18-9 statistical data 10-11 delimiters, programming 18-1 derivatives definition of 13-6 in Function aplet 13-22 in Home 13-21 determinant square matrix 15-11 differentiation 13-6 display 18-21 adjusting contrast 1-2 annunciator line 1-2 capture 18-21 clearing 1-2 date and time 18-28 element 15-5 elements 16-4 engineering 1-10 fixed 1-10 fraction 1-10 history 1-22 line 1-23 matrices 15-5 parts of 1-2 printing contents 18-26 rescaling 2-13 scientific 1-10 scrolling through history 1-25 soft key labels 1-2 standard 1-10 divide 13-3 drawing circles 17-4 keys 17-4 lines and boxes 17-3 drawing commands ARC 18-19 BOX 18-20 ERASE 18-20 FREEZE 18-20 LINE 18-20 PIXOFF 18-20 PIXON 18-20 TLINE 18-20 E e 13-8 edit line 1-2 editing matrices 15-4 notes 17-2 programs 18-5 Editline Program catalog 18-2 editors 1-30 eigenvalues 15-11 eigenvectors 15-11 element storing 15-6 E-lessons 1-12 engineering number format 1-11 equals for equations 13-17 logical test 13-19 equations solving 7- 1 erasing a line in Sketch view 18-20 error messages bad guesses 7-7 constant? 7-7 exclusive OR 13-1 9 exiting views 1-19 exponent fit 10-13 minus 1 13-10 of value 13-17 raisin g to 13-5 expression defining 2-1, R-1 entering in HOME 1-19 evaluating in aplets 2-3 literal 13-18 plot 3-3 extremum 3-10 F factorial 13-12 FastRes variable 18-32 fit a curve to 2VAR da ta 10-17 choosing 10-12 defining your own 10-13 fixed number format 1-10 HP 3 9gs Engl ish. book Pa ge 3 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
I-4 font size change 3-8, 17-5 forecasting 10-20 fraction number format 1-11 full-precision display 1-10 function analyze graph with FCN tools 3-4 definition 2-2, R-1 entering 1-19 gamma 13-12 intersection point 3-5 math menu R-13 slope 3-5 syntax 13-2 tracing 2-8 Function aplet 2-20, 3-1 function variables area 18-32 axes 18-32 connect 18-32 fastres 18-32 grid 18-33 in menu map R-7 indep 18-3 3 isect 18-34 labels 18-34 Recent er 18-3 4 root 18-34 ycross 18-37 G glossary R-1 graph analyzing statistical data in 10 -19 auto scale 2-14 box-and-whisker 10-16 capture cu rrent display 18-21 cobweb 6-1 compar ing 2-5 connected points 10-17 defining the independent variable 18-36 drawing axes 2-7 expressions 3-3 grid points 2-7 histogr am 10-15 in Solve aplet 7-7 one-var iable stat istics 10-18 overlayin g 2-15 scatter 10-15, 10-17 split-sc reen view 2-14 splitting into plot and close-up 2-13 splitting into plot and table 2-13 stairsteps 6-1 statistical data 10-15 t values 2-6 tickmarks 2-6 tracing 2-8 two-variable statistics 10-18 Graphic commands â GROB 18-21 DISPLAY â 18-21 GROBNOT 18-21 GROBOR 18-21 GROBXOR 18-22 MAKEGROB 18-22 PLOT â 18-22 REPLACE 18-22 SUB 18-22 ZEROGROB 18-23 graphics copying 17-6 copying into Sketch view 17-6 storing and recalling 17-6 , 18-21 H histogram 10-15 adjusting 10-16 range 10-18 setting min/max values for bars 18-33 width 10-18 history 1-2, 18-26 Home 1-1 calculating in 1-19 display 1-2 evaluating expressions 2-4 reusing lines 1-23 variables 14-1, 14-7, R-6 horizontal zoom 18-38 hyperbolic maths functions 13-10 hyperbolic trigonometry ACOSH 13-9 ALOG 13-9 ASINH 13-9 ATANH 13-9 COSH 13-9 EXP 13-10 HP 3 9gs Engl ish. book Pa ge 4 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
I-5 EXPM1 13-10 LNP1 13-10 SINH 13-9 TANH 13-9 hypothesis alternative 11-2 inference tests 11-8 null 11-2 tests 11-2 I i 13-8 implied multiplication 1-20 importing graphics 17-6 notes 17-8 increasing display contrast 1-2 indefinite integral using symbolic variables 13-23 independent values adding to table 2-18 independent variable defined for Tracing mode 18-33 inference confidence intervals 11-15 hypothesis tests 11-8 One-Proportion Z-Interval 11-17 One-Sample Z-Interval 11-15 One-Sample Z-Test 11-8 Two-Proportion Z-Interval 11-1 7 Two-Proportion Z-Test 11-11 Two-Sample T-Inte rval 11-19 Two-Sample Z-Interval 11-16 infinite result R-18 infrared transmission of aplets 19-5 initia l guess 7-5 input forms resetting default values 1-9 setting Modes 1-11 insufficient memory R-18 insufficient statistics data R-18 integer rank matrix 15-12 integer scaling 2-14, 2-15 integral definite 13-6 indefinite 13-23 integration 13-6 interpreting intermediate guesses 7-7 intersect ion 3-11 invalid dimension R-18 statistics data R-18 syntax R-19 inverse hyperbolic cosi ne 13-9 inverse hy perbolic functions 13-1 0 inverse hyperbolic sine 13-9 inverse hyperbolic tangent 13-9 inverting matrices 15-8 isect v ariable 18-34 K keyboard editing keys 1-5 entry k eys 1-5 inactive keys 1-8 list keys 16-2 math functions 1-7 menu keys 1-4 Notepad keys 17-8 shifted keystrokes 1-6 L labeling axes 2-7 parts of a sketc h 17-5 letters, typing 1-6 library, managing aplets in 19-6 linear fit 10-13 Linear Solver aplet 8-1 list arithmetic with 16-7 calculate sequence of e lements 16-8 calculating product of 16-8 composed from differences 16-7 concatenating 16-7 counting elements in 16-9 creating 16-1, 16-3, 16 -4 , 16- 5 deleting 16-6 deleting list items 16-3 displaying 16-4 displaying list elements 16-4 editing 16-3 finding statistical values in list ele- ments 16-9 HP 3 9gs Engl ish. book Pa ge 5 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
I-6 generate a series 16-8 list function syntax 16-6 list variables 16-1 returning position of element in 16-8 revers ing orde r in 16-9 sending and receiving 16-6 sorting elements 16-9 storing elements 16- 1 , 16-4 , 16-5 storing one element 16-6 logarithm 13-4 logarithmic fit 10-13 functions 13-3 logical operators AND 13-19 equals (logical test) 13-19 greater than 13-19 greater than or equal to 13-19 IFTE 13-19 less than 13-18 less than or equal to 13-18 NOT 13-19 not equal to 13-1 9 OR 13-19 XOR 13-19 logistic fit 10-13 loop commands BREA K 18-24 DO...UNTIL...END 18-23 FOR I= 18-24 WHILE...REPEAT...END 18-23 loop func tions ITERATE 13-10 RECUR SE 13-10 summation 13-11 low battery 1-1 lowercase letters 1-6 M mantissa 13-15 math functions complex number 13-7 hyperbolic 13-10 in menu map R-13 keyboard 13-3 logical operators 13-18 menu 1-7 polynomial 13-11 probability 13-12 real-number 13-13 symbolic 13-17 trigonometry 13-19 MATH menu 13-1 math operations 1-19 enclosing arguments 1-21 in scientific notation 1-20 negative numbers in 1-20 matrices adding rows 18-24 addition a nd subtraction 15-6 arguments 15-10 arithmetic operations in 15-6 assembly from vectors 15-1 changing row position 18-25 column norm 15-10 comma 16-7 commands 15-10 condition number 15-11 create identity 15-13 creating 15-3 creating in Home 15-5 deleting 15-5 deleting columns 18-24 deleting rows 18-24 determinant 15-11 display eigenvalues 15-11 displaying 15-5 displaying matrix elements 15-5 dividing by a square matrix 15-8 dot product 15-11 editing 15-4 extracting a portion 18-25 finding the trace of a square ma- trix 15-13 inverting 15-8 matrix calculations 15-1 multiplying and dividing by scalar 15-7 multiplying by vector 15-7 multiplying row by value and add- ing result to second row 18-25 multiplying row number by value 18-25 negating elements 15-8 opening Matrix Editor 18-28 raised to a power 15-7 redimension 18-25 replacing portion of matrix or vec- tor 18-25 sending or receiving 15-4 HP 3 9gs Engl ish. book Pa ge 6 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
I-7 singular value decomposition 15-13 singular values 15-13 size 15-12 spectral norm 15-13 spectral radius 15-13 start Matrix Editor 18-24 storing elements 15-3, 15-5 storing matrix elements 15-6 swap column 18-25 swap row 18-25 transposing 15-13, 15-14 variables 15-1 matrix functions 15-10 COLNORM 15-10 COND 15-11 CROSS 15-11 DET 15-11 DOT 15-11 EIGENVAL 15-11 EIGENVV 15-11 IDENMAT 15-11 INVERSE 15-11 LQ 15-11 LSQ 15-11 LU 15-12 MAKEMAT 15-12 QR 15-12 RANK 15-12 ROWNORM 15-12 RREF 15-12 SCHUR 15-12 SIZE 15-12 SPECNORM 15-13 SPECRAD 15-13 SVD 15-13 SVL 15-13 TRACE 15-13 TRN 15-13 maximum real number 1-22, 13-8 memory R-18 clearing all R-3 organizing 14-9 out of R-19 saving 1-25, 19-1 viewing 14-1 menu lists searching 1-8 minimum real number 13-8 mixed fraction format 1-11 modes angle measure 1-10 decimal mark 1-11 number format 1-10 multiple solutions plotting to find 7-7 multiplication 13-3 implied 1-20 N name c onfli ct R-19 naming programs 18-4 natural exponential 13-3, 13-10 natural log plus 1 13-10 natural logarithm 13-3 negation 13-5 negative numbers 1-20 no equations checked R-19 Normal Z-distribution, confidence i n- tervals 11-15 note copying 17-8 editing 17-2 importing 17-8 printing 18-26 viewing 17-1 writing 17-1 Notepad 17-1 catalog keys 17-7 creating notes 17-6 writing in 17-6 nrng 2-6 n th root 13-6 null hypothesis 11-2 number format engine ering 1-11 fixed 1-10 fraction 1-11 in Solve aplet 7-5 mixed fraction 1-11 scientific 1-10 Standard 1-10 numeric prec ision 14-9 Numeric view adding values 2-18 automatic 2-16 build your ow n table 2-19 display defining function for col- umn 2-17 HP 3 9gs Engl ish. book Pa ge 7 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
I-8 recalc ulating 2-18 setup 2-16, 2-19 O off automatic 1-1 power 1-1 on/cancel 1-1 One-Proportion Z-Interval 11- 17 One-Sample T-Interval 11-18 One-Sample T-Test 11-12 One-Sample Z-Interval 11-15 One-Sample Z-Test 11-8 order of precedence 1-21 overlaying plots 2-15 , 4-3 P Ï 13-8 paired columns 10-11 parametric variables axes 18-32 connect 18-32 grid 18-33 in menu map R-8 indep 18-3 3 labels 18-34 recent er 18-3 4 ycross 18-37 parentheses to close arguments 1-21 to specify order of operation 1-21 pause 18-30 permutations 13-12 pictures attaching in Sketch view 17-3 plot analyzing statistical data in 10 -19 auto scale 2-14 box-and-whisker 10-16 cobweb 6-1 compar ing 2-5 connected points 10-17, 10-19 decimal scaling 2-14 defining the independent variable 18-36 drawing axes 2-7 expressions 3-3 grid points 2-7 histogr am 10-15 in Solve aplet 7-7 integer scaling 2-14 one-variable statistics 10-18 overlay plot 2-13 overlaying 2-15, 4-3 scaling 2-13 scatter 10-15, 10 -17 sequence 2-6 setting up 2-5, 3-2 split-sc reen view 2-14 splitting 2-14 splitting into plot and close-up 2-13 splitting into plot and table 2-13 stairsteps 6-1 statistical data 10-15 statistics parameters 10-18 t values 2-6 tickmarks 2-6 to capture current display 18-21 tracing 2-8 trigonometric scaling 2-14 two-variable statistics 10-18 plotting resolution and tracing 2-8 plot-view variables area 18-32 connect 18-32 fastres 18-32 function 18-32 grid 18-33 hmin/hmax 18-33 hwidth 18-33 isect 18-34 labels 18-34 recenter 18-34 root 18-34 s1mark-s5mark 18-35 statplot 18-35 tracing 18-33 umin/umax 18-36 ustep 18-36 polar variables axes 18-32 connect 18-32 grid 18-33 in menu map R-9 indep 18-33 labels 18-34 recenter 18-34 ycross 18-37 HP 3 9gs Engl ish. book Pa ge 8 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
I-9 polynomial coefficients 13-11 evaluation 13-11 form 13-11 roots 13-12 Taylor 13-7 polynomial functions POLYCOEF 13-11 POLYEVAL 13-11 POLYF ORM 13-11 POLYROOT 13-12 ports 19-5 position argument 18 -21 power (x raised to y) 13-5 preced ence 1-22 predicted values statistical 10-20 print contents of display 18-26 name and contents of variable 18-26 object in history 18-26 variables 18-26 probability functions ! 13-12 COMB 13-12 RANDOM 13-13 UTPC 13-13 UTPF 13-13 UTPN 13-13 UTPT 13-13 program commands 18-4 copying 18-8 creating 18-4 debugging 18-7 deleting 18-9 delimiters 18-1 editing 18-5 naming 18-4 pausing 18-30 printing 18-26 sending and receiving 18-8 structured 18-1 prompt commands beep 18-26 create choose box 18-26 create input form 18-29 display item 18-27 display message box 18-29 halt program execution 18-30 insert line breaks 18-29 prevent screen display being up- dated 18-28 set date and time 18-28 store ke ycode 18-29 Q quadratic extre mum 3-6 fit 10-13 function 3-4 quotes in program names 18-4 R random numbers 13-13 real number maximum 13-8 minimum 13-8 real p art 13-7 real-number functions 13-13 % 13-15 %CHANGE 13-15 %TOTAL 13-16 CEILING 13-13 DEGtoRAD 13-14 FNROOT 13-14 HMSto 13-14 INT 13-15 MANT 13-15 MAX 13-15 MIN 13-15 MOD 13-15 RADtoDEG 13-16 ROUND 13-16 SIGN 13-16 TRUNCATE 13-16 XPON 13-17 recalc ulation fo r table 2-18 receive error R-19 receiv ing aplet 19-5 lists 16-6 matrices 15-4 programs 18-8 redra wing table of numbers 2-17 reduced row eche lon 15-12 HP 3 9gs Engl ish. book Pa ge 9 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
I-10 regression analysis 10-17 fit models 10-13 formula 10-12 user-defined fit 10-13 relative error statistical 10-18 resetting aplet 19-3 calculator R-3 memory R-3 result copying to edit line 1-22 reusing 1-22 root interac tive 3-10 n th 13-6 variable 18-34 root-finding displaying 7-7 interac tive 3-9 operat ions 3-10 variables 3-10 S S1mark-S5mark variables 18-35 scaling automatic 2-14 decimal 2-10, 2-14 integer 2-10, 2-14, 2-15 options 2-13 resetting 2-13 trigonometric 2-14 scatter plot 10-15, 10 -17 connected 10-17 , 10-1 9 SCHUR decomposition 15-12 scientific number format 1-10, 1-20 scrolling in Trace mode 2-8 searching menu lists 1-8 speed searches 1-8 secant 13-20 sending aplets 19-4 lists 16-6 programs 18-8 sequence definition 2-2 sequence variables Axes 18-32 Grid 18-33 in menu map R-10 Indep 18-33 Labels 18-34 Recenter 18-34 Ycross 18-37 serial port connectivity 19-5 setting date 18-28 time 18-28 sign reversal 7-6 sine 13-4 inverse hyperbolic 13-9 singular value decomposition matrix 15-13 singular values matrix 15-13 sketches creating 17-5 creating a blank graphic 18-23 creating a set of 17-5 erasing a line 18-20 labeling 17-5 opening view 17-3 sets 17-5 storing in graphics variable 17-5 slope 3-10 soft key labels 1-2 solve error messages 7-7 initial guesses 7-5 interpreting intermediate guesses 7-7 interpreting results 7-6 plotting to find guesses 7-7 setting number format 7-5 solve variables axes 18-32 connect 18-32 fastres 18-32 grid 18-33 in menu map R-11 indep 18-33 labels 18-34 recenter 18-34 ycross 18-37 sorting 19-6 aplets in alphab etic order 19-6 HP 3 9gs Engl ish. book Pa ge 10 We dnes day, Dec embe r 7, 2005 11 : 24 PM
I-11 aplets in chronological order 19-6 elements in a list 16-9 spectral norm 15-1 3 spectral radius 15-13 square root 13-5 stack history printing 18-26 stairsteps graph 6-1 standard number format 1-10 statistics analysis 10-1 analyzing plots 10-19 angle mode 10-12 calculate one-variable 18-30 calculate two-variable 18-30 data set variables 18-41 data structure 18-41 define one-variable sample 18-30 define two-va riable data setâs de- pendent column 18-31 define two-variable data setâs in- dependent column 18 -31 defining a fit 10-12 defining a regression model 10-12 deleting data 10-11 editing data 10-10 frequency 18-30 inserting data 10-11 plot type 10-18 plotting data 10-15 predicted values 10-20 regression curve (fit) models 10-12 saving data 10-10 sorting data 10-11 specifying angle setting 10-12 toggling between one-variable and two-variable 10-12 tracing plots 10-19 troubleshooting with plots 10-19 zooming in plots 10-19 statistics variables Axes 18-32 Connect 18-32 Grid 18-33 Hmin/Hmax 18-33 Hwidth 18-33 in menu map R-12 Indep 18-33 Labels 18-34 Recenter 18-34 S1mark-S5mark 18-35 Ycross 18-37 step size of independent variabl e 18-37 storing list elements 16-1, 16-4, 16-5 , 16-6 matrix elements 15-3 , 15-5, 15-6 results of calculation 14-2 value 14-2 strings literal in symbolic operations 13-18 subtract 13-3 summation function 13-11 symbolic calculations in Function aplet 13-21 defining expressions 2-1 differentiation 13-21 displaying definitions 3-8 evaluating variab les in view 2-3 setup view for statistics 10-12 symbolic functions | (where) 13-18 equal s 13-17 ISOLATE 13-17 LINEAR? 13-17 QUAD 13-18 QUOTE 13-18 Symbolic view defining expressions 3-2 syntax 13-2 syntax errors 18-7 T table navigate around 3-8 numeric values 3-7 numeric view setup 2-16 tangent 13-4 inverse hyperbolic 13-9 Taylor polynomial 13-7 θ rng 2-6 θ step 2-6 tickmarks for plotting 2-6 time 13-1 4 HP 3 9gs Engl ish. book Pa ge 11 We dnes day, Dec embe r 7, 2005 11 : 24 PM
I-12 setting 18-28 time, converting 13-14 times sign 1-20 tmax 18-36 tmin 18-36 too few arguments R-19 tracing functions 2-8 more than one curve 2-8 not matching plot 2-8 plots 2-8 transmitting lists 16-6 matrices 15-4 programs 18-8 transposing a matrix 15-13 Triangle Solver aplet 9-1 trigono metric fit 10-13 functions 13-19 scaling 2-10, 2-14, 2-1 5 trigonometry functions ACOT 13-19 ACSC 13-20 ASEC 13-20 COT 13-20 CSC 13-20 SEC 13-20 trng 2-6 truncating values to decimal places 13-16 tstep 2-6, 18-37 Two-Pr oportion Z- Interval 11 -17 Two-Pr oportion Z- Test 11-11 Two-Sample T-Inte rval 11-19 Two-Sample T-tes t 11-14 Two-Sample Z-Interval 11-16 typing letters 1-6 U undefined name R-19 result R-19 un-zoom 2-11 upper-tail chi-squared probability 13-13 upper-tail normal probability 13-13 upper-tail Snedecorâs F 13-1 3 upper-tail studentâs t-probability 13-13 USB connectivity 19-5 user defined regression fit 10-13 V value recall 14-3 storing 14-2 variables aplet 14-1 categories 14-7 clearing 14-3 definition 14-1, 14-7, R-2 in equations 7-10 in Symbolic view 2-3 independent 18-36 local 14-1 previous result (Ans) 1-23 printing 18-26 root 18-34 root-finding 3-10 step size of independent 18-37 types 14-1, 14-7 use in calculations 14-3 VARS menu 14-4 , 14-5 vectors column 15-1 cross product 15-11 definition of R-2 views 1-18 configuration 1-18 definition of R-3 W warning symbol 1-8 where command ( | ) 13-18 X Xcross variab le 18-3 7 xrng 2-6 Y Ycross variable 18-37 yrng 2-6 HP 3 9gs Engl ish. book Pa ge 12 We dnes day, Dec embe r 7, 2005 11 : 24 PM
I-13 Z Z-Interval 11-15 zoom 2-17 axes 2-12 box 2-9 center 2-9 examples of 2-11 factors 2-13 in 2-9 options 2-9, 3-8 options within a table 2-17 out 2-9 redrawing table of numbers op- tions 2-17 square 2-10 un-zoom 2-11 within Numeric view 2-17 X-zoom 2-9 Y-zoom 2-10 HP 3 9gs Engl ish. book Pa ge 13 We dnes day, Dec embe r 7, 2005 11 : 24 PM
HP 3 9gs Engl ish. book Pa ge 14 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Notice REG ISTER Y OUR PRODU CT A T: w ww .register .hp.com TH IS MANUAL AND ANY EXAMPLE S CONT AI NED HEREIN ARE PRO VIDED â AS ISâ AND ARE SUBJECT T O CHANG E WITHOUT NO TICE. HEWLETT-P A CKARD COMP ANY MAKES N O W AR- R ANTY O F ANY KIND WITH REGARD T O TH IS MANU AL , INC L UDING , B UT NO T L IMI TE D T O , TH E IM P LIE D W AR RAN T IES OF MERCHANT ABI LI T Y , NON -INFR ING EMENT AN D FITNESS FOR A P ARTI C ULA R PURPOSE . HEWLET T -P ACKARD CO . SHAL L NO T BE LI ABLE FO R ANY ERRORS OR FOR IN CIDE NT AL OR CONSEQ UENT IAL D AMAGES IN CONNEC TION WI TH T HE FU RNISHING, PE RF ORMA NCE, OR USE OF THI S MANU AL OR THE EXAMPLES CONT AI NED HEREIN. © 19 9 4 -19 9 5, 19 9 9- 2000, 200 3, 2006 He w lett-P ack ar d De v el opment Compan y , L .P . Repr oducti on , adaptati on , or tr anslation o f this manual is pr ohibited w ithout pr ior w ritten per missi on of He w lett -P ack ard C ompan y , e x cept as allo w ed under the cop yr ight law s. Hew let t-P ack ar d Compan y 16 3 9 9 W es t Ber nar do Dri v e MS 8- 600 San Di ego , CA 9 212 7 -18 9 9 US A Pr inting His tory E ditio n 2 December 2003 Ed i t io n 3 J u n e 2 0 05 titl e.fm Pa ge i i T hurs day, July 13, 200 6 1 0:29 AM
i Contents Preface Manual conventions ............. ................ ................ ................. P-1 Notice .. ................. ................ ................ ................. ............. P-2 1 Getting started On/off, cancel o perations ........ ................ ................. ............. 1-1 The display ............... ................ ................. ................ .......... 1-2 The keyboard ...... ................ ................ ................ ............. .... 1-3 Menus ...... ................ ................ ................. ............. ............. 1-8 Input forms ... ................ ................. ................ ................ ....... 1-9 Mode settings ............ ................ ................. ............. ........... 1 -10 Setting a mode ...... ................ ................. ................ ........ 1-11 Aplets (E-lessons) ........... ................. ................ ................ ..... 1-12 Aplet library ............ ................. ................ ................ ..... 1-16 Aplet views ........... ............. ................ ................. ........... 1 -16 Aplet view c onfiguration............. ................ ................ ..... 1-18 Mathematical calcu lations ............... ................ ................ ..... 1-19 Using fraction s ..... ................ ............. ................ ................ .. 1-25 Complex numbers ................... ................ ................. ........... 1 -29 Catalogs and editors ............... ................ ................. ........... 1-30 2 Aplets and their views Aplet views .. ................ ............. ................. ................ .......... 2-1 About the Symbolic view ............... ................ ................ .... 2-1 Defining an expressio n (Symbo lic view) ....................... ....... 2-1 Evaluating exp ressions ........... ................. ................ .......... 2-3 About the Plot view ... ................. ................ ................ ....... 2-5 Setting up the plot (Plot view setup) ........... ................ .......... 2-5 Exploring the graph ...... ................ ................ ................ .... 2-7 Other views fo r scaling and splitting the graph ................ .. 2-13 About the numeric view .............. ................ ................ ..... 2-16 Setting up the table (Numeric view setup) ........ ................ .. 2-16 Exploring the table of numbers .... ................... ................ .. 2-17 Building your o wn table of numbers ... ................ ............... 2-19 âBuild Your Ownâ me nu keys ......... ................ ................ .. 2-20 Example: plotting a circle . ................ ................ ............... 2 -20 Ente rpri seTO C.fm Pa ge i Wed nesd ay, May 3, 2 006 5:01 PM
ii 3 Function aplet About the Function aple t ................. ............. ................ .......... 3-1 Getting started w ith the Function aplet ................ ................ 3-1 Function aplet intera ctive analysis ....... .................... ................ 3-9 Plotting a pie cewise-defined function ..... ................ ........... 3-12 4 Parametric aplet About the Parametric aplet ... ................. ................ ................ 4-1 Getting started w ith the Parametric aplet ................ ............. 4-1 5 Polar aplet Getting started w ith the Polar aplet ............ ................... .......... 5-1 6 Sequence aplet About the Sequence aplet ............... ................ ................. ...... 6-1 Getting started w ith the Sequence aplet .............. ................ 6-1 7 Solve aplet About the Solve aplet .. ................ ................ ................ .......... 7-1 Getting started w ith the Solve aplet .... ................ ................ 7-2 Use an initial gues s ..... ................ ................ ................ .......... 7-5 Interpreting results ...... ................ ................ .................... ...... 7-6 Plotting to find gue sses ...... ................ ................. ................ ... 7-7 Using variables in equations ........... ................ ................. .... 7-10 8 Linear Solver aplet About the Linear Solver aplet ....... ................ ................ .......... 8-1 Getting started w ith the Linear Solver aplet ....... ................... 8-1 9 Triangle Solve aplet About the Triangle Solver aplet .... ................ ................ .......... 9-1 Getting started w ith the Triangle Solver aplet ............. .......... 9-1 10 Statistics aplet About the Statistics aplet ........... ................ ................ ........... 1 0-1 Getting starte d with the Statistic s aplet ......... ................. .... 10-1 Entering and editing s tatistical data .... .................... .............. 10-6 Defining a regression model ....... ................ ................... 10-12 Computed st atistics .............. ................. ................ ............ 10-14 Plotting .................. ................. ................ ................ ......... 10-15 Plot types .............. ................ ............. ................ ......... 10-16 Fitting a curve to 2VAR data ......... .................... ............ 10-17 Setting up the plot (Plot setup view) ................. ............... 10-18 Trouble -shooting a plot .... ................. ................ ............ 10-19 Ente rpri seTO C.fm Pa ge i i We dnes day, May 3, 2006 5:0 1 PM
iii Exploring the graph ...... ................ ................ ................ 10-19 Calculating pre dicted values ....... ................ ................ ... 10-20 11 Inference aplet About the Inference a plet ...... ................ ................ ............... 11-1 Getting started with the Inference aplet ..................... ........ 11-1 Importing samp le statistics fro m the Statistics a plet ...... ........ 11-4 Hypothesis tes ts ... ................ ................ ................ ............... 11-8 One-Sample Z-Test .... ................. ................ ................ ..... 11-8 Two-Samp le Z-Test .... ................. ................ ............. ........ 11-9 One-Propo rtion Z-Test ....... ................ ................ ............. 11-10 Two-Proportion Z-Te st .... ................ ................ ................ 11-11 One-Sample T-Test ........ ................ ................ ................ 11-12 Two-Samp le T-Test ................. ................. ............. ......... 11 -14 Confidence intervals ... ................ ................. ................ ...... 11-1 5 One-Sample Z-Interval ... ................ ................ ................ 11-15 Two-Samp le Z-Interval ......... ............. ................ ............. 1 1-16 One-Propo rtion Z-Interval .. ................ ................ ............. 1 1-17 Two-Proportion Z-Interval ............... ................ ................ 11-17 One-Sample T-Interval ............ ................. ................ ...... 11-18 Two-Samp le T-Interval ................. ................ ................ ... 11-19 12 Using the Finance Solver Backgroun d ..... ................. ................ ................ ............. ..... 12-1 Performing TVM calculations ........... ................ ................ ..... 12-4 Calculating Amo rtizations ........... ................ ................ ..... 12-7 13 Using mathematical functions Math functions ........ ................ ................ ................. ........... 1 3-1 The MATH menu ....................... ................ ................... .. 13-1 Math functions by category ............. ................... ................ .. 13-2 Keyboard function s ................ ................. ................ ........ 13-3 Calculus functions .................. ................. ............. ........... 1 3-6 Complex number fu nctions...... ................. ................ ........ 13-7 Constants ............. ................ ................. ................ ........ 13-8 Conversions ....... ............. ................ ................ ............... 13-8 Hyperbolic trigon ometry ... ................ ................ ............... 13-9 List functions ......... ................ ................. ................ ...... 13-1 0 Loop functions .............. ................ ................ ................ 1 3-10 Matrix functions . ................ ................ ................. ......... 13-11 Polynomial fu nctions . ................. ................ ................ ... 13-11 Probability functions .. ................. ................... ................ 13-12 Real-number functio ns ......... ................ ................. ......... 13 -13 Ente rpri seTO C.fm Pa ge i ii W edne sday , Ma y 3, 200 6 5: 01 P M
iv Two-variab le statistic s ............. ............. ................ ......... 13-17 Symbolic functions .... ................... ................. ............... 13-17 Test functions ......... ................ ............. ................ ......... 13-18 Trigonom etry functions ......... ................ ................ ......... 13-19 Symbolic calc ulations .. ................ ................ ................ ...... 13 -20 Finding derivative s ....... ................ ................. ............... 13-21 Program consta nts and physical constants ..................... ...... 13 -24 Program constants ..... ................ ................ ................. .. 13-24 Physical constants .. ................ ................ ................ ...... 13-25 14 Variables and memory management Introduction ..... ................ ................ ................. ................ . 14-1 Storing and recalling variables .. ................ ................ ........... 14-2 The VARS menu ...... ................. ................ ................ ........... 14-4 Memory Manager ............ ................ ................. ................ . 14-9 15 Matrices Introduction ..... ................ ................ ................. ................ . 15-1 Creating an d storing matrices ...... ................ ................ ........ 1 5-2 Working with matrices ... ................ ................ ................. .... 15-4 Matrix arithmetic . ................ .................... ................ ........... 15-6 Solving systems of linear equa tions .... ................ .............. 15-8 Matrix functions a nd commands ......... .................... ............ 15-10 Argume nt conventions ......... ................ ................ ......... 15-10 Matrix functio ns ..... ................ ............. ................ ......... 15-10 Examples ..... ................. ............. ................ ................ ...... 15 -13 16 Lists Displaying and editing lis ts .......... ................... ................. .... 16-4 Deleting lists ............. ................ ................ ................. .... 16-6 Transmitting lists. ................. ................... ................ ........ 16-6 List functions. ................. ................ ................ ................. .... 16-6 Finding stat istical values for list ele ments........ ................ ........ 1 6-9 17 Notes and sketches Introduction ..... ................ ................ ................. ................ . 17-1 Aplet note view .......... ................ ................ ................ ........ 17-1 Aplet ske tch view.... ................. ................ ................ ........... 17-3 The notepad ....................... ................. ................ .............. 17-6 18 Programming Introduction ..... ................ ................ ................. ................ . 18-1 Program catalog ............. ................. ................ .............. 18-2 Creating an d editing programs .... ................ ................ ........ 18-4 Ente rpri seTO C.fm Pa ge i v We dnes day, May 3, 2006 5:0 1 PM
v Using programs ............ ................. ................ ................ ..... 18-7 Customiz ing an aplet ............ ................ ............. ................ .. 18-9 Aplet naming convention .................. ................ ............. 1 8-10 Example ......... ................ ................ ................ ............. 18-10 Programming co mmands....... ................ .................... ......... 18 -13 Aplet commands ................ ................ ................. ......... 18 -14 Branch commands ................. ................. ................ ...... 18-17 Drawing commands ................... ................ ................ ... 18-19 Graphic co mmands ......... ................ ................ ............. 1 8-21 Loop commands .... ................ ................. ............. ......... 18-23 Matrix commands ..... ................. ................ ................ ... 18-24 Print commands ............... ................ ................ ............. 18-26 Prompt commands . ................ ................. ................ ...... 18-2 6 Stat-One and Stat-Two c ommands ............... ................... 18-30 Stat-Two commands ............ ................ ................. ......... 18 -30 Storing and re trieving variables in programs . ................... 1 8-31 Plot-view variables ........... ................ ................ ............. 1 8-32 Symbolic-vie w variables ... ................ ................ ............. 1 8-39 Numeric-view variables ....... .................... ................ ...... 18-41 Note variable s ......... ................. ................ ................ ... 18-44 Sketch variables ....... ............. ................. ................ ...... 18-44 19 Extending aplets Creating new aplets based on ex isting aplets .... ................ ..... 19-1 Using a cus tomized aplet .............. ................ ................ .. 19-3 Resetting an a plet.... ................ ................ ................. ........... 1 9-3 Annotating an aplet with notes .............. ................ ............... 19-4 Annotating an aplet with sketches .......... ................ ............... 19-4 Downloading e-lessons from the web ... ................ ................ .. 19-4 Sending and re ceiving aplets ................ ................ ............... 19-4 Sorting items in the aplet library menu list ................... ........... 1 9-6 Refere nce information Glossary ......... ................. ................ ................ ................ .... R-1 Resetting the HP 39gs .............. ................ ................. ............. R-3 To erase all memo ry and reset defau lts...... ................ .......... R-3 If the calculator does not turn on ........... ................. ............. R-4 Operating details . ................ ................ ................ ................. R-4 Batteries ............... ................ ................. ................ .......... R-4 Variables ........ ............. ................. ................ ................ ....... R-6 Home variable s .................. ............. ................ ................. R-6 Function aplet variables .............. ................... ................ .... R-7 Parametric aplet variables ................ ................ ................. R-8 Ente rpri seTO C.fm Pa ge v Wed nesd ay, May 3, 2 006 5:01 PM
vi Polar aplet variable s .............. ................ ................ .......... R-9 Sequence aplet variables ........... ................ ................. .... R-10 Solve aplet variab les .............. ................ ................ ........ R-11 Statistic s aplet variables ................ ................. ............. .... R-12 MATH menu ca tegories .. ................ ................ ................. .... R-13 Math functions .......... ................ ................ ................. .... R-13 Program constants ........... .................... ................ ........... R-15 Physical Constants .......... ................. ................ .............. R-16 Program commands ........ ................. ................ .............. R-17 Status message s ............ ................ ................ ................. .... R-18 Limited Warranty Service ... ................. ................ ................ ................. ..... W-3 Regulatory info rmation............ ................ .................... ..... W-5 Index Ente rpri seTO C.fm Pa ge v i We dnes day, May 3, 2006 5:0 1 PM
P-1 Pr eface The HP 39gs is a feature-rich graphing calculator. It i s also a powerful mathematics learning tool. The HP 39gs is designed so that you can use it to explore mathematical functions and their prop erties. You can get more information on the HP 39gs from Hewlett-Packardâs Calcula tors web site. You can download customized aplets from the web site and load them onto your calculator. Customized aplets are special applications developed to p erform certain functions, and to demonstrate mathematical concepts. Hewlett Packardâs Calculators web site can be fou nd at: http://www.hp.com /calculators Manual conventions The following conventions are used in this manual to represent the keys that y ou press and the menu options that you choose to perform the described operations. ⢠K e y pr es se s ar e r epre sen ted a s fo llo w s: , , , et c. ⢠Shift k e y s, that is the k ey f uncti ons that y ou access b y pr essing the k ey f i rst , a r e r epres ented as fo llo w s: CLEAR , MODES , ACO S , et c. ⢠Numbers and letters ar e repr esented normally , as fo llo w s: 5, 7 , A, B , etc . ⢠Menu opti ons , that is, the f uncti ons that y ou se lect using the men u k e y s at the top of the k e yp ad ar e r epre sented as follo ws: , , . ⢠Input form f ields and choose list items are r epre sented as f ollo ws: Function , Polar , Parametric ⢠Y our entr ie s as the y appear on the command line or w ithin input for ms ar e r epr esented as f ollo w s: 2*X 2 -3X 5 HP 3 9gs Engl ish. book Pa ge 1 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
P-2 Notice This manual and any examples contained herein are provided as-is and are subject to change without notice. Except to the extent prohibit ed by law, Hewlett-Packard Company makes no express or implied warranty of any kind with regard to this manu al and specific ally disclaims the implied warranties and conditions of merchantability and fitness for a particular purpose and Hewlett-P ackard Company shall not be liable for any errors or for incidental or consequential damage in connection with the furnishing, performance or use of this manual and the examples herein. © 1994â1995, 1999 â2000, 2003â2006 Hewlett- Packard Developme nt Company, L.P. The programs that control your HP 39gs are copyrighted and all rights are reserved. Reproduction, adaptation, or translation of those programs without prior wri tten permission from Hewlett-Packard Company is also prohi bited. Pref ace. fm Page 2 Thur sday, Jul y 13 , 20 06 10:3 3 AM
Getting started 1-1 1 Get ting star ted On/off, cancel operations To turn on Press to turn on the calculator. To cancel When the calculator is on, the key cancels the current operation. To turn off Press OFF to turn the calculator off. To save power, the calculator turns itself off after sev eral minutes of inactivity. All stored and displayed information is saved. If you see the (( ⢠)) annunciator or the Low Bat message , then the calculator needs fresh batteries . HOME HOME is the calculatorâs home view and is common to all aplets. If you want to perform calculations, or you want to quit the current activity (such as an aplet, a program, or an editor), press . All mathematical functions are available in the HOME. The name of t he current aplet is displayed in the title of the home view. Protective cover The calculator is provided with a slide cover to protect the display and keyb oard. Remove the cover by graspi ng both sides of it and pu lling down. You can re verse the slide cover and slide it onto the back of the calculator. this will help prevent you losing the cover while you are using the calculator. To prolong the life of the calculator, always place the cover over the display an d keyboard when you are not using the calculator. HP 3 9gs Engl ish. book Pa ge 1 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
1-2 Getting started The display To adjust the contrast Simultaneously press and (or ) to increase (or decrease) the contrast. To clear the display ⢠Pr ess CANCEL to c lear the edit line . ⢠Pr ess CLEA R to c lear the edit line and the display history . Parts of the display Menu key or soft key labels. T he labels f or the menu k e ys â cur r ent meaning s. is the label f or the fir st menu k ey in this pi ctur e. âPr ess â means to pr ess the fir st menu k e y , that is , the leftmost top-r ow k ey on the calc ulator k e yboar d. Edit line. The line of c urrent entry. History. The HOME display ( ) shows up to four lines of history: the mo st recent input and output. Older lines scroll off the top of the display but are retained in memory. Title. The name of the current aplet is displayed at the top of the HOME view. RAD, GRD, DEG specify whether Radians, Grads or Degr ees angle mode i s set for HOME. The î and î symbols indicate whether there is more history in the HOME displa y. Press the and to scroll in the HOME display. NOTE This userâs guide contains images from the HP 39gs and does not display the menu key label. Title Edit line History Menu k e y labels HP 3 9gs Engl ish. book Pa ge 2 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Getting started 1-3 Annunciators . Annunciators are sy mbols that appear above the title bar and give you important status information. The keyboard Menu keys Annunciator Description Shift in effect for next keystrok e. To cancel, press again. α Alpha in effect for next keystroke. To cancel, press again. (( ⢠)) Low battery power. Busy. Data is being transferred via infrared or cable. HP 39g s Graphing Calc ulator Menu Key Labels Menu Keys Cursor Aplet Control Alpha Key Shift Key Enter Keys Key Keys HP 3 9gs Engl ish. book Pa ge 3 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
1-4 Getting started ⢠On the calc ulator k e y boar d, the top r ow of k ey s are called menu k ey s . The ir meanings depend on the conte xtâthatâs w h y their to ps ar e blank . The menu k e y s ar e sometimes called â so ft k ey s â . ⢠T he bottom line o f the displa y sho ws the la bels f or the menu k ey s â c u r r ent meanings . Aplet control keys The aplet control keys are: K e y Meaning Displays the Symbolic view for the current aplet. See âSymbolic viewâ on page 1-16. Displays the Plot view for the current aplet. See âPlot viewâ on page 1-16. Displays the Numeric vi ew for the current aplet. See âNumeric vie wâ on page 1-17. Displays the HOME view. See âHOMEâ on page 1 -1. Displays the Aplet Library menu. See âAplet libraryâ on page 1-1 6. Displays the VIEWS menu. See âAplet viewsâ on page 1-16. HP 3 9gs Engl ish. book Pa ge 4 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Getting started 1-5 Entry/Edit keys The entry and edit keys are: K e y Meaning ( CANCEL ) Cancels the current operation if the calculator is on by pressing . Pressing , then OFF turns the calculator off. Accesses the function printed in blue above a key. Returns to the HOME view, for performing calculations. Accesses the alphabetical characters printed in o range below a key. Hold down to enter a string of characters . Enters an input or exec utes an operation. In calculations, acts like â=â. When or is present as a menu key, acts the same as pressing or . Enters a negative number. To enter â25, press 25. Note: this is not the same operation that the subtract button performs () . Enters the independen t variable by inserting X , T, θ, or N into the edit line, depending on the current active aplet. Deletes the character under the cursor. Acts as a backsp ace key if the cursor is at the end of the line. CLEAR Clears all data on the screen. On a settings screen, for example Plot Setup, CLEAR returns all settings to their default values. , , , Moves the cursor around the display. Press first to move to the beginning, end, top or bottom. HP 3 9gs Engl ish. book Pa ge 5 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
1-6 Getting started Shifted ke ystrokes There are two shift keys that you use to access the operations and characters printed above the keys: and . CHARS Displays a menu of all a vailable characters. To type one, use the arrow keys to highlight it, and press . To select multiple character s, select each and press , then press . K e y Meaning (Continued) Key D e sc ri p t io n Press the key to access the operations printed in blue above the keys. F or insta nce, to a ccess th e Modes screen, press , then press . ( MODES is labe led in blue above the key). You do not need to hold down when you press HOME. This acti on is depicted in this manual as âpress MODES .â To cancel a shift, press again. The alphabetic keys are also shifted keystrokes. For instance, to type Z, press Z. (The letters are printed in orange to the lower right of each key.) To cancel Alpha, pre ss again. For a lower case letter, press . For a string of letters, hold down while typing. HP 3 9gs Engl ish. book Pa ge 6 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Getting started 1-7 HELPWITH The HP 39gs built-in help is available i n HOME only. It provides syntax help for bu ilt-in math functions. Access the HELPWITH command by pressing SYNTAX and then the math key for which you require syntax help. Example Pr ess SYNTAX Note: R emo ve the left par enthesis fr om built -in func tio ns such a s sine , cosine , and tangen t bef or e inv oking the HELPWI TH command . Math keys HOME ( ) is the place to do calculations. Keyboard keys. The most common operations are available from the keyboard, such as the arithmetic (like ) and trigonometric (like ) functions. Press to complete the operation: 256 displays 16. . MATH menu. Press to open the MATH menu. The MATH menu is a comprehensive list of math functions that do not appear on the keyboard. It also includes categories for all other functions and constants. The functions are grouped by category, ranging in alphabetical order from Calculus to Trigonometry. ⢠T he arr ow k e y s sc r oll thr ough the list ( , ) and mo ve fr om the category lis t in the left column to the ite m list in the r ight column ( , ) . ⢠Pr ess to ins ert the selected command onto the edit line . ⢠Pr ess to dismis s the MA TH menu w ithout selec ting a command . ⢠Pr essing displa ys the lis t of Pr ogram Co nstants . Y ou can use these in pr ogr ams that yo u de ve l op. HP 3 9gs Engl ish. book Pa ge 7 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
1-8 Getting started ⢠Pr essing displa y s a menu of ph y sical constants f r om the f ields o f chemistry , phy sic s, and quantum mec hanic s. Y ou can u se these consta nts in calc ulati ons . (See âPh ysi cal constants â on page 13- 2 5 f or mor e inf or mation .) ⢠Pr essing tak es yo u to the beginning of the MA TH men u . See âMath functions by categoryâ on page 13-2 for details of the math functions. HINT When using the MA TH menu , or any men u on the hp 3 9gs, pr essing an alpha ke y tak es y ou strai ght to the fir st menu option beg inning with that alpha char acte r . W ith this method , you do n ot need to pr ess fir st . Jus t pre ss the ke y that corr esponds to the commandâs beginning alpha char acter . Program commands Pressing CMDS displays the list of Program Commands. See âProgramming commandsâ on page 18 -13. Inactive keys If you press a key that does not operate in the curre nt context, a warning symbol like this appears. There is no beep. Menus A menu offers you a choice of items. Menus are displayed in one or two columns. ⢠Th e a rrow i n t h e displa y means more items belo w . ⢠Th e a rrow i n t h e display means mor e items abov e. To search a menu ⢠Pr ess or to sc ro ll thr ough the list . If y ou pr es s or , you âll go all the wa y to the end or the beginning o f the list . Highligh t the item y ou wa nt to select , then pres s (or ) . ! HP 3 9gs Engl ish. book Pa ge 8 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Getting started 1-9 ⢠If ther e are tw o columns , the left column sho ws gener al categori es and the righ t column sho w s spec ifi c cont ents w ithin a catego ry . Hi ghligh t a gener al category in the left column, then hi ghligh t an item in the r ight column. T he list in the ri ght column c hanges w hen a diffe r ent catego ry is highligh ted . Pr ess or w hen yo u hav e highlighted y our sele ction. ⢠T o speed-s earc h a list , t y pe the f irst le tter of the w ord . F or ex ample , to f ind the Matr i x category in , pr ess , the Alpha âM â k e y . ⢠T o go up a page , y ou can pr ess . T o go do w n a page, pr ess . To cancel a menu Press (for CANCEL ) or . This cancels the current operation. Input forms An input form shows several fields of information for you to examine and specify. After highlighting the field to edit, you can enter or edit a number (or expression). Yo u can also select options from a list ( ). Some input forms include items to check ( ). See below for examples input forms. Reset input form values To reset a field to its default values in an input form, move the cursor to that field and press . To reset all default field values in the input form, press CLEAR . HP 3 9gs Engl ish. book Pa ge 9 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
1-10 Getting started Mode settings You use the Modes inpu t form to set the modes for HOME. HINT Although the numeric setting in Modes affects only HOME, the angle setting controls HOME and the current aplet. The angle setting selecte d in Modes is the angle setting used in both HOME and current aplet. To further configure an aplet, you u se the SETUP keys ( and ). Press MODES to access the HOME MOD ES input form. Setting Options Angle Measure Angle values are: Degrees . 360 degrees in a circ le. Radians . 2 Ï radians in a circle. Grads . 400 grads in a ci rcle. The angle mode you set is the angle setting used in both HOME and the current aplet. This is done to ensure that trigonometric calculations done in the current aplet and HOME give the same result. Number Format The number format mode you set is the number format used in both HOME and the current aplet. Standard . Full-precision display. Fixed . Displays results rounded to a number of decimal places. Example: 123.456789 becomes 123.46 in Fixed 2 format. Scie ntific . Displays results with an exponent, one digit to the left of the decimal point, and the specified number of decimal places. Example: 123.456789 becomes 1.23E2 in Scientific 2 format. HP 3 9gs Engl ish. book Pa ge 10 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Getting started 1-11 Setting a mode This example demonstrates how to change the angle measure from the default mode, radians, to degrees for the current aplet. The procedure is the s ame for changing number format and decimal mark modes. 1. Pr ess MODES t o o p e n t h e H O M E M O D ES i n p u t form. Engineering . Displays result wit h an exponent that is a multiple of 3, an d the specified number of significant digits beyond the first one. Example: 123.456E7 becomes 1.23E9 i n Engineering 2 format. Fraction . Displays results as fractions based on the spec ified number of decimal places. Examples: 123.456789 becomes 123 in Fraction 2 format, and .333 bec omes 1/3 and 0.14285 7 becomes 1/7. See âUsing fractionsâ on page 1-25. Mixed Fraction . Displays results as mixed fractions based on the specified number of decimal places. A mixed fraction has an integer part and a fractional part. Examples: 123.456789 becomes 123 16/35 in Fraction 2 format, and 7÷ 3 returns 2 1/3. See âUsing fractionsâ on page 1-25. Decimal Mark Dot or Comma . Displays a number as 12456.98 (Dot mode) or as 12456,98 (Comma mode). Dot mode uses commas to separate elements in lists and matrices, and to separate function arguments. Comma mode uses periods (dot) as separators in these contexts. Setting Options (Continued) HP 3 9gs Engl ish. book Pa ge 11 We dnes day, Dec embe r 7, 2005 11 : 24 PM
1-12 Getting started T he cur sor (hi ghlight) is in the fir st f ield , Angle Measur e . 2 . Pr ess to display a li st of choic es. 3. P re s s to select Degrees , and pres s . The angle mea sur e changes to degrees . 4. Pr ess to r eturn to HOME . HINT Whenever an input form has a list of choices for a field, you can press to cycle through them instead of using . Aplets (E-lessons) Aplets are the application environments where you explore different classes of mathematical operations. You select the aplet that you want to work with. Aplets come from a variety of sources: ⢠Built-in the HP 3 9gs (initial pur chase). ⢠Aplets cr eated by sa v ing ex isting aplets, w hic h hav e been modified , with spec ific conf igurati ons. See âCr eating new aplets bas ed on ex isting aplets â on page 19-1. ⢠Do wnloaded fr om HPâs Calc ulators w eb site. ⢠Cop ied f r om another calculato r . Aplets are stored in the Aplet library. See âAplet libraryâ on page 1-16 for further information. You can modify configuration settings for the gr aphical, tabular, and HP 3 9gs Engl ish. book Pa ge 12 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Getting started 1-13 symbolic views of the aplets in the following table. See âAplet view configurationâ on page 1 -18 for further information. In addition to these aplets, wh ich can be u sed in a variety of applications, the HP 39 gs is supplied with two teaching aplets: Quad Explorer and Trig Explorer. You cannot modify configurati on settings for these aplets. A great many more teachi ng ap lets can be found at HPâs web site and other web sites created by educators, together with accompanying documentation, often with student work sheets. These ca n be download ed free of Aplet name Use this aplet to e xplore: Function Real-valued, rectangular functions y in terms of x . Example: . Inference Confidence intervals and Hypothes is tests based on the Normal and Students-t distributions. Parametric Parametric relations x and y in terms of t . Example: x = cos(t ) and y = sin(t ). Polar Polar functions r in terms of an angle θ . Example: . Sequence Sequence functions U in terms of n , or in terms of previous terms in the same or another sequence, such as and . Example: , and . Solve Equations in one or more real-valued variables. Example : . Finance Time Value of Money (TVM) calculatio ns. Linear Solver Solutions to sets of two or three linear equations. Triangle Solver Unknown values for the lengths and angles of triangles. Statistics One-variable ( x ) or two-variable ( x and y ) statistical data. y 2 x 2 3 x 5 = r 24 θ () cos = U n 1 â U n 2 â U 1 0 = U 2 1 = U n U n 2 â U n 1 â = x 1 x 2 x â2 â = HP 3 9gs Engl ish. book Pa ge 13 We dnes day, Dec embe r 7, 2005 11 : 24 PM
1-14 Getting started charge and transferred to the HP 39gs using the provided Connectivity Kit. Quad Explorer aplet The Quad Explorer aplet is used to investigate the behaviour of as the values of a , h and v change, both by manipulati ng the equation and seeing the change in the graph, and by manipulating the grap h and seein g the chang e in the eq uation. HINT More detailed documentation, and an accompanying student work sheet can be found at HPâs web site. Pr ess , selec t Quad Explorer , and then press . The Qu ad Exp lorer aplet opens in mode, in which the arro w keys, the and keys, and the key are used to change the shape of the graph. This changing shape is reflected in the equation displayed at the top right corner of the screen, while the original graph is retained for comparison. In this mode the graph controls the equation. It is also possible to have the equation control the graph. Pressing displays a sub-expression of your equation. Pressing the and key moves between sub- expressions, while pressing the and key changes their values. Pressing allows t he user to select whether all three sub-expressions will be explored at once or only one at a time. A button is provided to evaluate the studentâs knowledge. Pres sing displays a target q uadratic graph. The student must manipulate the equationâs parameters to make the equation match the target graph. When a student feels that they have correctly chosen the parameters a button eva luates the answer and provide f eedback. A n button is provided for those who give up! ya x h () 2 v = HP 3 9gs Engl ish. book Pa ge 14 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Getting started 1-15 Trig Explorer aplet The Trig Explorer aplet is used to investigate the behaviour of the graph of as the values of a , b , c and d change, both by manipulating the equation and seeing the change in the graph, or by manipulating the graph and seeing the change in the equation. Press , select Trig Explorer , and then press to display the screen shown right. In this mode, the graph controls the equation. Pressing the and keys transforms the graph, with these transformations reflected in the equation. The button labelled is a toggle between and . When is chosen, the âpoint of controlâ is at the origin (0,0) and the a nd keys control vertical and horizontal transformations. When is chosen the âpoint of controlâ is on the fir st extremum of the graph (i.e. for the sine graph at . The arrow keys change the amplitude and frequency of the graph. This is most easily seen by experimenting. Pressing displays the equation at the top of the screen. The equation is controlled by the graph. Pressing the and keys moves from parameter to parameter. Pressing the o r key changes the parameterâs values. The default angle setting for this aplet is radians. The angle setting can be changed to degrees by pressing . ya b x c () d sin = Origin Ï 21 , â () Extremum HP 3 9gs Engl ish. book Pa ge 15 We dnes day, Dec embe r 7, 2005 11 : 24 PM
1-16 Getting started Aplet library Aplets are stored in the Aplet library. To open an aplet Press to display the Aplet library menu. Se lect the aplet and press or . From within an aplet, you can return to HOME any time by pressing . Aplet views When you have configured an aplet to define th e relation or data that you want to explore, you c an display it in differ ent views. Here are illu strations of the three major aplet views (Symbolic, Plot, and Numeric), the six supporting aplet views (from the VIEWS menu ), and the two user-defined views (Note and Ske tch). Note : some apletsâsuch as the Linear Solver aplet an d the Triangle Solver apletâonly have a single view, the Numeric view. Symbolic view Pres s to display the apletâs S ymbolic v iew . Y ou use this v ie w to define the func tio n(s) or equati on(s) that y ou w ant to explor e. See âAbout the Symbolic viewâ on page 2-1 f or further information. Plot view Pr ess to display the apletâ s P l ot v ie w . In this v iew , the f uncti ons that y ou hav e defined ar e displa y ed gr aphi cally . See âAbout the Plot viewâ on page 2-5 for further information. HP 3 9gs Engl ish. book Pa ge 16 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Getting started 1-17 Numeric view Press to display the apletâs Numeric view. In this view, the functions that you have defined are displayed in tabular format. See âAbout the numeric viewâ on page 2 -16 for further information. Plot-Table view The VIEWS menu contains the Plot-Table view. Select Plot-Table Splits the screen into the plot and the data table. See âOther views for scaling and splitting the graphâ on page 2-13 for futher information. Plot-Detail view The VIEWS menu contains the Plot-Detail view. Select Plot-Detail Splits the screen into the plot and a close-up. See âOther views for s caling and splitting the graphâ on page 2-13 for further information . Overlay Plot view The VIEWS menu contains the Overlay Plot view. Select Overlay Plot Plots the current expression(s) without erasing any pre-existing plot(s). See âOther views for s caling and splitting the graphâ on page 2-13 for further information . HP 3 9gs Engl ish. book Pa ge 17 We dnes day, Dec embe r 7, 2005 11 : 24 PM
1-18 Getting started Note view Press NOTE to display the apletâs note view. This note is transferred with the aplet if it is sent to another calculator or to a PC. A note view contains text to supplement an aplet. See âNotes and ske tchesâ on page 17-1 for further information. Sketch view Press SKETCH to dis play the ap letâs sk etch view . Display s pictur es to supplement an aplet. See âNotes and sketchesâ on page 17-1 for further information. Aplet view configuration You use the SETUP keys ( , and ) to configure the aplet. For example, press SETUP - PLOT ( ) to display the input form for setting the apletâs plot settings. Angle measure is controlled using the MODES view. Plot Setup Press SETUP - PLOT . Sets parameters to plot a graph. Numeric Setup Press SE TUP - NUM . Sets parameters for building a table of numeric values. Symbolic S etup This vi ew is only availa ble in the Statistics aplet in mode, where it plays an important role in choosing data models. Press SETUP - SYMB . HP 3 9gs Engl ish. book Pa ge 18 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Getting started 1-19 To change views Each view is a separate environment. To change a view, select a different view by pressing , , keys or select a view from the VIEWS menu. To change to HOME, press . You do not explicitly close the current view, you just ente r another oneâlike passing from one room into another in a house. Data that you enter is automatically saved as you enter it. To save aplet configuration You can save an aplet config uration that you ha ve used, and transfer the aplet to other HP 39gs calculators. See âCreating new aplets based on existing apletsâ on page 19-1. Mathematical calculations The most commonly used math operations are available from the keyboard. Access to the rest of the math functions is via the MATH menu ( ). To access programming commands, press CMDS . See âProgramming commandsâ on page 18-13 for further information. Where to start The home base for the calculator is the HOME view ( ). You can do all calculations here, and you can access all operations. Entering expressions ⢠Enter an e xpre ssion int o the HP 3 9gs in the same left- to -ri ght order that y ou w ould wr i te the e x pr essi on. T his is ca lled algebr aic entry . ⢠T o enter functions, select the k e y or MA TH menu i tem fo r that functi on . Y ou can also enter a func tion b y using the A lpha k e y s to spell o ut its name . ⢠Pr ess to e valuate the e x pr ession y ou have in the edit line (w her e the blinking c urso r is) . An exp re ss io n can contain numbers , func tions , and va riab le s. HP 3 9gs Engl ish. book Pa ge 19 We dnes day, Dec embe r 7, 2005 11 : 24 PM
1-20 Getting started Example Calculate : Long results If the result is too long to fit on the display line, or if you want to see an expression in textbook format, press to highlight it and then press . Negative numbers Type to start a negative number or to insert a negative sign. To raise a negative number to a power, enclose it in parentheses. For example, (â5) 2 = 25, whereas â5 2 = â25. Scientific notation (powers of 10) A number like or is written in scientific notation , that is, in terms of powers of ten. This is simpler to work with than 50000 or 0.0 00000321. To enter numbers like these, use EEX . (This is easier than using 10 .) Example Calculate 4 EEX 13 6 EEX 23 3 EEX 5 Explicit and implicit multiplication Implied multiplication takes pl ace when two operands appear with no op erator in between. If you enter AB , fo r example, the result is A*B . 23 2 14 8 â 3 â --------------------------- - 45 () ln 23 14 8 3 45 51 0 4 Ã 3.21 10 7 â Ã 41 0 13 â Ã () 61 0 23 Ã () 31 0 5 â Ã ---------------------------------------------------- HP 3 9gs Engl ish. book Pa ge 20 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Getting started 1-21 However, for clarity, it is better to include the multiplication sign where you expect multiplication in an expression. It is clearest to enter AB as A*B . HINT Implied multiplication will not always work as expecte d. For example, entering A(B 4 ) will not give A*(B 4) . Instead an error message is displayed: âI nvalid User Functionâ. This is because the calculator interprets A(B 4) as meaning âevaluate function A at the value B 4 â, and function A does not exist. When in doubt, insert the * sign manually. Parentheses You need to use parentheses to enclose arguments for functions, such as SIN(45). You can omit the final parenthesis at the end of an edit line. The calculator inserts it automatically. Parentheses are also important in specifying the order of operation. Without parentheses, the HP 39gs calculates according to the order of algebraic precedence (the next topic). Following are some examples using parentheses. Entering ... Calculates... 45 Ï si n (45 Ï) 45 Ï sin (45) Ï 85 9 85 9 85 9 Ã 85 9 Ã HP 3 9gs Engl ish. book Pa ge 21 We dnes day, Dec embe r 7, 2005 11 : 24 PM
1-22 Getting started Algebraic precedence order of evaluation Functions within an expression are evaluated in the following order of precedence. Functions with the same precedence are evaluated in order from left to right. 1. E xpressions w it hin parenthe ses. Neste d p ar ent heses ar e ev aluated fr om inner to outer . 2 . Pr efi x functio ns, suc h as S IN and L OG . 3 . P ostfi x func tions , such a s ! 4. P o we r functi on , ^, NTHROO T . 5 . Negati on , multiplicati on , and di v ision . 6 . Additio n and subtr action . 7. A N D a n d N O T . 8. OR and X OR. 9 . L eft ar gument of | ( w her e) . 10. E quals, =. Largest and smallest numbers The smallest number the HP 39gs can represent is 1Ã1 0 â499 (1Eâ499). A sma ller result is displayed as zero. The largest number is 9.99999999999 à 10 499 (1E499). A greater result is displayed as this num ber. Clearing numbers ⢠c lears the char acter under the cu rso r . When the c urso r is positio ned after the last c har acte r , delete s the char acter t o the left of the c ursor , that is, it performs the same as a bac kspace ke y . ⢠CANCEL ( ) clear s the edit line . ⢠CLEAR c lears all inpu t and outpu t in the display , in c luding th e display history . Using previous results The HOME display ( ) shows you four lines of input/output history. An un limited (except by memory) number of previous lines c a n be displayed by scrolling. You can retrieve and reuse any of these values or expressions. Output Last output Inpu t Last input Edit line HP 3 9gs Engl ish. book Pa ge 22 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Getting started 1-23 When you highlight a previous input or result (by pressing ), the and menu labels appear. To copy a previous line Highlight the line (press ) and press . The number (or expression) is co pied into the e dit line. To reuse the last result Press AN S (last answer) to put the last result from the HOME display into an expression. ANS is a variable that is updated each time you press . To repeat a previous line To repeat the very last line, just press . Otherwise, highlight the line (press ) first, and then press . The highlighted expression or nu mber is re-entered. If the previous line is an expression c ontaining the ANS , the calculation is repeated it eratively. Example See how ANS retrieves and reuses the last result (50), and updates ANS (from 50 to 75 to 100). 50 25 You can use the last result as the first expression in the edit line without pressing ANS . Pressing , , , or , (or other operators th at require a preceding argument) automatically enters ANS before the operator. You can reuse any other expression or valu e in the HOME display by highlighting the expression (using the arrow keys), then pressing . See âUsing previous resultsâ on page 1-22 for more details. The variable ANS is different from the numbers in HOMEâs display history. A value in ANS is stored internally with the full precision of the calculated result, whereas the displayed numbers match the display mode. HP 3 9gs Engl ish. book Pa ge 23 We dnes day, Dec embe r 7, 2005 11 : 24 PM
1-24 Getting started HINT When you retrieve a number from ANS , you obtain the result to its full precision. When you retrieve a number from the HOMEâs display history, you obtain exactly what was displaye d. Pressing evaluates (or re-evaluates) the last input, whereas pressing ANS copies the last result (as ANS ) into the edit line. Storing a value in a variable You can save an answer in a variable and use the variable in later calculation s. There are 27 variables available for storing real values. These are A to Z and θ . See Chapter 14, âVariables and memory managementâ for more information on variables. For example: 1. P erf orm a calc ulation . 45 8 3 2 . Stor e the result in the A vari ab le. A 3 . P er f or m another calc ulatio n using the A v ari able . 95 2 A HP 3 9gs Engl ish. book Pa ge 24 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Getting started 1-25 Accessing the display history Pressing enables the highlight bar in the display history. While the highlight bar is active, the following menu and keyboard keys are very useful: Clearing the display history Itâs a good habit to cl ear the display his tory ( CLEAR ) whenever you have finish e d working in HOME. It saves calculator memory to clear the display history. Remember that all your previous inputs and results are saved until you clear them. Using fractions To work with fractions in HOME, you set the number format to Fraction or Mixed Fraction , as follows: Setting Fraction mode 1. In HOME , open the HO ME MODE S input f orm . MODES Key F u n c t i o n , Scrolls through the di splay history. Copies the highlighted expression to the position of the curso r in the edit line. Displays the current expre ssion in standard mathematical for m. Deletes the highlighted expression from the display history , unless there is a cursor in the edit line. CLEAR Clears all lines of display history and the edit line. HP 3 9gs Engl ish. book Pa ge 25 We dnes day, Dec embe r 7, 2005 11 : 24 PM
1-26 Getting started 2 . Select Number Format , pr ess to display the optio ns, and hi ghlight Fract ion or Mixed Fraction . 3 . Pr ess to sele ct the Number F ormat option , then mo ve to the prec ision value field . 4. Enter the prec ision v alue that yo u want to us e , and pr ess to set the pr ecisi on . Pres s to retur n to HOME . See âSetting fr action pr ec i si on â belo w for mor e infor mation . Setting fraction precision The fraction precision setting determines the pr ecision in which the HP 39gs converts a decimal value to a fraction. The greater the precision value that is set, the closer the fraction is to the decimal value. By choosing a precision o f 1 you are saying that the fraction only has to match 0.234 to at least 1 decimal place (3/13 is 0.23076... ). The fractions used are found using the technique of continued fractions. When converting recurring decimals this can be important. For ex ample, at precision 6 the decimal 0.6666 becomes 3333/5 000 (6666/10000) wher eas at precision 3, 0.6666 becomes 2/3 , which is probably what you would want. For example, when converting .234 to a fraction, the precis ion value has th e following effect: HP 3 9gs Engl ish. book Pa ge 26 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Getting started 1-27 ⢠Pr ec ision set to 1: ⢠Pr ec ision set to 2 : ⢠Pr ec ision set to 3: ⢠Pr ec ision set to 4 Fraction calculations When entering fractions: ⢠Y ou use the ke y to separate the numerator part and the denominator par t of the fr action. ⢠T o ent er a mi xed f r acti on , f or e x ample , 1 1 / 2 , y ou enter it in the f ormat (1 1 / 2 ). For example, to perform the following calc ulation: 3(2 3 / 4 5 7 / 8 ) 1. Set the Number f or mat mode to Fraction or Mixed Fraction and sp ec ify a pr ec ision v alue of 4. In this ex ample, w eâll select Fraction as our form a t.) MODES Select Fraction 4 HP 3 9gs Engl ish. book Pa ge 27 We dnes day, Dec embe r 7, 2005 11 : 24 PM
1-28 Getting started 2. E n t e r t h e c a l c u l a t i o n . 32 3 45 7 8 Note: Ensur e y ou ar e in the HOME v ie w . 3 . E valuat e the calc ulation . Note that if you had selected Mixed Fraction instead of Fraction as the Number format, the answer would have been expressed as 25 7/8. Converting decimals to fractions To convert a decimal value to a fraction: 1. Set the number f ormat mode to Fraction or Mixed Fraction . 2 . Eithe r r etr ie v e the v alue fr om the Hist ory , or en ter the v alue on the command line. 3 . Pres s to conv ert the number t o a fr action . When converting a decimal to a fraction, keep the following points in mind: ⢠When con v erting a rec u r r ing dec imal to a fr acti on , set the f r actio n pr ec ision to abou t 6, and e nsur e that y ou include mor e than six dec imal places in the r ec urr ing dec imal that y ou ent er . In this e x ample , the fr action pr ecisi on is set to 6. T he top calc ulation r eturns the corr ect r esult . The bottom one does no t . ⢠T o con vert an ex act decimal to a fr action, set the fr action pr ecisi on to at lea st two mor e than the number of dec imal plac es in the dec imal . HP 3 9gs Engl ish. book Pa ge 28 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Getting started 1-29 In this e x ample , the fr action pr ec ision is s et to 6. Complex numbers Complex results The HP 39gs can return a complex number as a result for some math functions. A comp lex number appears a s an ordered pair ( x, y ), where x is the real part and y is the imaginary part. For example, entering returns (0,1). To enter complex numbers Enter the number in either of these forms , where x is the real part, y is the imaginar y part, and i is th e imagina ry constant, : ⢠( x, y ) or ⢠x iy . To enter i : ⢠pr ess or ⢠pr ess , or keys t o sel e c t Cons tant , to mo v e to the r ight column o f the menu , to sele ct i , and . Storing comp lex numbers There are 10 variables available for storing complex numbers: Z0 to Z9. To store a complex number in a variable: ⢠Enter th e complex numb er , p r ess , enter the v ari able to s tor e the number i n , and pr ess . 45 Z 0 1 â 1 â HP 3 9gs Engl ish. book Pa ge 29 We dnes day, Dec embe r 7, 2005 11 : 24 PM
1-30 Getting started Catalogs and editors The HP 39gs has several catalogs and editors. You use them to create and manipulate objects. They access features and stored values (numbe rs or text or other items) that are independent of aplets. ⢠A catalog lists items, w hich y ou can delete or tr ansmit , for e xampl e an aplet . ⢠An edito r lets you c reate or modify items and number s, for e xample a no te or a matr i x . Catalog/Editor Contents Aplet library () Aplets. Sketch editor ( SKETCH ) Sketches and diagrams, See Chapter 17, âN otes and sketchesâ. List ( LIST ) Lists. In HOME, lists are enclosed in {}. See Chapter 16, âListsâ. Matrix ( MATRIX ) One- and two-dimensional arrays. In HOME, arrays are enclosed in []. See Chapter 15, âMatricesâ. Notepad ( NOTEPAD ) Notes (short text entries). See Chapter 17, âN otes and sketchesâ. Program ( PROGRM ) Programs that you create, or associated with user-defined aplets. See Chapter 18, âProgrammingâ. HP 3 9gs Engl ish. book Pa ge 30 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Aplets and their views 2-1 2 Aplets and t heir v ie w s Aplet views This section examines the options an d functionality of the three main views for the Function, Polar, Parametric, and Sequence aplets: Symbolic, Plot, and Numeric views. About the Symbolic view The Symbolic view is the defining view for the Functi on, Parametric, Polar, and Seque nce aplets. The other views are derived from the symbolic expression. You can create up to 10 different definitions for each Function, Parametric, Polar, and Sequence aplet. You can graph any of the relations (in the same aplet) simultaneously by selecting them. Defining an expression (Symbolic view) Choose the aplet from the Aplet Library. Pr ess or to select an aplet . T he F uncti on , P ar ametri c, P olar , and Sequence aplets s tart in the S ymbolic v ie w . If the highli ght is on an e x isting expr essio n , sc r oll to an empty lineâunless y ou don ât mind wr i ting o ver the e xpr essionâ or , clear o ne line ( ) or all line s ( CLEAR ). Expr es sions ar e selected (c heck mar ked) on entry . T o deselect an e xpressi on, pr ess . All selected e xpres sions ar e plotted. HP 3 9gs Engl ish. book Pa ge 1 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
2-2 Aplets and the ir views â For a Function definiti on , e nt er an e xpr es sio n to def ine F(X) . The only independent variab le in th e ex pre ss i on i s X. â Fo r a P arametric definiti on , e nt er a pair of e xpr essi ons to def ine X(T) and Y(T) . The o nly independent v ari able in the e xpr es sions is T . â Fo r a Pol a r definiti on , e nt er an e xpr es sio n to def ine R ( θ ). T h e only independent variab le in th e ex pre ss i on i s θ . â Fo r a S eq u e n c e definiti on , e ither enter the f irst ter m , or the fi rst and second terms, for U (U1 , or ... U9 , or U0 ) . Then def i ne the n th ter m of the seq uence in ter ms of N or of the pr ior t erm s, U(Nâ1) and/or U(Nâ2) . The e xpres sions should pr oduce r eal- v alued sequences w ith integer domains . Or define the n th ter m as a non-r ec ursi ve e xpr essi on in terms o f n onl y . In this case , the calc ulator inserts the f irs t two te rms bas ed on the expr essi on that y ou def ine. â Note : Y ou w i ll hav e to enter t he second term if the hp 3 9gs is unable to calc ulate it automatically . T y picall y if U x(N) depends on U x(Nâ2) then y ou must enter U x(2) . HP 3 9gs Engl ish. book Pa ge 2 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Aplets and their views 2-3 Evaluating expressions In aplets In the Symbolic view, a variable is a symbol only, and does not represent one specif ic value. To evaluate a function in Symbolic view, press . If a function calls another function, then reso lves all references to other functions in terms of their independent variable. 1. Choo se the F unction apl et . Sele ct Function 2 . Enter the e xpr es sions in the F unction ap letâs S y mbolic vi ew . A B F1 F2 3 . Highligh t F3(X) . 4. Pr ess Note h o w the value s fo r F1(X) and F2(X) ar e sub stituted in to F3(X) . HP 3 9gs Engl ish. book Pa ge 3 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
2-4 Aplets and the ir views In HOME You can also evaluate any expression in HOME by entering it into the edit line and pressing . For example, define F4 as below. In HOME, type F4(9) and press . This evaluates the expression, substituting 9 in place of X into F4 . SYMB view keys The following table details the menu keys that you use to work with the Symbolic view. K e y Meaning Copies the highlighted expression to the edit line for editing. Press when done. Checks/unchecks the current expression (or set of expressions). Only checked expression(s) are evaluated in the Plot and Numeric views. Enters the independent variable in the Function aplet. Or, you can use the key on the keyboard. Enters the independent variable in the Parametric aplet. Or, you can use the key on the keyboard. Enters the independent variable in the Polar aplet. Or, you can use the key on the keyboard. Enters the independent variable in the Sequence aple t. Or, you can use the key on the keyboard. Displays the curren t expression in text book form. Resolves all references to other definitions in terms of va riables and evaluates all arithmetic express ions. Displays a menu for entering variable names or contents of variables. HP 3 9gs Engl ish. book Pa ge 4 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Aplets and their views 2-5 About the Plot view After entering and selecting (check marking) the expression in the Symbolic view, press . To adjust the appearance of the graph or the interval that is displayed, you can change the Plot view settings. You can plot up to ten expressions at the same time. Select the expressions you want to be plotted together. Setting up the plot (Plot view setup) Press SETUP - PLOT to define any of the se ttings shown in the next two table s. 1. Hi ghlight the f ield to edit . â If there is a n umber to enter , t y pe it in and pr ess or . â If there is an opti on to ch oose , pre ss , highli ght y our c hoi ce , and pres s or . As a shortcut to , j ust highlight the field to change and pr ess to cy cle thr ough the optio ns. â If there is an option to select or deselect, pr ess t o ch e ck o r u nch e ck i t. 2 . Pr ess to vi e w mor e settings . 3 . When done , pr ess to vi ew the ne w plot . Displays the menu for en tering math operations. CHARS Di splays special characters. To enter one, place the cursor on it and press . To remain in the CHARS menu and enter another special character, press . Deletes the highlighted expression or the current character in the edit line. CLEAR Deletes all expressions in the list or clears the edit line. K e y Meaning (Continued) HP 3 9gs Engl ish. book Pa ge 5 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
2-6 Aplets and the ir views Plot view settings The plot view settings are: Those items with space for a checkmark are settings you can turn on or off. Press to display the second page. F ield Meaning XRNG, YRNG Specifies the minimum and maximum horizontal ( X ) and vertical ( Y ) values for the plotting window. RES For function plots: Resolution; âFasterâ plots in alternate pixel columns; âDetailâ plots in every pixel column. TRNG Parametric aplet: Specifies the t- values ( T ) for the graph. θ RNG Polar aplet: Specifies the angle (θ ) value range for the graph. NRNG Sequence aplet: Specifies the index ( N ) values for the graph. TSTEP For Parametric plots: the increment for the independent variab le. θ STEP For Polar plots: the increment value for the independent variable. SEQPLOT For Sequen ce aplet: Stairste p or Cobweb types. XTICK Horizontal spacing for tickmarks. YTICK Vertical spacing for tickmarks. F ield Meaning SIMULT If more than one relation is being plotted, plots them simultaneously (otherwise sequentially). INV. CROSS Cursor crosshairs invert the status of the pixels they cover. HP 3 9gs Engl ish. book Pa ge 6 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Aplets and their views 2-7 Reset plot settings To reset the default values for all plot settings, press CLEAR in the Plot Setup view. To reset the default value for a field, highlight the field, and pres s . Exploring the graph Pl o t v i ew g iv e s y ou a se l ec t io n of k ey s a n d m e nu k ey s to explore a graph further. The options vary from aplet to aplet. PLOT view keys The following table details the keys that you use to work with the graph. CONNECT Connect the plotted points. (The Sequence aplet always connects them.) LABELS Label the axes with XRNG and YRNG values. AXES Draw the axes. GRID Draw grid points using XTICK and YTICK spacing. F ield Meaning (Continued) K e y Meaning CLEAR Erases the plot and ax es. Offers additional pre-defined views for splitting the screen and for scaling (âzoomingâ) the axes. Moves cursor to far left or far right. Moves cursor between relations. or Interrupts plotting. Continues plotting if interr upted. HP 3 9gs Engl ish. book Pa ge 7 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
2-8 Aplets and the ir views Trace a graph You can trace along a function using the or key which moves the cur sor along the graph. The display also shows the current coordinate position ( x, y ) of the cursor. Trace mode and the coordinate di splay are automatically set when a plot is drawn. Note: Tracing might not appe ar to exactly follow your plot if the resolution (in Plot Setup view) is set to Faster. This is because RES: FASTER plots in only every other column, whereas tracing al ways uses every column. In Function and Sequence Aplets: Yo u can also scroll (move the cursor) left or right beyond the edge of the display window in trace mode, giving you a vi ew of more of the plot. To move between relations If there is more than one relation displayed, press or to move between relations. Turns menu-key labels on and off. When the labels are off, pressing turns th em back on. ⢠Pr essing once display s the full r ow o f labels . ⢠Pr essing a second time r emo ves the r ow of labels to displa y onl y the gr aph . ⢠Pr essing a thir d time displa y s the coordinate mode . Displays the ZOOM menu list. Turns trace mode on/off. A white box appears over the on . Opens an input form for you to enter an X (or T or N or θ ) value. Enter the value and press . The cursor jumps to the point on the graph that you entered. Function aplet only: turns on menu list for root-finding functions (see âAnalyse graph with FCN functionsâ on page 3-4). Displays the current, defining expression. Press to restore the menu. K e y Meaning (Continued) HP 3 9gs Engl ish. book Pa ge 8 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Aplets and their views 2-9 To jump directly to a value To jump straight to a value rather than using the Trace function, use the menu key. Press , then enter a value. Press to jump to the value. To turn trace on/off If the menu labels are no t displayed, press first. ⢠T urn o ff tr ace mode by pr essing . ⢠T urn on tr ac e mode by pre ssing . ⢠T o turn the c oor dinate displ a y off , pr ess . Zoom within a graph One of the menu key options is . Zooming redraws the plot on a larger or smaller scale. It is a shortcut for changing the Plot Setup. The Set Factors... option enables you to set the factors by which you zoom in or zoom out, and whether the zoom is centered about the cursor. ZOOM options Press , select an option, and press . (If is not displayed, press .) Not all options are available in all aplets. Option Meaning Center Re-centers the plot around the current position of the cursor without changing the scale. Box... Lets you draw a box to zoom in on. See âOther views for scaling and splitting the graphâ on page 2-13. In Divides horizontal and vertical scales by the X-factor and Y-factor. For instance, if zoom factors are 4, then zooming in results in 1 /4 as many units depicted per pixel. (see Set Factors... ) Out Multiplies horizontal and vertical scales by the X-factor and Y-factor (see Set Factors... ). X-Zoom In Divides horizontal scale only, using X-factor. X-Zoom Out Multiplies horizontal scale, using X-factor. HP 3 9gs Engl ish. book Pa ge 9 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
2-10 Aplets and the ir views Y-Zoom In Divides vertical sc ale only, using Y-factor. Y-Zoom Out Multiplies v ertical scale only, using Y-factor. Square Changes the vertical scale to match the horizontal scale. (Use this after doing a Box Zoo m, X-Zoom, or Y-Zoom.) Set Factors... Sets the X-Zoom and Y-Zoom factors for zooming in or zooming out. Includes option to recenter the plot before zooming. Auto Scale Rescales the vertical axis so that the display shows a representative piece of the plot, for the supplied x axis settings. (For Sequence and Statistics aplets, autoscaling rescales both axes.) The autoscale process uses the first selected function only to determine the best scale to use. Decimal Rescales both axes so each pixel = 0.1 units. Resets defaul t values for XRNG (â6.5 to 6.5) and YRNG (â3.1 to 3.2). (Not in Sequence or Statistics aplets.) Integer Rescales horizontal axis only, making each pixel =1 unit. (Not available in Sequence or Statistics aplets.) Trig Rescales horizontal axis so 1 pixel = Ï /24 radians, 7 .58, or 8 1 / 3 grads; rescales vertic al axis so 1 pixel = 0.1 uni t. (Not in Sequence or Statistics aplets.) Option M eaning (Continued) HP 3 9gs Engl ish. book Pa ge 10 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Aplets and their views 2-11 ZOOM examples The following screens show the effects of zooming options on a plot of . Plot of Zoom In : In Un-zoom : Un-zoom Note: Press to move to the bottom of the Zoom list. Zoom Out : Out Now un -zoom . X-Zoom In : X-Zoom In Now un -zoom . X-Zoom Out : X-Zoom Out Now un -zoom . Un-zoom Returns the display to the previous zoom, or if there has been only one zoom, un-zoom displays the graph with the original plot settings. Option M eaning (Continued) 3 x sin 3 x sin HP 3 9gs Engl ish. book Pa ge 11 We dnes day, Dec embe r 7, 2005 11 : 24 PM
2-12 Aplets and the ir views Y-Zoom In: Y-Zoom In Now un-zoom. Y-Zoom Out: Y-Zoom Out Zoom Square: Square To box zoom The Box Zoom option lets you dr aw a box aroun d the area you want to zoom in on by selecting the endpoints of one diagonal of the zoom rectangle. 1. If necessary , pr ess to tur n on the menu -k ey labels . 2. P r e s s a n d s e l e c t Box... 3 . P osition the c ursor on one cor ner of the r ectangle . Pr ess . 4. Use the cursor k ey s ( , etc.) to drag to the op posite corner . 5 . Pr ess to z oom in on the box e d ar ea . HP 3 9gs Engl ish. book Pa ge 12 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Aplets and their views 2-13 To set zoom factors 1. In the P lot v iew , pr ess . 2. P r e s s . 3. Se l e c t Set Factors... and pr es s . 4. Enter the z oom fac tors . Ther e is one z oom fac tor f or the hor i z ontal sc ale ( XZOOM ) and one f or the vertical sca le ( YZOOM ). Z ooming out multipli es the s cale by the fac tor , so that a gr eater scale distance appears on the sc r een. Z ooming in div ide s the scale b y the fact or , so that a shorter s cale dist ance appear s on the sc r een . Other views for scaling and splitting the graph The preset viewing options menu ( ) contains options for drawing the plot using certain pre-defined configurations. This is a shortcut for changing Plot vi ew settings. For instance, if you have define d a trigonometric function, then you could select Trig to plot your function on a trigonometric scale. It also contains split-screen options. In certain aplets, fo r example those that you download from the world wide web, the preset viewing options menu can also contain options that relate to the aplet. VIEWS menu options Press , select an option, and press . Option Meaning Plot- Detail Splits the screen into the plot and a close-up. Plot-Table Splits the screen into the plot and the data table. Overlay Plot Plots the current expression(s) without erasing any pre-existing plot(s). HP 3 9gs Engl ish. book Pa ge 13 We dnes day, Dec embe r 7, 2005 11 : 24 PM
2-14 Aplets and the ir views Split the screen The Plot-Detail view can give you two simultaneous views of the plot. 1. Pr ess . Se lect Plot-Detai l and pr ess . The gr aph i s plotted twi ce. Y ou can no w z oom in on the r ight si de. 2. P r e s s , selec t the z oom method and pres s or . This z ooms the r ight si de. Her e is an e x ample of s plit scr een w ith Zoom In . â The P lot menu k e ys are a vailable as f or the f ull plot (f or tr ac ing, coor dinate displa y , equation displa y , and so on) . Auto Scale Rescales the vertical axis so that the display shows a representative piece of the plot, for the supplied x axis settings. (For Sequence and Statistics aplets, autoscaling rescales both axes.) The autoscale process uses the first selected function only to determine the best scale to use. Decimal Rescales both axes so each pixel = 0.1 unit. Resets default values for XRNG (â6.5 to 6.5) and YRNG (â3.1 to 3.2). (Not in Sequence or Statistics aplets.) Integer Rescales horizontal axis only, making each pixel = 1 unit. (Not available in Sequence or Statistics aplets.) Trig Rescales horizontal axis so 1 pixel = Ï /24 r adian, 7 .58, o r 8 1 / 3 grads; rescales vertical axis so 1 pixel = 0.1 unit. (Not in Sequence or Statistics aplets.) Option M eaning (Continued) HP 3 9gs Engl ish. book Pa ge 14 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Aplets and their views 2-15 â mo ves the leftmost c ursor to the scr eenâs left edge an d mo ves the ri ghtmost c ursor to the s cr een âs ri ght edge . â The menu k e y copi es the r ight plot t o the left plot . 3 . T o un -split the sc reen , pre ss . The left si de tak es o ver the wh ole scr e en . The Plot-Table view gives you two simultaneous views of the pl ot . 1. Pr ess . Select Plot-Table and pr ess . The scr een display s the plot on th e left side and a table of numbers on the right side. 2 . T o mov e up and do wn the ta ble , use the and c urso r k ey s. T hese k ey s mo ve the tr a.ce point le ft or r ight along the plot , and in the table , the cor r espo nding value s ar e highlighted . 3 . T o mo ve between f uncti ons, us e the and c urso r k e y s to mo v e the c ursor fr om one graph to another . 4. T o r eturn to a full Nume r ic (o r P lot) v ie w , pr ess (or ). Overlay plots If you w ant to pl ot over an ex isting plot withou t erasing that plot, then use Overlay Plot inste ad of . Note that tracing follows only the curre nt functions from the current aplet. Decimal scaling Decimal scaling is the default scaling. If you have changed the scaling to Trig or Integer, you can change it back with Decimal. Integer scaling Integer scaling compresses the axes so that e ach pixel is and the origin is near the scr een center. Trigonometric scaling Use trigonometric scaling whenever you are plotting an expression that includes trigonometric functions. Trigonometric plots are more li kely to intersect the axis at points factored by Ï . 11 Ã HP 3 9gs Engl ish. book Pa ge 15 We dnes day, Dec embe r 7, 2005 11 : 24 PM
2-16 Aplets and the ir views About the numeric view After entering and selecting (check marking) the expression or expressions that you want to explore in the Symbolic view, press to view a table of data values for the independent variable ( X , T, θ , or N ) and dependent variables. Setting up the table (Numeric view setup) Press NUM to define any of the table settings. Use the Numeric Setup input form to configure the table. 1. Hi ghlight the f ield to edit . Use the ar r ow k ey s to mo ve f r om f ield to f ield . â If there is a n u mber to en ter , t y pe it in and pr ess or . T o modi fy an ex isting number , press . â If there is an opti on to choos e , pre ss , highli ght y our c hoi ce, and pr ess or . â Shortc ut : Pr ess the ke y to copy v a lue s fr om the Plot Setup into NUMSTART and NUMSTEP . Effecti vel y , the menu k ey allo ws y ou to mak e the table match the p i x el columns in the gr aph v ie w . 2 . When do ne , pr ess to v ie w the table o f numbers. HP 3 9gs Engl ish. book Pa ge 16 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Aplets and their views 2-17 Numeric view settings The following table details the fields on the Numeric Setup input form. Reset numeric settings To reset the default values for all table settings, press CLEAR . Exploring the table of numbers NUM view menu keys The following table details the menu keys that you use to work with the table of numbers. Zoom within a table Zooming redraws the table of numbers in greater or lesser detail. F ield Meaning NUMSTART The independent variableâ s starting value. NUMSTEP The size of the increment from one independent v ariable value to the next. NUMTYPE Type of numeric table: Automatic or Build Your Own. To build your own table, you must type each independent value into the table yourself. NUMZOOM Allows you to zoom in or out on a selected value of the independent variable. K ey Meaning Displays ZOOM menu list. Toggles between two character sizes . Displays th e defining function expression for the highlighted column. To cancel this display, press . HP 3 9gs Engl ish. book Pa ge 17 We dnes day, Dec embe r 7, 2005 11 : 24 PM
2-18 Aplets and the ir views ZOOM options The following table lists the zoom options: The display on the right is a Zoom In of the display on the left. The ZOOM factor is 4. HINT To jump to an independent va riable value in the table, use the arrow keys to place the cursor in the independent variable column, then enter the value to jump to. Automatic recalculation You can enter any new value in the X column. When you press , the values for the dependent variables are recalculated, and the entire table is regenerated with the same interval between X values . Option Meaning In Decreases the intervals for the independent variable so a narrower range is show n. Uses the NUMZOOM factor in Numeric Setup. Out Increases the intervals for the independent variable so that a wider range is shown. Uses the NUMZOOM factor in Numeric Setup. Decimal Changes intervals for the independent variable to 0.1 units. Starts at zero. (Shortcut to changing NUMSTART and NUMSTEP .) Integer Changes intervals for the independent variable to 1 un it. Starts at zero. (Shortcut to changing NUMSTEP .) Trig Changes interv als for independent variable to Ï /24 radian o r 7.5 degrees or 8 1 / 3 grads. Starts at zero. Un-zoom Returns the display to the previous zoom. HP 3 9gs Engl ish. book Pa ge 18 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Aplets and their views 2-19 Building your own table of numbers The default NUMTYPE is âAutomaticâ, which fills the table with data for regular intervals of the independent ( X , T , θ , or N ) variable. With the NUMTYPE option set to âBuild Your Ownâ, you fill the table yourself by typing in the independent-variable values yo u want. The dependent values are then calculated and displayed. Build a table 1. S tart with an e xpressi on def ined (in S ymboli c v ie w) in th e ap let of you r choic e . Not e: F uncti on , P olar , P ar ametric , and Sequenc e aplets onl y . 2 . In the Numer ic Setup ( NUM ) , choo se NUMTYPE: Build Your Own . 3 . Open the Numeri c v ie w ( ) . 4. Clear e xisting dat a in the table ( CLEAR ). 5 . Ente r the independent v alues in the left -hand column . T ype in a number and pr ess . Y ou do not hav e to enter them in or der , becaus e the functi on can rear r ange them . T o inser t a number bet w een two others , use . Clear data Press CLEAR , to er ase the data from a table. F1 and F2 entries are generated automatically You enter numbers into the X column HP 3 9gs Engl ish. book Pa ge 19 We dnes day, Dec embe r 7, 2005 11 : 24 PM
2-20 Aplets and the ir views âBuild Your Ownâ menu keys Example: plotting a circle Plot the circle, x 2 y 2 = 9 . First rearrange it to read . To plot both the positive and negative y values, you need to define two equations as follows: and K e y Meaning Puts the highlighted independent value ( X , T , θ , or N ) into the edit line. Pressing replaces this variable with its current value. Inserts a zero value at the position of the highlight. Replace a zero by typing the number you want and pressing . Sorts the independent variable values into ascending or descending order. Press and select the ascending or descending option from the menu, and press . Toggles between two character sizes. Displays the defining function expression for the highlighted column. Deletes the highlighted row. CLEAR Clears all data from the table. y 9 x 2 â ± = y 9 x 2 â = y 9 x 2 â â = HP 3 9gs Engl ish. book Pa ge 20 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Aplets and their views 2-21 1. In the F unction aplet , spec ify the functi ons . Select Function 9 9 2 . Rese t the gr aph se tup to the de fa ult setting s. SETUP - PLOT CLEAR 3 . P lot the two func tions and hide the men u so that y ou can see all the ci rc l e. 4. R eset the n umer ic s etup to the def ault se ttings. SETUP - NUM CLEAR 5 . Displa y the functio ns in numer ic f orm . HP 3 9gs Engl ish. book Pa ge 21 We dnes day, Dec embe r 7, 2005 11 : 24 PM
HP 3 9gs Engl ish. book Pa ge 22 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Function aplet 3-1 3 F unc tion aplet About the Function aplet The Function aplet enables you to explore up to 10 real-valued, rectangu lar functions y in terms of x . For example . Once you have defined a function you can: ⢠cr eate gr aphs to fi nd r oots, int er cepts, slope , signed ar ea, and e x tr ema ⢠cr eate tables to evaluate f uncti ons at par tic ular va lu es . This chapter demonstrates the basic tools of the Function aplet by stepping you through an example. See âAplet viewsâ on page 2-1 for furth er information about the functionality of the Symbolic, Numeric , and Plot views. Getting started with the Function aplet The following example involves two functions: a linear function and a quadratic equati on . Open the Function aplet 1. Open the Functi on aplet . Select Fun ction T he F uncti on aple t starts in the S ymboli c v ie w . The Symbolic view is the defining view for Function, Parametric, Polar, and Seq uence aplets. The other views are derived from the symbolic expression. y 2 x 3 = y 1 x â = yx 3 () 2 2 â = HP 3 9gs Engl ish. book Pa ge 1 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
3-2 Function aplet Define the expressions 2 . T her e are 10 f uncti on def inition f ields on the F uncti on apletâs S y mbolic v ie w sc r een . Th ey ar e labeled F1(X) to F0(X). Highligh t the func tion de f inition f ield y ou w ant to use , and en ter a n e xpr es si on . (Y o u can pr ess to delete an e xis ting line , or CLEAR to clear all lines .) 1 3 2 Set up the plot You can change the scales of the x and y axes, graph resolution, and the spacing of the axis ticks. 3 . Display plot s ettings. SETUP - PLOT Note: F or our e x ample , you can lea v e the plot settings at t heir def ault values since we w ill be using the Auto Scale f eatur e to c hoose an appr opr iate y ax is fo r our x axis s ettings. If y our settings do not matc h this e x ample , pre ss CLEAR to r estor e th e defau lt valu es. 4. Spec ify a gri d f or the gr aph . Plot the functions 5 . P lot the functi ons. HP 3 9gs Engl ish. book Pa ge 2 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Function aplet 3-3 Change the scale 6 . Y ou can chan ge the scale to see mo r e or le ss of your gr aphs . In this e xam ple , ch oose Auto Scale . (See âVIEW S menu options â on page 2 -13 f or a de scr ip t ion of Aut o Sc al e) . Select Auto Scale Trace a graph 7 . T race the linear f uncti on . 6 times Note: B y default , the tr acer is acti ve . 8. Jum p fr om the linear functi on to the q uadra tic func tion . HP 3 9gs Engl ish. book Pa ge 3 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
3-4 Function aplet Analyse graph with FCN functions 9. Display the Plot view menu. From the Plot view menu, you can use the functions on the FCN menu to find roots, intersections, slopes, and areas for a function defined in the Function aplet (and any Function-based ap lets). The FCN fun ctions act on the currently selecte d graph. See âFCN func tions â on page 3-10 fo r further infor matio n. To find a root of the quadratic function 10. Mov e the cur sor to the gr aph of the quadr atic equati on by pr es sing the or ke y . Then mo ve the c urs or so that it is near by pr essing the or ke y . Sele ct Root T he root v alue is display ed a t the bottom of the sc r een. Note: If ther e is more tha n one root (a s in our exam p l e ) , t he coor dinates of the r oot c lose st to the c urr ent c ursor position ar e display ed. To find the intersection of the two functions 11. F ind the inte rsec tion o f the two f uncti ons . x 1 â = HP 3 9gs Engl ish. book Pa ge 4 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Function aplet 3-5 12 . Cho ose the linear f unction w hose int ers ecti on w ith the quadr atic functi on you w ish to f ind. T he coor dinates o f the inters ecti on poin t ar e display ed at the bottom of the scr een. Note: If ther e is more than one inter secti on (as in our e xam ple) , the coor dinates of the inter sec tion po int c lose st to the c urr ent c ursor po sition ar e displa ye d. To find the slope of the quadratic functio n 13 . F ind the slope of the quadr atic f uncti on at the inters ecti on poin t . Sele ct Slope T he slope v alue is display ed at the bottom of th e sc r een. To find the signed area of the two functio ns 14. To find the area between the two functions in the range â2 ⤠x ⤠â1, fir st mo v e the c urso r to and selec t the signed ar ea optio n . Sele ct Signed area F 1 x () 1 x â = HP 3 9gs Engl ish. book Pa ge 5 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
3-6 Function aplet 15 . Mo v e the c urso r to x = â2 by pr essing the or key . 16 . Pr es s to acce pt using F2(x) = (x 3) 2 â 2 as the other boundar y for the integr al. 17 . Choo se the end v alue for x . 1 Th e cu rs or ju mps t o x = â 1 on the linear func tion . 18. Displa y the numerical value of the integral. Note: See âShading ar eaâ o n page 3-11 for ano ther method of calc ulating ar ea . To find the extremum of the quadratic 19 . Mov e the cu rso r to the quadr atic equati on and f ind the e xtr emum o f the quadrati c . Select Extremum The coordina tes of t he ext re mu m a re display ed a t the bottom of the sc r een . HP 3 9gs Engl ish. book Pa ge 6 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Function aplet 3-7 HINT The Root and Extremum functions return one value only even if the function has more than one r oot or extremum. The function finds the value closest to the position of the cursor. You need to re- locate the cursor to find oth er roots or extrema that may exist. Display the numeric view 20. Display the numer ic v ie w . Set up the table 21. Display the n umer ic se tup . SETUP - NUM See âSettin g up the table (Numeric v iew s etup)â on page 2 -16 for mor e infor mation . 2 2 . Matc h the table settings to the pi xel co lumns in the gr aph v iew . Explore the table 2 3 . Displa y the ta ble of v alues. HP 3 9gs Engl ish. book Pa ge 7 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
3-8 Function aplet To navigate around a table 2 4. Mo v e to X = â5 .9 . 6 times To go directly to a value 2 5. Mov e direc tly to X = 10. 1 0 To access the zoom options 2 6 . Z oom in on X = 10 by a fact or of 4. Note: NUMZOOM has a setting of 4 . In To change font size 2 7 . Displa y table n umbers in lar ge fon t . To display the symbolic definition of a column 2 8. Displa y the s ymboli c def initio n for the F1 column . The symbolic definition of F1 is display ed at the bottom of the screen. HP 3 9gs Engl ish. book Pa ge 8 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Function aplet 3-9 Function aplet interactive analysis From the Plot view ( ), you can use the functions on the FCN menu to find r oots, intersections, slopes, and areas for a function defined in the Function aplet (and any Function-based aplets). See âFCN functionsâ on page 3- 10. The FCN operations act on the currently sele cted graph. The results of the FCN function s are saved in the following variables: ⢠Area ⢠Extr emum ⢠Isec t ⢠R oot ⢠Slope For example, if you use the Root function to find the root of a plot, you can use the result in calculations in HOME. Access FCN variables The FCN variables are cont ained on the VARS menu. To access FCN variables in HOME: Sele ct Plot FCN or to choo se a va riab l e To access FCN variable in th e Function apletâs Symbolic view: Sele ct Plot FCN or to choo se a var iable HP 3 9gs Engl ish. book Pa ge 9 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
3-10 Function aplet FCN functions The FCN functions are: Function Description Root Select Root to find the root of the current function nearest the cursor. If no root is found, but only an extremum, then the result is labeled EXTR: instead of ROOT: . (The root-finder is also used in the Solve aplet. See also âInterpreting resultsâ on page 7-6.) The cursor is moved to the root value on the x-axis and the resu lting x -value is saved in a variable named ROOT. Extremum Sel ect Extremum to find the maximum or minimum of the current function nearest the cursor. This displays the coordinate values and mov es the cursor to the extremum. The resulting value is saved in a variable named EXTREMUM . Slope Select Slope to find the numeric derivative at the current position of the cursor. The result is saved in a variable named SLOPE. Signed area Select Signed area to find the numeric integral. (If there are two or more expressions checkmarked, then you will be asked to choose the second expression from a list that includes the x -axis.) Select a starting point, then move the cursor to selection ending point. The result is saved in a variable named AREA. HP 3 9gs Engl ish. book Pa ge 10 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Function aplet 3-11 Shading area You can shade a selected area between functio ns. This process also gi ves you an appro ximate measurement of the area shaded. 1. Open the F unction aplet. T he Func tion aplet opens in the S ymbolic v ie w . 2 . Select the e xpr essi ons wh ose c ur v es y ou w ant to stu dy . 3 . Pres s to plot the f unctions . 4. Pr es s or to po sitio n the c ursor at the starting point o f the area y ou want to shade . 5. P re s s . 6 . Pr ess , t hen select Signed area and pr ess . 7 . Pr ess , ch oose the f uncti on that w ill act as the boun dary of the shaded ar ea , and pr es s . 8. Pr ess the or k e y to shade i n the ar ea . 9 . Pr ess to calculat e the ar ea . The ar ea measur ement is display ed near the bottom of the screen. To remove the shading, press to re-draw the plot. Intersection Select Intersection to find the intersection of two graphs nearest the cursor. (You need to have at least two selected expressions in Symbolic view.) Disp lays the coordinate values and moves the cursor to the intersection. (Uses Solve function.) The resulting x - value is saved in a variab le named ISECT. Function Description (Continued) HP 3 9gs Engl ish. book Pa ge 11 We dnes day, Dec embe r 7, 2005 11 : 24 PM
3-12 Function aplet Plotting a piecewise-defined function Suppose you wanted to plot the following piecewise- defined function. 1. Open the F unction apl et . Sele ct Function 2 . Highlight the line you wan t to us e , and ente r the e xpre ssion . (Y ou can pre ss to delete an e xisting line , or CLEAR to c lear all lines .) 2 CHARS ⤠1 CHARS > 1 AND CHARS ⤠1 4 CHARS > 1 Note: Y ou can us e the menu k ey to as sist in the entry of equations . It has the same e ffect as pr essing . fx () x 2 x 1 â ⤠; x 2 1 â x 1 ⤠< ; 4 xx 1 ⥠; â ⩠⪠⨠⪠⧠= HP 3 9gs Engl ish. book Pa ge 12 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Parametric aplet 4-1 4 Pa r a m e t r i c a p l e t About the Parametric aplet The Parametric aplet allows you to explore parametric equations. These are equ ations in which both x and y are defined as functions of t . They take the forms and . Getting started with the Parametric aplet The following example uses the parametric equations Note: This examp le will produce a circle. For this example to work, the angle measure must be set to degrees. Open the Parametric aplet 1. Open the P arametri c aplet. Select Parametric Define the expressions 2 . Define the e xpre ssio ns. 3 3 xf t () = yg t () = xt () 3 t yt () 3 t cos = sin = HP 3 9gs Engl ish. book Pa ge 1 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
4-2 Parametric aple t Set angle measure 3 . Set the angle measu r e to degrees. MODES Select Degrees Set up the plot 4. Display the graphing options. PLOT T he P lot Setu p inpu t for m has t w o f ields n ot inc luded in the Func tion aplet , TRNG and TSTEP . TRNG spec if ies the r ange of t val ue s. TSTEP spec if ies the step value between t values. 5 . Set the TRNG and TSTEP so that t steps fr om 0 ° to 360 ° in 5 ° steps. 360 5 Plot the expression 6 . P lot the e xpre ssion . 7 . T o see all the c irc le, pr ess tw ice . HP 3 9gs Engl ish. book Pa ge 2 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Parametric aplet 4-3 Overlay plot 8. Plot a triangle graph over the existing circle graph. PLOT 120 Sele ct Overlay Plot A tri angle is displa yed r ather than a c irc le ( with out c hanging the equati on) becaus e the c hanged value o f TSTEP ensur es that points be ing plot ted ar e 120 ° apart instea d of near l y continuou s. Y ou ar e able to e xplor e the graph u sing tr ace, z oom , split sc reen , and scaling func tio nality available in the F unction aplet . See âExplor ing the gr aph â on page 2 - 7 fo r fur t h er i nfo rma t ion. Display the numbers 9 . Displa y the table of v alues. Y ou can highli ght a t -value , t y pe in a r eplac ement v alue, and see the table j ump to that v alue . Y ou can also z oom in or z oom out on an y t -v alue in t he ta ble . You are able to explore the table using , , build your own table, and split screen functionality available in the Function aplet. See âExploring the table of numbersâ on page 2-17 for further information. HP 3 9gs Engl ish. book Pa ge 3 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
HP 3 9gs Engl ish. book Pa ge 4 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Polar aplet 5-1 5 Po l a r a p l e t Getting started with the Polar aplet Open the Polar aplet 1. Open the P olar aplet . Sele ct Polar L ik e the F unction aple t , the P o lar aplet opens in the S ymboli c v ie w . Define the expression 2 . Define the po lar equati on . 2 Ï 2 Specify plot settings 3 . S pec ify the plot settings . In this ex ample, w e w ill use the def ault se ttings, e x cept f or the θ RNG fi el d s. SETUP - PLOT CLEAR 4 Ï Plot the expression 4. P lot the expr essi on . r 2 Ïθ 2 â () θ () 2 cos cos = HP 3 9gs Engl ish. book Pa ge 1 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
5-2 Polar aplet Explore the graph 5 . Displa y the Plot v ie w menu k ey labels . Th e Pl ot vi ew op t i on s av ailable ar e the same as those f ound in the F u ncti on aplet . See âExplor ing the gra ph â on page 2 - 7 fo r further informati on . Display the numbers 6 . Displa y the table of v alue s for θ and R1. Th e N u m eric view optio ns av ailable ar e the same as th o se fo und in the F uncti on aplet . See âExplor ing the table of n umber s â on pa g e 2-1 7 fo r fur t h er in for ma t ion. HP 3 9gs Engl ish. book Pa ge 2 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Sequence aplet 6-1 6 Sequence aplet About the Sequence aplet The Sequence aplet allows you to explore sequences. You can define a sequence named, for example, U1: ⢠in terms of n ⢠in terms of U1 ( nâ1) â¢i n ter ms of U1 ( nâ2) ⢠in ter ms of another sequence , for e xample , U2 ( n) ⢠in an y combination of the a bov e. The Sequence aplet allows you to create two types of graphs: â A Stairstep s gr aph pl ots n o n the hor i z ontal ax is and U n on the ve rtical ax is. â A Cob web gr aph plots U nâ 1 on the hor iz ont al ax is and U n on the v ertical ax is. Getting started with the Sequence aplet The following example defines and then plots an expression in the Sequence aplet. The sequence illustrated is the well-known Fibonacci sequ ence where each term, from the third term on, is the sum of the preceding two terms. In this example, we specify three sequence fields: the first term, the second te rm and a rule for generating all subsequent terms. However, you can also define a sequence by specifying just the first term and the rule for generating all subsequent terms. Y ou w ill , though , hav e to enter the second te rm if the hp3 9gs is unable to calc ulate it automatical l y . T ypically if the n th t erm in the s equence depends on n â 2 , then you must enter the second term . HP 3 9gs Engl ish. book Pa ge 1 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
6-2 Sequence aple t Open the Sequence ap let 1. Open the Sequ ence aplet . Sele ct Sequence The Sequence ap let starts in the S ymboli c view . Define the expression 2 . Def ine the F ibonacc i sequence, in w hich eac h term (after the f irst tw o) is the sum of the pr eceding tw o terms: , , for . In the S ymboli c v ie w of the Seq uence aplet , highlight the U 1 (1) fi eld and begin def ining y our sequence . 1 1 Note: Y ou can us e the , , , , and menu k ey s to assist in the entry of equati ons . Specify plot settings 3. In Plo t Setup , fir st se t the SEQPLOT optio n to Stairstep . Re set the de fa ult plot settings b y clear i ng the P lot Setup v iew . SETUP - PLOT CLEA R 8 8 U 1 1 = U 2 1 = U n U n 1 â U n 2 â = n 3 > HP 3 9gs Engl ish. book Pa ge 2 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Sequence aplet 6-3 Plot the sequence 4. P lot the Fibonacc i sequ ence. 5. In Plot Setup, set the SEQPLOT option to Cobweb. SETUP - PLOT Select Cobweb Display the table 6 . Di spla y the table of values f or this ex amp le . HP 3 9gs Engl ish. book Pa ge 3 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
HP 3 9gs Engl ish. book Pa ge 4 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Solve aple t 7-1 7 Solve aplet About the Solve aplet The Solve aplet solves an equation or an expression for its unknown variable . You define an equation or expression in the symbolic view, then supply values for all the variables exce pt one in the numeric view. Solve works only with real numbers. Note the differences between an equation and an expression: ⢠An equati on contains an equals si gn. Its s oluti on is a v alue for the unkno wn v ari able that mak es bo th sides hav e the same value . ⢠An ex p res si on does not contain an eq uals sign . Its solu tion is a r oot , a v alue fo r the unkno w n v ari able that mak es the e x pr ession hav e a value of z er o . You can use the Solve aplet to solve an equation for any one of its variables. When the Solve aplet is started, it opens in the Solve Symbolic view. ⢠In S ymbolic v ie w , you spec if y the e xpr ession or equation to solve . Y ou can d ef ine up to ten equations (or e xpr essions), named E0 to E9 . E ach equati on can contain up to 2 7 r eal vari ables, named A to Z and θ. ⢠In Numeri c vi ew , y ou spec ify the values of the know n v ari ables , hi ghlight the v ariable that y ou w ant to sol v e fo r , and pr ess . You can s olve the e quation as many times as you want, using new values for the knowns and highlighting a different unknown. Note: It is not possible to solv e for more than one variable at once. Simultaneous linear equations, for example, should be solved using the Li near Solver aplet, matrices or graphs in the Function aplet. HP 3 9gs Engl ish. book Pa ge 1 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
7-2 Solve ap let Getting started with the Solve aplet Suppose you want to find th e acceleration needed to increase the speed of a car from 16.67 m/sec (60 kph) to 27.78 m/sec (100 kph) in a distance of 1 00 m. The equation to solve is: Open the Solve aplet 1. Open the Solv e aplet. Sele ct Solve T he Sol v e aplet st arts in the s y mbolic v iew . Define the equation 2. Define the equ ation. V U 2 A D Note: Y ou can us e the menu k ey to as sist in the entry of eq uations . Enter known variables 3 . Display the Solve numer ic vie w scr een. V 2 U 2 2 AD = HP 3 9gs Engl ish. book Pa ge 2 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Solve aple t 7-3 4. Enter the v alues f or the kno wn var iables . 2 7 7 8 1 6 6 7 1 0 0 HINT If the Decimal Mark setting in the Modes input form ( MODES ) is set to Comma, use instead of . Solve the unknown variable 5. Sol v e f or the unkno wn var iable ( A ). T her ef or e , the accelerati on needed to inc r ease the speed of a car fr om 16.6 7 m/sec (6 0 kph) to 2 7 .7 8 m/sec (100 kph) in a di st ance of 100 m is appro ximatel y 2 .4 7 m/s 2 . Becaus e the va ri able A in the equati on is linear w e kno w that we need not loo k fo r an y other soluti ons . Plot the equation T he P lot v ie w sho w s one gr aph for eac h side of the selected equation. Y ou can choose an y of the v ari able s to be the independen t va ri able . T he c urr ent equati on is . One of these is , w i th , that is, . This gr aph w ill be a hor i z ontal line . T he other gr aph w ill be , w ith and , that is, . This gr aph is also a line . The desir ed solutio n is the va lue of A w here these two lines intersect . V 2 U 2 2 AD = YV 2 = V 27.78 = Y 771.7284 = YU 2 2 AD = U 16.67 = D 100 = Y 200 A 277.8889 = HP 3 9gs Engl ish. book Pa ge 3 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
7-4 Solve ap let 6. Plo t the equati on fo r var iable A . Sele ct Auto Scale 7 . T race along the gr aph r epr esen ting the left side of the equati on until the c ursor nears the inter sec tion . 20 times Note the v alue o f A display ed near the bottom left corner of the scr een. T he Plo t vi e w pr o v ides a con v enien t wa y to f ind an appr ox imation to a solu tion instead of u sing the Numer ic v ie w Sol ve opti on . See âPlotting to f ind gu esses â o n pa ge 7 - 7 for m ore inform at ion. Solve apletâs NUM view keys The Solve apletâs NUM view keys are: Key M e a n i n g Copies the highlighted value to the edit line for editing. Press when done. Displays a message about the solution (see âInterpreting resultsâ on page 7-6). Displays other pages of variable s, if any. Displays the symbolic definition of the current expression. Press when done. Finds a solution for the highlighted variable, based on the values of the other var iables. HP 3 9gs Engl ish. book Pa ge 4 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Solve aple t 7-5 Use an initial guess You can usually obtain a fa ster and more accurate solution if you supply an estimated valu e for the unknown variable before pressing . Solve starts looking for a solution at the initial guess. Bef or e plottin g , make sur e the unkno wn v ariable is highli ghted in the nume ri c v ie w . P lot the equati on to help y ou s elect an initi al gues s w hen y ou don ât kno w the r ange in whi c h to look fo r the solution . See âP lotting to find guesses â on pa ge 7 - 7 for f urt her infor mation. HINT An initial guess is especially important in the case of a curve that could have more than one solution. In this case, only the solution closest to the initial guess is re turned. Number format Yo u can change the number fo rmat for the Solve aplet in the Numeric Setup view. The options are the same as in HOME MODES: Standard, Fixed, Scientific , and Engineering. For the latter three, you also specify how many digits of accuracy you want. See âMode settings â on page 1-10 for more information. You might find it handy to set a different number format for the Solve aplet if, for example, you define equations to solve for the value of money. A number format of Fixed 2 would be appropriate i n this case. Clears highlighted variable to zero or deletes current character in edit line, if edit line is active . CLEAR Resets all variable values to zero or clears the edit line, if cursor is in edit line. K ey M eaning (Continued) HP 3 9gs Engl ish. book Pa ge 5 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
7-6 Solve ap let Interpreting results After Solve has returned a solution, press in the Numeric view for more information. You will see one of the following three messages. Press to clear the message. Messa ge Condition Zero The Solve aplet found a point where both sides of the equation were equal , or wher e the expression was zero (a root), within the calculator's 12-digit accuracy. Sign Reversal Solve found two points where the difference between the two side s of the equation has opposite signs, bu t it cannot find a point in between where the value is zero. Similarly, for an expression, where the value of the express ion has different si gns but is not precisely zero. This might be because either the two points are neighbours (they differ by one in the twelfth digit), or the equation is not real-valued between the two points. Solve returns the point where the value or difference is closer to zero. If the equation or expression is continuously real, this poi nt is Solveâs best approximation of an actual solution. Extremum Solve found a point where the value of the expression approximates a local minimum (for posi tive values) or maximum (for negative values). This point may or may not be a solution. Or: Solv e stopped sea rching at 9.99999999999E4 99, the largest number the calculator can represent. Note that the value returned is probably not valid. HP 3 9gs Engl ish. book Pa ge 6 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Solve aple t 7-7 If Solve could not find a solution, you will see one of the following two messages. HINT It is important to check the information relating to the solve process. For example, the solution that the Solve aplet finds is not a solution, but the closest that the function gets to zero. Only by checking the information will you know that this is the case. The Root-Finder at work You can watch the process of the root-finder calculating and searching for a root. Immediately after pressing to start the root-finder, press any key except . You will see two intermediate guesses and, to the left, the sign of the expression evaluated at each gue ss. For example : 2 2.2193305 55745 â 1 21.31111111149 You can watch as the root-finder either finds a sign reversal or converges on a local extrema or does not converge at all. If there is no convergence in process, you might want to cancel the operation (press ) and start over with a different initial guess. Plotting to find guesses The main reason for plotting in the Solve aplet is to help you find initial guesses and so lutions for thos e equations that have difficult-to-find or multi ple solutions. Consider the equation of motion for an ac celerating body: Message Condition Bad Guess(es) The initial guess lies outside the domain of the equation. Therefore, the solution was not a real number or it caused an error. Constant? The value o f the equation is the same at every point sampled. 2 2 0 AT T V X = HP 3 9gs Engl ish. book Pa ge 7 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
7-8 Solve ap let where X is distance, V 0 is initial velocity, T is time, and A is acceleration. This is actually two equations, Y = X and Y = V 0 T (AT 2 ) / 2 . Since this equation is quadratic for T , there can be both a positive and a negative solution. However, we are concerned only with posi tive so lutions, since only positive distance makes sense. 1. Selec t the Sol v e aplet and ente r the equati on . Sele ct Solve X V T A T 2 2. Find the solution for T (time) when X = 30, V =2 , and A =4 . Enter the values for X , V , and A ; then highlight the independent variable, T . 30 2 4 to highlight T 3. Use the Plot view to find an initial guess for T . First set appropriate X and Y ranges in the Plot Setup. With equation X = V x T A x T 2 /2 , the plot will produce two graphs: one for and one for X = V x T A x T 2 /2 . Since we have set in this example, one of the graphs will be . Therefor e, make the YRNG â 5 to 35. Keep the XRNG default of â 6.5 to 6.5. SETUP- PLOT 5 35 4. P lot the gr aph. YX = X 30 = Y 30 = HP 3 9gs Engl ish. book Pa ge 8 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Solve aple t 7-9 5. Move the cursor near the positive (right-side) intersection. This cursor value will be an initial guess for T . Pr ess until the c urs or is at the inters ecti on. Th e t wo p oi nt s of inter sec tion sho w that ther e ar e tw o soluti ons f or this equati on . Ho w e ve r , on ly po si t ive va l ue s fo r X mak e sense , so we w ant to fi nd the soluti on f or the int ers ecti on on the r ight side of the y -ax is . 6 . R etur n to the Numer ic vi ew . Note: the T -value is fi lled in w ith the positi on of the c ursor from the Plot vie w . 7. Ensur e that the T value is highli ghted , and solv e the equati on . Use this equation to solve fo r another variab le, such as velocity. How fast must a bodyâs initial velocity be in order for it to travel 50 m within 3 seconds ? Assume the same acceleration, 4 m/s 2 . Leave the last value of V as the initial guess. 3 50 HP 3 9gs Engl ish. book Pa ge 9 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
7-10 Solve ap let Using variables in equations You can use any of the real variable names, A to Z and θ . Do not use variable nam es defined for other type s, such as M 1 (a matrix variable). Home variables All home variables (other than t hose for aplet settings, like Xmin and Ytick ) are globa l , which means they are shared throughout the different aplets of the calcu lator . A value that is assigned to a home variable anywhere remains with that variable wh erever its name is used. Therefore, if you have defined a value for T (as in the above example) in another aplet or even another Solve equation, that value shows up in the Numeric view for this Solve equation. When you th en redefine the value for T in this Solve equation, that value is applied to T in all other contexts (until it is changed again). This sharing allows you to work on the same problem in different plac es (such as HOME and the Solve aplet) without having to update the value whenever it is recalculated. HINT As the Solve aplet uses existing variable values, be sure to check for existing variable values that may affec t the solve process. (You can use CLEAR to reset all values to zero in the Solve apletâs Numeric view if you wish.) Aplet variables Functions defined in other aplets can also be referenc ed in the Solve aplet. For example, if, in the Function aplet, you define F1(X)=X 2 10 , you can enter F1(X)=50 in the Solve aplet to solve the equation X 2 10=50 . HP 3 9gs Engl ish. book Pa ge 10 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Linear Solve r aplet 8-1 8 Li n e a r S o lve r a p l e t About the Linear Solver aplet The Linear Solver aplet allows you to solve a set of Linear Equations. The set can contain two or three linear equations. In a two-equation set, each equation must be in the form . In a three-equation set, e ach equation must be in the form . You provide values for a , b , and k (and c in three- equation sets) for each equation, and the Linear Solver aplet will attempt to solve for x and y (and z in three- equation sets). The hp39gs will alert you if no solution can be found, or if there is an infinite number of solutions. Note that the Linear Solver aplet only has a nume ric view. Getting started with the Linear Solver aplet The following example defines a set of three equations and then solves for the unknown variables. Open the Linear Solver aplet 1. Open the Linear Sequence ap let . Select Linear Solver T he L inear E quati on Sol ver opens . ax by k = ax by cz k = HP 3 9gs Engl ish. book Pa ge 1 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
8-2 Linear Solver aplet Choose the equation set 2 . If the last time y ou us ed the L inear Sol v er aplet yo u so l ve d fo r t wo equati ons, the tw o - equati on input f orm is display ed (as in the e x ample in the pr ev ious step) . T o solv e a th r e e -equation set , pre ss . No w the input f or m displa y s thr ee equati ons . If the three-equation input fo rm is displaye d and you want to solve a two-equation set, press . In this example, we are going to solve the following equation set: Hence we need the three-equation input form. Define and solve the equations 3 . Y o u def ine the equati ons y ou w ant to so lv e by ente r ing the co -eff ic ients o f eac h var iable in eac h equati on and the const ant ter m . Notice that the c urso r is immediately positi oned at the co -effi c ient of x in the fir st equation . Enter that co -eff ic ient and pr ess or . 4. T he cur sor mo v es to the ne xt co -effi c ient . Enter that co - eff ic ient , pres s or , and contin ue doing lik e w i se un til y ou ha v e def ined all the equati ons . Note : y ou can enter the name of a var iable f or any co -effi c ient or consta nt . Pr ess and begin enter ing the name. T he menu k e y appears. Pr ess that k ey to lock alphabetic entry mode. Pr ess it again to cancel the lock . Once y ou ha v e enter ed enough values f or the sol ver to be able to gener ate soluti ons, those solutions appear on the displa y . In the e x ample at the r ight , the so lv er wa s able t o f ind so lutio ns f or x , y , and z as 6 x 9 y 6 z 5 = 7 x 10 y 8 z 1 0 = 6 x 4 y 6 = HP 3 9gs Engl ish. book Pa ge 2 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Linear Solve r aplet 8-3 soon as the f irst co -eff ic ient o f the last eq uation was enter ed. As you enter each of the r emaining kno wn v alues , the soluti on c hanges . T he ex ample at the ri ght sho ws the fi nal soluti on once all th e c o - efficient s a nd constants are e nter ed for the set o f equati ons w e set out to solve . HP 3 9gs Engl ish. book Pa ge 3 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
HP 3 9gs Engl ish. book Pa ge 4 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Triangle Solve apl et 9-1 9 T riangle Solv e aplet About the Triangle Solver aplet The Triangle Solver aplet a llows you to determine the length of a side of a triangle, or the ang le at the vertex of a triangle, from information you supply about the other lengths and/or other angles. You need to specify at leas t three of the six possible valuesâthe lengths of the three sides and the size of the three ang lesâbefore the solver ca n calculate t he other values. Moreover, at least one valu e you specify must be a length. For example, you could specify the lengths of two sides and one of the angl es; or you could specify two angles and one length; or all three lengths. In each case, the solver will calculate the remaining lengths or angles. The hp39gs will alert you if no solution can be found, or if you have provided insuffi cient data. If you are determining the properties of a right-angled triangle, a simpler input for m is available by pressing the menu key. Note that the Triangle Solver aplet only has a numeric view. Getting started with the Triangle Solver aplet The following example solves f or the unk nown le ngth of the side of a triangle whose two known sidesâof lengths 4 and 6âmeet at an angle of 30 degrees. Before you begin : You should make sure that your angle measure mode is appro priate. If the angle information you have is in degrees (as in this example) and your current angle measure mode is ra dians or grads, change the mode to degrees before running the solver. (See âMode settingsâ on page 1-10 for instructions.) Because the angle measure mode is associated with the aplet, you should start the aplet first and then change the setting. HP 3 9gs Engl ish. book Pa ge 1 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
9-2 Triangle Solv e aplet Open the Triangle Solver aplet 1. Open the T r iangle S olv er aplet. Sele ct Triangle Solver The T r iangle Solv er aplet open s . Note : if y ou h a v e alr eady u sed the T ri angle Sol v er , the entries and re sul ts fr om the pre v ious use w i ll still be display ed. T o start the T r iangle Solv er a fr esh, c lear the pr ev ious entr ies and results b y pr es sing CLEAR . Choose the triangle type 2 . If the last time y ou us ed the T r iangle S olv er aplet you used the ri ght -angled tr iangle input f orm , that input form i s di sp l ayed again (as in the e x ample at the r ight). If the tri angle y ou ar e inv estigating is n ot a ri ght -angled tr iangle , or you ar e not sur e what ty pe it is, y ou should use the gener al input f orm (illustr ated in the pr e v i ous st ep) . T o s witc h to the gener al input f orm , pres s . If the gener al input for m is display ed an d y ou ar e inv estigating a r ight-angled tri angle , pr es s to displa y the simpler input f orm . Specify the known values 3 . Using the arr ow k e ys , mov e to a f ie ld wh os e value y ou know , enter the value and pr ess or . Repeat f or each kno w n value . Note that the lengths of the side s ar e labeled A , B , and C , and the angles are la beled α , β , and δ . It is important that y ou enter the kno wn value s in the appr opr iate f ields . In our e xam ple , w e kno w the length of tw o sides and the angle at w hic h thos e side s meet . Hence if w e spec if y the le ngths of si des A and B, w e must enter the angle as δ (since δ is the angle wher e A an d B meet) . If instead we enter ed the HP 3 9gs Engl ish. book Pa ge 2 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Triangle Solve apl et 9-3 lengths as B and C, w e would ne ed to spec if y the angle as α . T he illustr a ti on on the displa y w ill help y ou determine wher e to enter t he know n values. Note: if y ou need to change the angle measur e mode , pres s MOD E S , c hange the mode , and then pr ess to r etur n to the aplet . 4. Pr ess . T he solv er calc ulates the values of the unkno w n va r iab les and display s. As the illustr ation at the r igh t sho w s, the lengt h of the unkno wn side in our e x ample is 3 .2 29 6. (The other two angle s hav e also been calc ulated.) Note: if two si des and an adjacent ac ute angle ar e enter ed and ther e are tw o solu tion s, onl y one w ill be display ed initially . In this case , an menu k ey is display ed (as in this e x ample) . Yo u p r e s s t o display the second solu tion , and again to r eturn to the fir st soluti on. Errors No solution with given data If you are using the general input form and you enter more than 3 values, the values might not be consistent, that is, no triangle could poss ibly have all the values you specified. In these cases, No sol with give n data appear s on the screen. The situation is similar if you are using the simpler input form (for a right-angled tria ngle) and you enter more than two values. HP 3 9gs Engl ish. book Pa ge 3 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
9-4 Triangle Solv e aplet Not enough data If you are using the general input form, you need to specify at least three values for the Triangle Solver to be able to calculate the remaining attributes of the triangle. If you specify less than three , Not enough data appears on the screen. If you are using the simplified input form (for a right- angled triangle), you must specify at least two values. In addition, you cannot specify only angles and n o lengths. HP 3 9gs Engl ish. book Pa ge 4 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Statistics aplet 10-1 10 Statis tic s a ple t About the Statistics aplet The Statistics aplet can store up to ten data sets at one time. It can perform one- variab le or two-variable statistical analysis of one or more sets of data. The Statistics aplet starts with the Numeric view which is used to enter data. The Symbol ic view is used to specify which columns contain data and which column contains frequencies. You can also compute stat istics values in HOME and recall the values of specif ic statistics variables. The values computed in the Stat istics aplet are saved in variables, and many of these variables are listed by the function accessible from the Statistics apletâs Numeric view screen. Getting started with the Statistics aplet The following example asks y ou to enter and analyze the advertising and sales data (i n the table below), compute statistics, fit a curve to the data, and predict the effect of more advertising on sales. Adver tisin g mi nute s (independent, x) Resulting Sales ($) (dependent, y) 21 4 0 0 1 9 2 0 31 1 0 0 52 2 6 5 52 8 9 0 42 2 0 0 HP 3 9gs Engl ish. book Pa ge 1 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
10-2 Statistics aplet Open the Statistics aplet 1. Open the S tatisti cs a plet and c lear ex isting data b y pr essing . Select Statistics Th e S ta t is ti cs ap l et starts in the Numer ical view . At an y time the Statisti cs aplet is conf igur ed for o nly one of t wo types of sta tistical explorations: one - var iable ( ) or tw o-v ariable ( ) . The 5th menu k ey label in the Numer ic vi e w toggles betw een these tw o options and show s the cur r ent opti on . 2 . Select . Y ou need to selec t because in this e x ample w e are anal yzing a dataset compr ising two v ar iable s: ad v ertising minut es and r esulting s ales . Enter data 3 . Ente r the data into the columns . 2 1 3 5 5 4 to mo ve to the ne xt column 1400 9 20 1100 2 2 6 5 2 8 90 2 200 1VAR/2VAR men u k ey l abel HP 3 9gs Engl ish. book Pa ge 2 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Statistics aplet 10-3 Choose fit and data columns 4. Selec t a fit in the S ymboli c setup v ie w . SETUP - SYMB Sele ct Linear Y ou c a n cre at e u p t o five ex p lo ra t io n s of t wo - va ri ab l e data , named S1 to S5 . I n t hi s exa m pl e, we wil l cre a te jus t o n e: S1 . 5 . Spec ify the columns that hold the data yo u w ant to analyz e. Yo u c o u l d h a v e e n t e r e d y our data int o columns other than C1 and C2 . Explore statistics 6 . F ind the mean adv ertising time ( MEANX ) and the mean sales ( MEANY ). MEANX is 3 .3 minu tes and MEANY is ab out $17 9 6 . 7 . Sc r oll dow n to dis play the v alue for the corr elatio n coeff ic ient ( CORR ). T he CORR v alue i ndicates ho w w ell the linear model f its the data . 9 times T he value is .8 99 5 . HP 3 9gs Engl ish. book Pa ge 3 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
10-4 Statistics aplet Setup plot 8. Change the plo tting range to e nsur e all the data points ar e plot ted (and select a diff er ent point mar k, if yo u wi s h ) . SETUP - PLOT 7 100 400 0 Plot the graph 9 . P lot the gr aph. Draw the regression curve 10. Dra w the reg r essi on c urve (a c ur ve to fi t the data points). T his dra w s the r egr ession line fo r the best linear f it. Display the equation for best linear fit 11. Retur n to the S ymbo lic v ie w . 12 . Displa y the equ ation f or the be st linear f it . to mov e to the FIT1 fie l d T he full FIT1 e xpr essi on is sho wn . T he slope ( m ) i s 425.87 5. Th e y -inter cept ( b ) is 3 7 6. 25. HP 3 9gs Engl ish. book Pa ge 4 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Statistics aplet 10-5 Predict values 13 . T o f ind the pr edic ted sales f igur e if ad v ertising w er e to go up to 6 minute s: S ( to highlight Stat-Two ) (to highligh t PREDY ) 6 14. Retu rn to the P lot vi e w . 15 . Jum p to the indicat ed point on the r egr essi on line . 6 Observ e the pr edict ed y -v alue in the left bottom corner of the screen. HP 3 9gs Engl ish. book Pa ge 5 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
10-6 Statistics aplet Entering and editing statistical data The Numeric view ( ) is used to enter dat a into the Statistics aplet. Each column represents a variable named C0 to C9 . After entering the data, you must define the data set in the Symbolic view ( ). HINT A data column must have at least four data points to provide vali d two-variable statistics, or two data points for one-var iable stat istics. You can also store statistical da ta values by copying lists from HOME into Statistics data columns. For ex ample, in HOME, L1 C1 stores a copy of the list L1 into the data-column var iable C1 . Statistics apletâ s NUM view keys The Statistics apletâs Numeric view keys are: Key M e a n i n g Copies the highlighted item into the edit line. Inserts a zero value above the highlighted cell. Sorts the specified independ ent data column in ascending o r descending order, and rearr anges a specified dependent (o r frequency) data column accordingly. Switches between larger and smaller font sizes. A toggle switch to select one- variable or two-variable statistic s. This setting affects the statistical calculations and plots. The label indicates which setting is current. Computes descriptive statistics for each data set specified in Symbolic view. HP 3 9gs Engl ish. book Pa ge 6 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Statistics aplet 10-7 Example Yo u are measuring the height of students in a classroom to find the mean height. The first five students have the following measurements 160cm, 165cm, 1 70cm, 175cm, 180cm. 1. Open the Stati stics aplet . Sele ct Statistics 2 . Enter the measurement data. 160 16 5 17 0 17 5 180 3 . F ind the mean of the sampl e. Ensur e the / menu k ey label re a ds . Pr ess to see the statis tic s calc ulated fr om the sample data in C1 . Deletes the currently highlighted value. CLEAR Clears the current column or all columns of data. Pregss CLEAR to display a menu list, then select the current colu mn or all columns option, and press . cursor key Moves to the first or last row, or first or last column. K ey Meaning (Conti nued) HP 3 9gs Engl ish. book Pa ge 7 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
10-8 Statistics aplet Note that the title o f the colu mn o f st atis ti cs i s H1 . Ther e a r e 5 data set de f initions a vailable for one -v ari able sta tis tics : H1âH5 . If data is entered in C1 , H1 is automatically set to use C1 fo r data , and the fr equency of eac h data point is set to 1. Y ou can select other columns o f data fr om the St atisti cs S ymbo lic s etup v ie w . 4. Pr ess to c lose the statisti cs w indow and pr ess k ey to see the data set definiti ons. T he firs t column indicates the ass oc iated column of data for eac h data set def inition , and the second column indicate s the constant f r equenc y , or the column that holds the frequ en c ies. T he ke ys y ou can use f r om this w indo w ar e: Key M e a n i n g Copies the column variable (or variable expression) to the edit line for editing. Press when done. Checks/unchecks the current data set. Only the checkmarked data set(s) are computed and plotted. or Typing aid for the column variables ( ) or for the Fit expressions ( ). Displays the current variable expression in standard mathematical form. Press when done. Evaluates the variables in the highlighted column (C1, etc.) expression. HP 3 9gs Engl ish. book Pa ge 8 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Statistics aplet 10-9 To continue our example, supp ose that the heights of the rest of the students in the class are measured, but each one is rounded to the nearest of the five values first recorded. Instead of entering all the new data in C1 , we shall simply add another column, C2 , that holds the frequencies of our five data points in C1 . 5 . Mo ve the highli ght bar into the r ight column of the H1 def inition and r eplace the f r equenc y v alue of 1 w ith the name C2 . 2 Displays the menu for en tering variable names or contents of variables. Displays the menu for entering math operations. Deletes the highlighted variable or the current character in the edit line. CLEAR Resets default specifications for the data sets or clears the edit line (if it was ac tive). Note: If CLEAR is used the data sets will need to be selected again before re-use. K ey Meaning (Conti nued) Heig ht (cm) Freq ue ncy 160 5 165 3 170 8 175 2 180 1 HP 3 9gs Engl ish. book Pa ge 9 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
10-10 Statistics aplet 6 . R eturn t o the numer ic vi ew . 7 . Ente r the fr equency data sho wn in the a bo ve t able . 5 3 8 2 1 8. Displa y the computed sta tis tics. The mean height is approxim ately 167.63cm. 9 . Setup a histogr am plot for the data . SETUP - PLOT Enter s et up inf or matio n appropriate to your data. 10. P lot a histogr am of the data. Save data The data that you enter is automatically saved. When you are finished entering data values, y ou can press a ke y for another Statistics view (like ), or you can switch to another aplet o r HOME. Edit a data set In the Numeric view of the Statistics aplet, highlight the data value to change. Type a new value and press , or press to copy the valu e to the edit line for modification. Press after modifying the value on the edit line. HP 3 9gs Engl ish. book Pa ge 10 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Statistics aplet 10-11 Delete data ⢠T o delete a single data item, highli ght it and pr ess . T he value s belo w the delet ed cell w ill scr oll up one ro w . ⢠T o delete a column of data , highli ght an entry in that column and press CLEAR . Select the co lumn name . ⢠T o delete all columns of data , pres s CLEAR . Sele ct All columns . Insert data Highlight the entry following the point of insertion. Press , then enter a numbe r. It will write over t he zero that was inserted. Sort data values 1. In Numer ic v ie w , highli ght the column y ou want to sort , and pr ess . 2 . S pec ify the Sort Order . Y ou can choo se either Ascending or Descending . 3 . Spec ify the INDEPENDENT and DEPENDENT data columns. S orting is by the independent column . For instance , if Age is C1 and Income is C2 and y ou w ant to sort by Income , then you mak e C2 the independen t column for the s orting and C1 the dependent column. â T o sort jus t one column , choo se None f or the dependent column . â F or one -v ari able stat istic s w ith two data columns , spec ify the fr equenc y column as the depende nt column. 4. Pr ess . HP 3 9gs Engl ish. book Pa ge 11 We dnes day, Dec embe r 7, 2005 11 : 24 PM
10-12 Statistics aplet Defining a regression model The Symbolic view includes an expression (Fit1 through Fit5) that defines the regression model, or âfitâ, to use for the regression analysis of each two-variable data set. There are three ways to select a regression model: ⢠Accept the d efa ult opt ion to f it th e data to a straight line . ⢠Selec t one of the a v ailable f it options in S y mbolic Setup v ie w . ⢠Enter y our o w n mathematical e xpres sio n in S ymboli c v ie w . This e xpr ession w ill be plot ted, bu t it w ill not be fi tted to the data po ints . Angle Setting You can ignore the angle measurement mode unless your Fit definition (in Symbo lic view) involves a trigonometric function. In this case, you should specify in the mode screen whether the trigonometric units are to be interpreted in degrees, radians, or grads. To choose the fit 1. In Numer ic vi e w , make sur e is set . 2. P r e s s SETUP - SYMB to display the S ymbolic Setup v ie w . Hi ghlight the F it number ( S1FIT to S5FIT ) y ou w ant to define . 3 . Pr ess and select f r om the list. Pr ess when done . Th e r egr essi on f orm ula fo r the fit is displa y ed in S ymboli c v ie w . Fit models T en fit models are available: F it model M eaning Linear (Default.) Fits the data to a straight line, y = mx b . Uses a least-squares fit. Logarithmic Fits to a logarithmic curve, y = m ln x b . Exponential Fits to an exponential curve, y = be mx . Power Fits to a power curve, y = bx m . HP 3 9gs Engl ish. book Pa ge 12 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Statistics aplet 10-13 To define your own fit 1. In Numer ic v ie w , mak e sure is set . 2 . Display the S y mbolic v iew . 3 . Highligh t the F it expr es sion ( Fit1 , et c.) f or the desir ed data set. 4. T ype in an e xpr ess ion an d pr ess . The independent variable must be X , and the e xpr essi on mu st not cont ain any unkn o wn v aria bles. Ex ample: . This automatically changes the Fit type ( S1FIT , etc.) in the Symbolic Setup view to User Defined . Quadratic Fits to a quadratic curve, y = ax 2 bx c . Needs at least three points. Cubic Fits to a cubic curve, y = ax 3 bx 2 cx d . Needs at least four points. Logistic Fits to a logistic curve, , where L is the saturation value for growth. You can store a positive real value in L , orâif L = 0âlet L be computed automatically. Exponent Fits to an exponent curve, . Trigonometric Fits to a trigonometric curve, . Needs at least three points. User Defined Define your own expression (in Symbolic view.) F it model Meaning (Continued) y L 1 ae bx â () ------------------------- - = ya b x = ya b x c () sin â d = 1.5 x cos à 0.3 x sin à HP 3 9gs Engl ish. book Pa ge 13 We dnes day, Dec embe r 7, 2005 11 : 24 PM
10-14 Statistics aplet Computed statistics One-variable When the data set contains an odd number of values, the data setâs median value is no t us ed when calculating Q1 and Q3 in the table above. For example, for the following data set: { 3,5,7,8,15,16,17} only the first three items, 3, 5, and 7 are used to calculate Q1, and only the last three ter ms, 15, 16, and 17 are used to calculate Q3. Statistic Definition N Σ Number of data points. TOT Σ Sum of data values (with their frequencies). MEAN Σ Mean value of data se t. PVAR Σ Population variance of data set. SVAR Σ Sample variance of data set. PSDEV P opulation standard deviation of data set. SSDEV Samp le standard deviation of da ta set. MIN Σ Mi nimum data value in data set. Q1 First quartile: median of values to left of median. MEDIAN Median value of da ta set. Q3 Third quartile: median of values to right of median. MAX Σ Maxi mum data value in data set. HP 3 9gs Engl ish. book Pa ge 14 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Statistics aplet 10-15 Two-variable Plotting You can plot: ⢠histogr ams ( ) ⢠bo x -and-whisk er plots ( ) ⢠scat ter plots ( ) . Once you have ente red your data ( ), defined your data set ( ), and defined your Fit model for two- variable statistics ( SETUP - SYMB ), you can plot your data. You can plot up to five scatter or box-an d-whisker plots at a time. You can plot only one histogram at a time. Statistic Definition MEANX Mean of x - (independent ) values. Σ X Sum of x -values. Σ X2 Sum of x 2 -values. MEANY Mean of y - (dependent) values. Σ Y Sum of y -values. Σ Y2 Sum of y 2 -values. Σ XY Sum of each xy . SCOV Sample covarianc e of independent and dependent data columns. PCOV Population covariance of independent and dependent data columns CORR Correlation c oefficient of the independent and dependent data columns for a linear fit only (regardless of the Fit chosen). Returns a value from 0 to 1, where 1 is the best fit. RELERR The relati ve error for the selected fit. Provides a measure of accuracy for the fit. HP 3 9gs Engl ish. book Pa ge 15 We dnes day, Dec embe r 7, 2005 11 : 24 PM
10-16 Statistics aplet To plot statistical data 1. In S ymboli c v ie w ( ) , select ( ) the data sets y ou w ant to plot . 2 . Fo r one -var iable dat a ( ) , selec t the plot type in P lot Setup ( SETUP - PLOT ) . Highli ght ST A TPLOT , pr ess , select either Histogram or BoxWhisker , and pr es s . 3 . F or any plot , but espec iall y fo r a histogr am, adj ust the plottin g scale and range in th e P l ot Setup v ie w . If y ou find histogr am bars too fat or too thin, y ou can adjus t them b y adj usting the HWIDTH sett in g . 4. Pr ess . If y ou ha ve not adj usted the P lot Se tup y ours elf , you can try se le ct Auto Scale . Auto Scale can be relied upon to give a good starting scale which can then be adjusted in the Plot Setup view. Plot types Histogram One-variable statistics . The numbers below the plot mean that the current bar (where the cursor is) starts at 0 and ends at 2 (not including 2), and the frequency for this column, (that is, the number of data elements that fall between 0 and 2) is 1. You can see information about the n ext bar by pressing the k ey. Box and Whisker Plot One-variable statistics . The left whisker marks the minimum data value. The box marks the first quartile, the median (where the cursor is), and the third quartile. The right whisker marks the maximum data value. The numbers below the plot mean that this column has a median of 13. HP 3 9gs Engl ish. book Pa ge 16 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Statistics aplet 10-17 Scatter Plot Tw o-variable statistics . The numbers below the plot indicate that the cursor is at the first data point for S2, at (1, 6). Press to move to the next data point and display information about it. To connect the data points as they are plotted, checkmark CONNECT in the second page of the Plot Setup. This is not a regression curve. Fitting a curve to 2VAR data In the Plot view, press . This draws a curve to fit the checked two-variable data set(s). See âT o choose the fitâ on page 10-12. The e xpressi on in Fit2 sho ws that the slope = 1.98 08 21917 81 and the y - i n t e r c e p t = 2. 26 57 . Correlation coefficient The correlation coeffici ent is stored in the CORR variable. It is a measure of fit to a line ar curve only. Regardless of the Fit model you have chosen, CORR relates to the linear model. HP 3 9gs Engl ish. book Pa ge 17 We dnes day, Dec embe r 7, 2005 11 : 24 PM
10-18 Statistics aplet Relati ve Error The relative error is a measure of the error between predicted values and actual va lues based on the specified Fit. A smaller number means a better fit. The relative error is stored in a variable named RELERR . The relative error provides a measur e of fit accuracy for all fits, and it does depend on the Fit model you have chosen. HINT In order to access the CORR and RELERR variables after you plot a set of statistics, you must press to access the numeric view and then to display the correlation values. The values are stored in the variables when you access the Symbolic view. Setting up the plot (Plot setup view) The Plot Setup view ( SETUP - PLOT ) sets most of the same plotting parameters as it does for the other built-in aplets. See âAbout the Plot viewâ on page 2-5. Sett ings unique to the Statistics aplet are as follows: Plot type (1VAR) STATPLOT enables you to specify eithe r a histogram or a box-and-whisker plot for one-variable statistics (when is set). Press to change the highlighted setting Histogram width HWIDTH enables you to spec ify the width of a his togram bar. This determines how many bars will fit in the display, as well as how the data is di stributed (how many values each bar represents). Histog ram rang e HRN G enables you to specify th e range of values for a set of histogram bars. The r ange runs from the left edge of the leftmost bar to the right edge of the rightmost bar. You can limit the range to exclude any values you suspe ct are outliers. Plotting mark (2VAR) S1MARK through S5MARK enables you to specify one of five symbols to use to plot each data set. Press to change the highlighted setting. Connected points (2VAR) CONNECT (on the second page), when checkmarked, connects the data points as they are plotted. The resulting line is not the regression curve. The order of plotting is according to the ascending order of independent values. HP 3 9gs Engl ish. book Pa ge 18 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Statistics aplet 10-19 For instance, the data set (1,1 ), (3,9), (4,16), (2,4) would be plotted and traced in the order (1,1), (2,4), (3,9), (4,16). Trouble-shooting a plot If you have problems plotting, check that you have the following: ⢠T he cor r ect or menu label o n (Numer ic vi ew ) . ⢠T he corr ect fit (r egres sion model), if the data set is tw o -v ar ia ble . ⢠Only the data sets to compute or plot are chec kmarked (S y mbolic v iew ) . ⢠T he corr ect plotting r ange . T r y using Auto Scale (instead o f ), or adjust the plotting par ameters (in Plo t Setup) fo r the range s of the ax es and the w idth of hist ogr am bars ( HWIDTH ). In mode, ensure that both paired columns contain data, and that they are the same length. In mode, ensure that a paired column of fre quency values is the same length as th e data column that it refers to. Exploring the graph The Plot view has menu keys for zooming, tracing, and coordinate display. There are also scaling options under . These options are desc ribed inâEx ploring the graphâ on page 2-7. Statistics apletâs PLOT view keys K e y Meaning CLEAR Erases the plot. Offers additional pre-defined views for splitting the screen, overlaying plots, and autoscaling the axes. Moves cursor to far left or far right. HP 3 9gs Engl ish. book Pa ge 19 We dnes day, Dec embe r 7, 2005 11 : 24 PM
10-20 Statistics aplet Calculating predicted values The functions PREDX and PREDY estimate (predict) values for X or Y given a hypothetical value for the other. The estimation is made based on the curve that has been calculated to fit the data a ccording to the specified fit. Find predicted values 1. In P lot v iew , dra w the r egr essi on curve f or the data set. 2 . Pres s to mo ve to the r egr essio n c urve . 3 . Pres s and enter the v alue of X . T he c urso r jumps to the specif ied point on the curve and th e coor dinate displa y sho ws X and the pr edicted v alue of Y . In HOME: ⢠Enter PREDX ( y-value ) to find the pr edic ted v alue for the indepe ndent v ar iable gi ven a h y potheti cal dependen t value . Displays ZOOM menu. Turns trace mode on/off. The white box appears next to the option when Trace mode is active. Turns fit mode on or off. Turning on draws a curve to fit the data points according to the current regression model. (2var statistics only) Enables you to spe cify a value on the line of best fit to jump to or a data point number to jump to. Displays the equation of the regression curve. Hides and displays the menu key labels. When the la bels are hidden, any menu key displays the (x,y) coordinates. Pressing redisplays the menu labels. K e y Meaning (Continued) HP 3 9gs Engl ish. book Pa ge 20 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Statistics aplet 10-21 ⢠Enter P RED Y( x-value ) to f ind the pr edicted v alue of the dependent var iable gi ven a h ypothetical independent va riab l e. You can type PREDX and PREDY into the edit line, or you can copy these function names from the MATH menu under the Stat-Two category. HINT In cases where more than one fit curve is displayed, the P RED Y function uses the most recently calculated curve. In order to avoid errors with th is function, uncheck all fits except the one that you want to work w ith, or use the Plot View method. HP 3 9gs Engl ish. book Pa ge 21 We dnes day, Dec embe r 7, 2005 11 : 24 PM
HP 3 9gs Engl ish. book Pa ge 22 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Inference aplet 11-1 11 Inference aplet About the Inference aplet The Inference capabilities include calculation of confidence intervals and hy pothesis tests based on the Normal Z-distribution or Studentâs t-distribution. Based on the statistics from one or two samples, you can test hypotheses and find confidence intervals for the following quantities: ⢠mean ⢠pro portion ⢠diff erence betw een two means ⢠diff erence between two proportions Example data When you first access an input form for an Inference test, by default, the input form contai ns example data. This example data is designed to return meaningful results that relate to the test. It is useful for gaining an understanding of what the test does, and for demonstrating the test. The calculatorâs on-line help provides a descripti on of what the example data represents. Getting started with the Inference aplet This example describes the Inference apletâs options and functionality by stepping you through an example using the examp le data for the Z-Te st on 1 mean. Open the Inference aplet 1. Open the Inference aplet. Select Inference . The Inference aplet opens in the Symbolic view. HP 3 9gs Engl ish. book Pa ge 1 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
11-2 Inference a plet Inference apletâs SYMB view keys The table below summarizes the options available in Symbolic view. If you choose one of the hypoth esis tes ts, you can choose the alternative hypothesis to test against the null hypothesis. For each test, th ere are three possible choices for an alternative hypothesis based on a quantitative comparison of two quantiti es. The null hypothesis is always that the two quantities are equal.Thus, the alternative hypotheses cover th e various cases for the two quantities being unequal: <, >, and â . In this section, we will use th e example data for the Z-Test on 1 mean to illustrate how the aplet works and what features the various views present . Hypothesis Tests Confidence Intervals Z: 1 μ , the Z-T est on 1 mean Z-Int: 1 μ , the confidence interval for 1 mean, based on the Normal distribution Z: μ 1 â μ 2 , the Z-Test on the difference of two means Z-Int: μ 1 â μ 2 , the confidence interval for the difference of two means, based on the Normal distribution Z: 1 Ï , the Z-Te st on 1 proportion Z-Int: 1 Ï , the confidence interval for 1 proportion, based on the Normal distribution Z: Ï 1 â Ï 2, the Z-Test on the difference in two proportions Z-Int: Ï 1 â Ï 2, the con fidence interval for the difference of two proportions, based on the Normal distribution T: 1 μ , the T-Test on 1 mean T-Int: 1 μ , the confidence interval for 1 mean, based on the Studentâs t-distribution T: μ 1 â μ 2 , the T- Test on the difference of two means T-Int: μ 1 â μ 2 , the confidence interval for the difference of two means, based on the Studentâs t-distribution HP 3 9gs Engl ish. book Pa ge 2 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Inference aplet 11-3 Select the inferential method 2. Select the Hypothesis Test inferential method. Select HYPOTH TEST 3. Define the type of test. ZâTest: 1 μ 4. Select an alternative hypothesis. μ< μ0 Enter data 5. Enter the sample statis tics and population parameters. setup-NUM The table below lists the fields in this view for our current Z-Test: 1 μ example. Field name Definition μ 0 Assumed population mean Ï Population standard deviatio n Sample mean n Sample size α Alpha level for the test x HP 3 9gs Engl ish. book Pa ge 3 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
11-4 Inference a plet By default, each field already contains a value. These values constitu te the example database and are expla ined in the feature of this aplet. Display on-line help 6. To display the on-line help, press 7. To close the on-line help, press . Display test results in numeric format 8. Display the test results in numeric format. The test dis tribution value and its associated probability are displayed, along with the critical value(s) of the test and the associated critical value(s) of the statistic. Note: You can access the on-line help in Numeri c view. Plot test results 9. Display a graphic view of the test results. Horizontal axes are presented for both the distribution variable and the test statistic. A generic bell curve repre sents the probability distribution func tion. Vertical lines mark the critical value(s) of the test, as well as the value of the test statistic. The rejection region is marked and the test numeric results are displayed betwee n the horizontal axes. Importing sample statistics from the Statistics aplet The Inference aplet supports th e calculation of confidence intervals and the testing of hypotheses based on data in the Statistics aplet. Computed statistics for a sample of data in a column in any St atistics-based aplet can be imported for use in the Infe rence aplet. The following example illustrates the process. R HP 3 9gs Engl ish. book Pa ge 4 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Inference aplet 11-5 A calculator produces the following 6 random number s: 0.529, 0.295, 0.95 2, 0.259, 0.925, and 0. 592 Open the Statistics aplet 1. Open the Statistics aplet and reset the current settings. Select Statistics The Statistics aplet opens in the Numeric view. Enter data 2. In the C1 column, enter the random numbers produced by the calculator. 529 295 952 259 925 592 HINT If the Decimal Mark setting in the Modes input form ( modes ) is set to Comma, use instead of . 3. If necessary, select 1-va ri able statistics. Do this by pressing the fifth menu key until is displayed as its menu label. Calculate statistics 4. Calculate statistics. The mean of 0.592 seems a little large compared to the expected value of 0.5. To see if the difference is statistically significant, we will use the statist ics computed here to construct a confidence inter val for the true mean of the population of random numbers and see whether or not this interval contains 0.5. 5. Press to close the computed statistics window. HP 3 9gs Engl ish. book Pa ge 5 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
11-6 Inference a plet Open Inference aplet 6. Open the Inference aplet and clear current s ettings. Select Inference Select inference method and type 7. Select an inference me thod. Select CONF INTERVAL 8. Select a distribution statistic type. Select T-Int: 1 μ Set up the interval calculation 9. Set up the interval calculation. Note: The default values are derived from sample data from the on-line help example. Setup-NUM HP 3 9gs Engl ish. book Pa ge 6 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Inference aplet 11-7 Import the data 10. Import the data from the Statistics aple t. Note: The data from C1 is disp layed by default. Note: Press to see the statistics before importing them into the Numeric Setup view. Also, if there is more than one ap let based on the Statistics aplet, you are prompted to choose one. 11. Specify a 90% confidence interval in the C: field. to move to the C: field 0.9 Display Numeric view 12. Display the confi dence interval in the Numeric view. Note: The interval setting is 0.5. Display Plot view 13. Display the confidence interval in the Plot view. You can see, from the second text row, that the mean is contained within the 90% confidence interval (CI) of 0.346981 4 to 0.8370186. Note: The graph is a simple, generic bell-c urve. It is not meant to accurately represent the t-distribution with 5 degrees of freedom. HP 3 9gs Engl ish. book Pa ge 7 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
11-8 Inference a plet Hypothesis tests You use hypothesis tests to test the validity of hypotheses that relate to the statistical parameters of one or two populations. The tests are base d on statistics of samples of the populations. The HP 39gs hypothesis tests use the Normal Z-distribution or Studentâ s t-distribution to calcula te probabilities. One-Sample Z-Test Menu name Z-Test: 1 μ On the basis of statistics from a single sample, the One-Sample Z-Test measures th e strength of the evidence for a selected hypothesis against the null hypothesis. The null hypothesis is that the population mean equals a specified value Î 0 : μ = μ 0 . You select one of the following alternative hypothese s against which to test the null hypothesis: Inputs The inputs are: H 1 : μ 1 μ 2 < H 1 : μ 1 μ 2 > H 1 : μ 1 μ 2 â Field name Definition Sample mean. n Sample si ze. μ 0 Hypothetical population mean. Ï Population standard devi ation. α Significance level. x HP 3 9gs Engl ish. book Pa ge 8 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Inference aplet 11-9 Results The results are: Two-Sample Z-Test Menu name Z-Test: μ 1â μ 2 On the basis of two samples, each from a separate population, this test measu res the strength of the evidence for a selected hypothesis against the null hypothesis. The null hypothesis is that the mean of the two populations are equal (H 0 : μ 1= μ 2). You select one of the following alternative hypothe ses against which to test the null hypothesis: Inputs The inputs are: Result Description Test Z Z-test statistic. Prob Probability associated with the Z-Test statistic. Critical Z Boundary values of Z associated with the α level that you supplied. Critical Boundary values of required by the α value that you supplied. x x H 1 : μ 1 μ 2 < H 1 : μ 1 μ 2 > H 1 : μ 1 μ 2 â Field name Definiti on Sample 1 mean. Sample 2 mean. n1 Sample 1 size. n2 Sample 2 size. Ï 1 Po pulation 1 standa rd deviation. x 1 x 2 HP 3 9gs Engl ish. book Pa ge 9 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
11-10 Inference a plet Results The results are: One-Proportion Z-Test Menu name Z-Test: 1Ï On the basis of statistics from a single sample, this test measures the strength of the evidence for a selected hypothesis against the null hypothesis. The null hypothesis is that the proportion of su ccesses in the two populations is equal: H 0 : Ï = Ï 0 You select one of the following alternative hypothese s against which to test the null hypothesis: Ï 2 Population 2 standard deviation. α Significance level. Field name Definition (Continued) Result Description Test Z Z-Test statistic. Prob Probability associated with the Z-Test statistic. Critical Z Boundary value of Z associated with the α level that you supplied. H 1 : ÏÏ 0 < H 1 : ÏÏ 0 > H 1 : ÏÏ 0 â HP 3 9gs Engl ish. book Pa ge 10 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Inference aplet 11-11 Inputs The inputs are: Results The results are: Two-Proportion Z-Test Menu name Z-Test: Ï 1 â Ï 2 On the basis of statistics fr om two samples, each from a different population, the Two-Proportion Z-Test measures the stre ngth of the evidence for a selected hypo thesis against the null hypothesis. The null hypothesis is that the proportion of successes in th e two populations is equal H0: Ï 1 = Ï 2 . You select one of the following alternative hypothe ses against which to test the null hypothesis: Field name Definitio n x Number of successes in the sample. n Sample size. Ï 0 Population proportion of successes. α Significance level. Result Description Test P Proportion of successes in the sample. Test Z Z- Test statist ic. Prob Probability associated with the Z-Test statistic. Critical Z Boundary value of Z associ ated with the level you supplied. H 1 : Ï 1 Ï 2 < H 1 : Ï 1 Ï 2 > H 1 : Ï 1 Ï 2 â HP 3 9gs Engl ish. book Pa ge 11 We dnes day, Dec embe r 7, 2005 11 : 24 PM
11-12 Inference a plet Inputs The inputs are: Results The results are: One-Sample T-Test Menu name T-Test: 1 μ The One-sample T-Test is used when the population standard deviation i s not know n. On the basis of statistics from a single sample, this tes t measures the strength of the evidence for a selected hypothesis against the nu ll hypothesis. The null hypothesis is that the sample mean has some assumed value, Î 0 :μ = μ 0 You select one of the following alternative hypothese s against which to test the null hypothesis: Field name Definition X1 Sample 1 mean. X2 Sample 2 mean. n1 Sample 1 size. n2 Sample 2 size. α Significance level. Result Description Test Ï 1â Ï 2 Difference between the proportions of successes in the two samples. Test Z Z-Test statistic. Prob Probability associated with the Z-Test statistic. Critical Z Boundary values of Z associated with the α level that you supplied. H 1 : μμ 0 < H 1 : μμ 0 > H 1 : μμ 0 â HP 3 9gs Engl ish. book Pa ge 12 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Inference aplet 11-13 Inputs The inputs are: Results The results are: Field name Definiti on Sample mean. Sx Sample standard de viation. n Sample size. μ0 Hypothetical population mean. α Significance level. x Result Description Test T T-Test statistic. Prob Probability associated with the T-Test statistic. Critical T Boundary value of T assoc iated with the α level that you supplied. Critical Boundary value of required by the α value that you supplied. x x HP 3 9gs Engl ish. book Pa ge 13 We dnes day, Dec embe r 7, 2005 11 : 24 PM
11-14 Inference a plet Two-Sample T-Test Menu name T-Test: μ 1 â μ 2 The Two-sample T-Test is used when the population standard deviation i s not know n. On the basis of statistics from two samples, each sample from a different population, this test measures the strength of the evidence for a selected hypothesis against the null hypothesis. The null hypothesis is that the two populations means are equal H 0 : μ 1 = μ 2 . You select one of the following alternative hypothese s against which to test the null hypothesis Inputs The inputs are: H 1 : μ 1 μ 2 < H 1 : μ 1 μ 2 > H 1 : μ 1 μ 2 â Field name Definition Sample 1 mean. Sample 2 mean. S1 Sample 1 standard dev iation. S2 Sample 2 standard dev iation. n1 Sample 1 si ze. n2 Sample 2 si ze. α Si gnificance level. _Pooled? Check this option to pool samples based on their standard d eviations. x1 x2 HP 3 9gs Engl ish. book Pa ge 14 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Inference aplet 11-15 Results The results are: Confidence intervals The confidence interval calculations that the HP 39gs can perform are based on the Normal Z-distribution or Studentâs t-distribution. One-Sample Z-Interval Menu name Z-INT: μ 1 This option uses the Normal Z-distributio n to calculate a confidence interval for m, the true mean of a population, when the true population standard deviation, s, is known. Inputs The inputs are: Result De scription Test T T-Test statistic. Prob Probability associated with the T-T est statistic. Critical T Boundary values of T assoc iated with the α level that you supplied. Field name Definition Sample mean. Ï Population stand ard deviation. n Sample size. C Confidence level. x HP 3 9gs Engl ish. book Pa ge 15 We dnes day, Dec embe r 7, 2005 11 : 24 PM
11-16 Inference a plet Results The results are: Two-Sample Z-Interval Menu name Z-IN T: μ1 â μ2 This option uses the Normal Z- distribution to calculate a confidence interval for the difference between the means of two populations, μ 1 â μ 2 , when the population st andard deviations, Ï 1 and Ï 2 , are known. Inputs The inputs are: Results The results are: Result Description Critical Z Critical value for Z. μ min Lower bound for μ . μ max Upper bound for μ . Field name Definition Sample 1 mean. Sample 2 mean. n1 Sample 1 si ze. n2 Sample 2 si ze. Ï 1 Population 1 s tandard deviation. Ï 2 Population 2 s tandard deviation. C Confidence level. x1 x2 Result Description Critical Z Critical value for Z. μ Min Lower bound for μ 1 â μ 2 . μ Max Upper bound for μ 1 â μ 2 . Î Î HP 3 9gs Engl ish. book Pa ge 16 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Inference aplet 11-17 One-Proportion Z-Interval Menu name Z-INT: 1 Ï This option uses the Normal Z-distributio n to calculate a confidence interval for the proportion of successes in a population for the case in wh ich a sample of size, n , has a number of successes, x . Inputs The inputs are: Results The results are: Two-Proportion Z-Interval Menu name Z-I NT: Ï 1 â Ï 2 This option uses the Normal Z-distributio n to calculate a confidence interval for the difference between the proportions of successes in two populations. Inputs The inputs are: Field name Definition x Sample success count. n Sample size. C Confidence level. Result Description Critical Z Critic al value for Z. Ï Min Lower bound for Ï . Ï Max Upper bound for Ï . Field name Definition Sample 1 success count. Sample 2 success count. x 1 x2 HP 3 9gs Engl ish. book Pa ge 17 We dnes day, Dec embe r 7, 2005 11 : 24 PM
11-18 Inference a plet Results The results are: One-Sample T-Interval Menu name T-INT: 1 μ This option uses the Studentâs t-distribution to ca lculate a confidence interval for m, the true mean of a population, for the case in which the true population standard deviation, s, is unknown. Inputs The inputs are: n1 Sample 1 si ze. n2 Sample 2 si ze. C Confidence level. Field name Definition (Continued) Result Description Critical Z Critical value for Z. Ï Min Lower bound for the difference between the proportions of succes ses. Ï Max Upper bound for the difference between the proportions of succes ses. Î Î Field name Definition Sample mean. Sx Sample standard deviatio n. n Sample size. C Confidence level. x 1 HP 3 9gs Engl ish. book Pa ge 18 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Inference aplet 11-19 Results The results are: Two-Sample T-Interval Menu name T-INT: μ 1 â μ 2 This option uses the Studentâs t-distribution to calculate a confidence interval for the difference between the means of two populations, μ 1 â μ 2, when the population standard deviations, s1 and s2, are unknown. Inputs The inputs are: Result Description Critical T C ritical value for T. μ Min Lo wer bound for μ . μ Max Upper bound for μ . Field name Definition Sample 1 mean. Sample 2 mean. s1 Sample 1 standard deviation. s2 Sample 2 standard deviation. n1 Sample 1 size. n2 Sample 2 size. C Confidence level. _Pooled Whether or not to pool the samples based on their stand ard deviations. x1 x2 HP 3 9gs Engl ish. book Pa ge 19 We dnes day, Dec embe r 7, 2005 11 : 24 PM
11-20 Inference a plet Results The results are: Result Description Critical T Critical value for T. μ Min Lower bound for μ 1 â μ 2 . μ Max Upper bound for μ 1 â μ 2 . Î Î HP 3 9gs Engl ish. book Pa ge 20 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Using th e Finance So lver 12-1 12 Using the Finance Solver The Finance Solver, or Fin ance aplet , is available by using the APLET key in your calculator. Use the up and down arrow keys to select the Finance aplet. Your screen should look as follows: Press the key or the soft m enu key to activate the aplet. The result ing screen shows the different elements involved in the soluti on of financial problems with your HP 39gs c alculator. Background information on and applications of financial calculations are provided next. Background The Finance Solver applicatio n provides you with the ability of solving time-value-of-money (TVM) and amortization problems. Th ese problems can be used for calculations involving compound interest applications as well as amortization tables. Compound interest is the process by which earned interest on a given princip al amount is added to the principal at specified compounding perio ds, and then the HP 3 9gs Engl ish. book Pa ge 1 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
12-2 Using the Fina nce Solver combined amount earns interest at a certain rate. Financial calculations involvin g compound interest include savings accounts, mo rtgages, pension funds, leases, and annuities. Time Value of Money (TVM) calculations, as the name implies, make use of the notion that a dollar today will be worth more than a dollar sometime in the future. A dollar today can be inv ested at a certain interest rate and generate a return that the same dollar in the future cannot. This TVM pri nciple under lies the not ion of interest rat es, compound interest and rates of return. TVM transactions can be represented by using cash flow diagrams . A cash flow diagram is a time line divided into equal segments re presenting the compounding periods. Arrows represent the cash flow s, which could be positive (upward arrows) or negati ve (downward arrows), depending on the poin t of view of the lender or borrower. The following cash flow diagram sho ws a loan from a borrower's point of view: On the other hand, the following cash flow diagram shows a load from the lender's point o f view: In addition, cash flow diagrams specify when payments occur relative to the compounding periods: at the beginning of each period or at the end . The Finance Solver application pr ovides both of these payment modes: Begin mode and End mode. The following cash Pres ent v alue (PV) (Loan) Money rece iv ed is a positi ve number Money paid out is a negati ve number E qual per iods 1 23 4 5 (P MT) F uture value (FV) E qual pa yments Pa y m e n t (P MT) Pa y m e n t (P MT) Pa y m e n t (P MT) Pa y m e n t (P MT) } } } } } FV E qual pa yments 1 23 4 5 } } } } PM T } PM T PM T PM T PM T E qual per iods PV Loan } HP 3 9gs Engl ish. book Pa ge 2 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Using th e Finance So lver 12-3 flow diagram shows lease payments at the beginning of each period. The following cash flow diagram shows deposits into an account at the end of each period. As these cash-flow diagrams imply, there are five TVM variables: PV 1 23 4 5 FV Capital i zed value of lease } PM T PM T PM T PM T PM T PV 1 23 4 5 FV PM T PM T PM T PM T PM T N The total number of compounding periods or payments. I%YR The nominal annual interest rate (or investment rate). This rate is divided by the number of paymen ts per year (P/YR) to compute the nominal interest rate per compounding period -- which is the interest rate actually used in TVM calculations. PV The present value of the initial cash flow. To a lender or borrower, PV is the amount of the loan; to an investor, PV is the initial investment. PV always occurs at the beginning of the first period. HP 3 9gs Engl ish. book Pa ge 3 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
12-4 Using the Fina nce Solver Performing TVM calculations 1. La unch the F inanc ial S olv er as indicated at the beginning of this secti on . 2 . Use the arr o w k e ys to hi ghlight the diff ere nt f ields and enter the kno wn var iables in the T VM calc ulations , pr essing the soft -menu k ey after enter ing each kno wn value . Be sure that values ar e enter ed for at least f our of the f iv e TVM var ia bles (namel y , N , I%YR , PV , P MT , and FV) . 3 . If necessar y , enter a differ ent v alue for P/YR (def ault value is 12 , i .e., monthl y pa ymen ts) . 4. Pr es s the k e y to change the P ay ment mode (Beg or End) as re quired . 5 . Us e the arr ow k ey s to highlight the TVM var i able y ou w ish to sol v e fo r and pres s the soft -men u k ey . PMT The periodic payment amount. The payments are the same amount each period and the TV M calculation assumes that no payments are sk ipped. Payments can occur at the beginning or the end of each compounding period -- an option you control by se tting the Payment mode to Beg or End. FV The future value of the transaction: the amount of the final cash flow or the compounded value of the series of previous cash flows. For a loan, this is the size of the final balloon payment (beyond any regular payment due). For an investment this is the cash value of an investment at the end of the investment period. HP 3 9gs Engl ish. book Pa ge 4 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Using th e Finance So lver 12-5 Example 1 - Loan calculations Suppose you finance the purcha se of a car with a 5-year loan at 5.5% annual intere st, compounded monthly. The purchase price of the car is $19,500, and the down payment is $3,000. What are the r equired monthly payments? What is the largest loan you can afford if your maximum monthly payment is $300? Assume that the payments start at the end of the first period. Solution. The following cash flow diagram il lustrates the loan calculations: Start the Finance Solver, selec ting P/YR = 12 and End payment option. ⢠Enter the kn o w n TVM var ia bles as sh o wn in the diagr am abov e. Y our input form should look as fo llo w s: ⢠Hi ghlighting the P MT fi eld , pr ess the soft menu k ey to obtain a pa y ment of -315 .17 (i .e ., P MT = -$315 .17) . ⢠T o deter mine the max imum loan possible if the monthl y pay ments are onl y $3 00, t y pe the value â300 in the P MT f ie ld, highlight the PV fie ld, and pr ess the soft men u k e y . The r esulting v alue is PV = $15, 7 0 5 .85 . PV = $1 6,500 1 2 59 60 FV = 0 l%YR = 5 .5 N = 5 x 12 = 60 P/YR = 12 ; End mode PMT = ? HP 3 9gs Engl ish. book Pa ge 5 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
12-6 Using the Fina nce Solver Example 2 - Mortgage with balloon payment Suppose you have taken out a 30-year, $150,000 house mortgage at 6.5% annual interest. You expect to sell the house in 10 years, repaying the loan in a balloon payment. Find the size of the balloon payment, the value of the mortgage after 10 years of payment. Solution. The following cash flow diagram illustrates the case of the mortgage with balloon payment: ⢠St art the F inance Sol v er , selecting P/YR = 12 and End pa yment opti on. ⢠Enter the kno wn TV M v ari ables as sho w n in the diagr a m abo ve . Y our input f orm , f or calc ulating monthl y pa ymen ts fo r the 30 -y r mortgage , should look as fo llo w s: ⢠Highlighting the P MT field , pre ss the soft menu k ey to obtain a pa yment of -9 4 8.10 (i .e ., P MT = -$9 48.10) ⢠T o dete rmine the balloon pay ment or f utur e value (FV) for the mo rtgage a fter 10 years , use N = 120, highli ght the FV f ield , an d pr es s the soft menu k e y . The r esulting value is FV = -$12 7 ,164.19 . T he negativ e value indicates a p a y ment fr om the homeo wner . C heck that the r equir ed balloon pay ments at the end of 20 years (N=2 40) and 2 5 y ears (N = 300) ar e -$83, 4 9 7 .9 2 and -$48 , 4 5 6.2 4, r especti vel y . PV = $15 0,000 1 2 59 60 l%YR = 6 .5 N = 30 x 12 = 360 (for PMT) N = 10 x 12 = 120 (f or balloon pa yment) P/YR = 12 ; End mode PMT = ? Balloon pa yment , FV = ? HP 3 9gs Engl ish. book Pa ge 6 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Using th e Finance So lver 12-7 Calculating Amortizations Amortization calculations, which also use the TVM variables, determine the amounts applied towards principal and interest in a payment or series of payments. To calculate amortizations: 1. St art the F inance So lv er as indicated at the beginning of t hi s se ction. 2 . Se t the follo w ing T VM v ari ables: a Number of pa y ments per y ear (P/YR) b P a yment at beginning or end of per iods 3 . Stor e values f or the T VM var iable s I%YR , PV , P MT , and FV , w hic h def ine the pa y ment schedule . 4. Pr ess the soft men u k e y and enter the number o f pay ments to amorti z e in this batc h. 5 . Pr ess the soft menu k e y to amorti ze a batc h of pay m ents. T he calculator w ill pro v ide for y ou the amount applied to inter est , to pr inc ipal, and the r emaining balance after this set of pay ments hav e been amor ti z ed. Example 3 - Amortization for home mortgage For the data of Example 2 abov e, find the amortization of the loan after the first 10 years (12x10 = 120 payments). Pressing the soft menu key produces the screen to the left. Enter 120 in the PAYMENTS field, and press the soft menu key to produce the results shown to the right. To continue amortizing the loan: 1. Pr ess the soft menu ke y to stor e th e new balance after the pr ev ious amorti z ation a s PV . 2 . Ente r the number of pa y ments to amorti z e in the ne w batch . HP 3 9gs Engl ish. book Pa ge 7 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
12-8 Using the Fina nce Solver 3 . Pr ess the soft menu k ey to amorti z e the new batch o f pay ments . Repeat st eps 1 thr ough 3 as often as needed. Example 4 - Amortization for home mortgage For the results of Example 3, show the amortization of the next 10 years of the mortgage loan. First, press the soft menu key. Then, keeping 120 in the PAYMENTS field, press the soft menu key to produce the results shown below. To amortize a ser ies of future payments starting at payment p: 1. Calc ulate the balance of the loan at pay ment p-1 . 2 . Stor e the ne w balance in PV using the soft menu k ey . 3 . Amorti z e the ser ies of pa yments s tarting at the new PV . The amortization operation reads the v alues from the TVM variables, rounds the nu mbers it gets from PV and PMT to the current display mode, then calculates the amortization rounded to the same setti ng. The original variables are not c hanged, except for PV, whic h is updated after each amortization. HP 3 9gs Engl ish. book Pa ge 8 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Using mathemati cal functions 13-1 13 Using math ematical func tions Math functions The HP 39gs contains many math func tions. The functions are grouped in categories. For example, the Matrix category contains functions for manipulating matrices. The Probability category (shown as Prob. on the MATH menu) contains functions for working with probability. To use a math function, you enter the function onto the command line, and include the ar guments in parentheses after the function. You can also select a math function from the MATH menu. The MATH menu The MATH menu provides access to math functions, physical constants, and programming constants. The MATH menu is organized by category . For each category of functions on the left, there is a list of function names on the right. The hi ghlighted category is the current category . ⢠When y ou pr ess , you s ee the menu list o f Math categor ies in the left column and the cor r espo nding func tions o f the highli ghted cate gory in the ri ght column. T he menu ke y indi cates that the MA TH FUNCT IONS men u list is acti ve . To select a function 1. Pr ess to display the MA TH menu . The categori es appear in alphabetical or der . Pr ess or to sc ro ll thr ough the cat egor ies . T o skip dir ectl y to a category , pr ess the f irst le tter of the categoryâs name . Note: Y ou do not need to pr ess fir st . HP 3 9gs Engl ish. book Pa ge 1 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
13-2 Using math ematical functions 2 . The list o f func tions (on the r ight) applie s to the c urr ently hi ghlighted category (on the left) . U se and to sw itch bet w een the categor y list and th e func tion lis t . 3 . Hi ghlight the name of the func tion y ou wan t and pr ess . This copi es the fu nctio n name (and an initial par enthesis, if appr opr iate) to the edit line . Function categories Math functions by category Syntax Each functionâs definiti on incl udes its syntax, that is, the exact order and spelling of a functionâs name, its delimiters (punctuation), and its arguments. Note that the syntax for a function does not require spaces. Functions common to keyboard and menus These functions are common to the keyboard and MA TH menu. Ï F or a desc ripti on , see â Ï â on page 13-8. ARG F or a desc r ipti on , see â ARGâ on page 13- 7. F or a desc ripti on , see â â on page 11- 7 . AND F or a desc r iption , see â AND â on page 13-19. â ⢠Cal culus ⢠Comp l ex num be rs ⢠Const ant ⢠Conver t ⢠Hyperb olic trigonometr y (Hy perb .) ⢠Li st s ⢠Lo o p ⢠Matri x ⢠Po l y n o m i a l ⢠Probabil it y ⢠Real n umbers (Real) ⢠Tw o - v a r i a b l e stat istics (Stat-T wo) ⢠Sym b o l i c ⢠Te s t s ⢠T rigonometr y (T r ig) HP 3 9gs Engl ish. book Pa ge 2 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Using mathemati cal functions 13-3 Keyboard functions The most frequently used functions are available directly from the keyboard. Many of the keyboard functions also accept complex numbers as arguments. ,, , Add, Subtract, Multiply, Di vide. Also accepts complex numbers, lists and matrices. va lu e 1 va lu e 2 , etc. e x Natural exponential. Also accepts complex numbers. e^ val u e Example e^5 re t u r n s 148.41315910 3 Natural logarithm. Also accepts complex numbers. LN ( val u e) Example LN(1) ret u r ns 0 ! F or a d esc ription , see âCO MB(5,2) r eturns 10. T hat is, ther e ar e ten diff er ent w ay s that fi ve things can be combined tw o at a time.!â on page 13-12. â F or a d esc ription , see â Σ â on page 13-11. EEX F or a d esc ription , see âSc ientifi c notati on (po w ers of 10)â on page 1- 20. F or a d esc ription , see â â on page 11- 7 . The multiplicative inverse function finds the inverse of a square matrix, and the multiplicative inve rse of a real or complex number. Also works on a list containing only these object types. â« â« x 1 â HP 3 9gs Engl ish. book Pa ge 3 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
13-4 Using math ematical functions 10 x Exponential (antilogarithm). Also acc epts complex numbers. 10^ val u e Example 10^3 r etur ns 1000 Common logarithm. Also accepts co mplex numbers. LOG ( val u e) Example LOG(100) r eturns 2 ,, Sine, cosine, tangent. Inputs and outputs depend on the current angle format (Degrees, Radi ans, or Grads). SIN ( val u e) COS ( val u e) TAN ( val u e) Example TAN(45) r eturns 1 (Degrees mode) . ASIN Arc sine: sin â1 x. Output range is from â90° to 90°, â Ï /2 to Ï /2, or â100 to 100 grads. Inputs and outputs depend on the current angle format. Also accepts complex numbers. ASIN ( val u e) Example ASIN(1) r eturns 90 (Degrees mode) . ACOS Arc cosine: cos â1 x . Output range is from 0° to 180°, 0 to Ï , or 0 to 200 grads. Inp uts and outputs depend on the current angle format. Also accepts complex numbers. Output will be complex for values outside the normal COS domain of . ACOS ( val u e) Example ACOS(1) ret u r ns 0 (Degrees mode). 1 â x 1 â¤â¤ HP 3 9gs Engl ish. book Pa ge 4 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Using mathemati cal functions 13-5 ATAN Arc tangent: tan â1 x . Output range is from â90° to 90°, 2 Ï /2 to Ï /2, or â100 to 100 grad s. Inputs and outputs depend on the current an gle format. Also accept s complex numbers. ATAN ( valu e) Example ATAN(1) ret u rn s 45 (Degrees mode). Square. Also accept s complex numbers. va lu e 2 Example 18 2 r eturns 324 Square root. Also accepts complex numbers. val ue Example r etur ns 18 Negation. Also accepts complex numbers. â val u e Example -(1,2) r eturns (-1,-2) Power ( x raised to y ). Also accepts complex numbers. va lu e ^ po w er Example 2^8 r eturns 256 ABS Absolute value. For a c omplex number, this is . ABS ( val ue ) ABS (( x ,y)) Example ABS(â1 ) r eturns 1 ABS((1,2)) ret u rn s 2.2360679775 324 x 2 y 2 HP 3 9gs Engl ish. book Pa ge 5 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
13-6 Using math ematical functions Takes the n th root of x . ro ot NTHROOT val ue Example 3 NTHROOT 8 r eturns 2 Calculus functions The symbols for differentiation and integration are available directly form the k eyboardâ and S respectivelyâas well as from the MATH menu. Differentiates expr ession with respect to the vari able of differentiation. From the command line, use a formal name (S1, etc.) for a non-numeric result. See âFinding derivativesâ on p age 13-21. va riab l e ( exp re ss io n ) Example s1(s1 2 3*s1) re t u r n s 2*s1 3 Integrates expression from lower to upper limits with respect to the variable of integration. To find the definite integral, both limits must ha ve numeric values (that is, be numbers or real variables). To find the indefinite integral, one of the limits must be a formal variable (s1, etc). ( l o w e r, u p p e r, e x p r e s s i o n , v a r i a b l e ) See âUsing f or mal var iables â on page 13- 20 f or fur t her de ta il s. Example (0,s1,2*X 3,X) finds the indefinite result 3*s1 2*(s1^2/2) See âT o find the indef inite inte gr al using f ormal v ari ables â on page 13- 2 3 f or mor e i nf or mation on finding inde f inite integr als. n â â â â« â« â« HP 3 9gs Engl ish. book Pa ge 6 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Using mathemati cal functions 13-7 TAYLOR Calculates the n th order Taylor polynomial of expression at the point where the given variab le = 0. TAYLOR ( e xpr ession , var iable , n ) Example TAYLOR(1 sin(s1) 2 ,s1,5) w ith Radians angle measur e and F rac tion n umber f ormat (s et in MODE S) r etur ns 1 s1^2-1/3*s1^4 . Complex number functions These functions are for com plex numbers only. You can also use complex numbers with all trigonometric and hyperbolic functions, and with some real-number and keyboard functions. Enter co mplex numbers in the form ( x,y ), where x is the real part and y is the imaginary part. ARG Argument. Finds the angle de fined by a complex number. Inputs and outputs use the current angle format set in Modes. ARG (( x, y)) Example ARG((3,3)) r eturns 45 (Degr ees mode) CONJ Complex conjugate. Conjugation is the negation (sign reversal) of the imaginary part of a complex number. CONJ (( x, y)) Example CONJ((3,4)) r eturns (3,-4) IM Imaginary pa rt, y, of a c omplex number, ( x, y ). IM (( x, y)) Example IM((3,4)) r eturns 4 RE Real part x , of a complex number, ( x, y ). RE (( x, y)) Example RE((3,4)) r eturns 3 HP 3 9gs Engl ish. book Pa ge 7 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
13-8 Using math ematical functions Constants The constants available from the MATH FUNCTIONS menu are mathematical constants. These are described in this section. The hp 39gs has two other menus of constants: program constant s and physical constants. These are described in âProgram constants and physical constantsâ on page 13-24. e Natural logarithm base. Internally represented as 2.71828182846. e i Imaginary value for , the complex number (0,1). i MAXREAL Maximum real number. Internally represented as 9.99999999999 x 10 499 . MAXREAL MINREAL Minimum real number. In ternally re presented as 1 x 10 -499 . MINREAL Ï Internally represented as 3.14159265359. Ï Conversions The conversion functions ar e found on th e Convert menu. They enable you to make the following conversions. â C Convert from Fahrenheit to Celcius. Example â C(212) r eturns 100 â F Convert from Celcius to Fahrenheit. Example â F(0) r eturns 32 â CM Convert from inches to centimeters. 1 â HP 3 9gs Engl ish. book Pa ge 8 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Using mathemati cal functions 13-9 â IN Convert from centimeters to inches. â L Convert from US gallons to liters. â LGAL Convert from liters to US gallons. â KG Convert from pounds to kilograms. â LBS Convert from kilograms to pounds. â KM Convert from miles to kilometers. â MILE Convert from kilometers to miles. â DEG Convert from radians to degrees. â RAD Conve rt from degrees to radians. Hyperbolic trigonometry The hyperbolic trigonometry functions can also take complex numbers as arguments. ACOSH Inverse hyperbolic cosine : cosh â1 x . ACOSH ( valu e) ASINH Inverse hyperbolic sine : sinh â1 x . ASINH ( valu e) ATANH Inverse hyperbolic tangent : tanh â1 x . ATANH ( valu e) COSH Hyperbolic cosine COSH ( valu e) SINH Hyperbolic sine. SINH ( valu e) TANH Hyperbolic tangent. TANH ( valu e) ALOG Antilogarithm (exponential). Th is is more accurate than 10^x due to limitations of the power function. ALOG ( valu e) HP 3 9gs Engl ish. book Pa ge 9 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
13-10 Using mathe matical functions EXP Natural exponential. This is mor e accurate than due to limitations of the power function. EXP ( val u e) EXPM1 Exponent minus 1 : . This is more accurate than EXP when x is close to zero. EXPM1 ( val ue ) LNP1 Natural log plus 1 : ln( x 1 ). This is more accurate than the natural logarithm function when x is close to zero. LNP1 ( val u e) List functions These functions work on list da ta. See âList fu nctionsâ on page 16-6. Loop functions The loop functions display a result after evaluating an expression a given number of times. ITERATE Repeatedly for #times evaluates an expression in terms of variable . The value for variable is updated each time, starting with initialvalue. ITERATE( e xpre ssion , va riab l e , initial value , #times ) Example ITERATE(X 2 ,X,2,3) r eturns 256 RECURSE Provides a method of defini ng a sequence without using the Symbolic view of the Seque nce aplet. I f used with | (âwhereâ), RECURSE will step through the evaluation. RECURSE( seq uencename , ter m n , term 1 , term 2 ) Example RECURSE(U,U(N-1)*N,1,2) U1(N) St or es a f actor ia l-calculating f unction named U1. When y ou enter U1(5) , f or e xam ple , the functi on calc ulates 5! ( 120 ). e x e x 1 â HP 3 9gs Engl ish. book Pa ge 10 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Using mathemati cal functions 13-11 Σ Summation. Finds the sum of expression with respect to variable from initialvalue to finalvalue. Σ ( v ar iable = initial v alue , fin a lval u e, e xp ression ) Example Σ (C=1,5,C 2 ) r etur ns 5 5 . Matrix functions These functions are for matr ix data stored in matrix variables. See âMatrix func tions and commandsâ on page 15-10. Polynomial functions Polynomials are products of constants ( coefficien ts ) and variables raised to powers ( terms ). POLYCOEF Polynomial coefficients. Returns the coefficients of the polynomial with the specified roots . POLYCOEF ([ roo t s ]) Example T o f ind the pol y nomial w ith roots 2 , â3, 4, â5: POLYCOEF([2,-3,4,-5]) r eturns [1,2,-25, -26,120] , r epr esenting x 4 2x 3 â25x 2 â26x 120 . POLYEVAL Polynomial evaluation. Evaluates a polynomial with the specified coefficients for the value of x . POLYEVAL([ coeff ic ients ] , va lu e ) Example Fo r x 4 2x 3 â25x 2 â26x 120 : POLYEVAL([1,2,-25,-26,120], 8) re t ur n s 3432 . POLYFORM Polynomial form. Creates a polynomial in variable1 from expression. POLYFORM ( expression , var iable1 ) Example POLYFORM((X 1)^2 1,X) ret u rn s X^2 2*X 2 . HP 3 9gs Engl ish. book Pa ge 11 We dnes day, Dec embe r 7, 2005 11 : 24 PM
13-12 Using mathe matical functions POLYROOT Polynomial roots. Return s the roots for the n th-order polynomial with the specified n 1 coeffici ents . POLYROOT ([ coe ff ic ien ts ]) Example Fo r x 4 2x 3 â25x 2 â26x 120 : POLYROOT([1,2,-25,-26,120]) r eturns [2,-3,4,-5] . HINT The results of POLYROOT will often not be easily seen in HOME due to the number of decimal places, especially if they are complex numbers. I t is better to store the results of POLYROOT to a matrix. For example, POLYROOT([1,0,0,-8] M1 will store the three complex cube roots of 8 to matri x M1 as a complex vector. Then you can see them easily by g oing to the Matrix Catalog. and access them individually in calculations by referring to M1(1), M1(2) etc. Probability functions COMB Number of combination s (without regard to order ) of n things taken r at a time: n!/(r!(n-r)) . COMB (n, r ) Example COMB(5,2) r eturns 10 . T hat is, ther e ar e ten differ ent wa y s that fi ve things can be combined tw o at a time .! Factorial of a positive integer. For non-integers, ! = Î (x 1) . This calculates the gamma function. value! PERM Number of permutations (w ith regard to order) of n things taken r at a time: n!/(r!(n-r)! PERM ( n, r ) Example PERM(5,2) r eturns 20 . T hat is, ther e ar e 20 differ ent permutati ons of f i v e things tak en t w o at a time . HP 3 9gs Engl ish. book Pa ge 12 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Using mathemati cal functions 13-13 RANDOM Random number (between zero and 1). Produced by a pseudo-random number sequence. The algorithm used in the RANDOM function uses a seed number to begin its sequence. To ensure that two calculators must produce different results for the RANDOM function, use the RANDSEED function to seed different starting values before using RANDOM to produce the numbers. RANDOM HINT The setting of Time will be different for each c alculator, so using RANDSEED(Time) is guar anteed to produce a set of numbers which are as close to random as possible. You can set the seed using the command RANDSEED. UTPC Upper-Tail Chi-Squared Probability given degrees of freedom, evaluated at value . Returns the probability that a Ï 2 random variable is greater than value. UTPC ( degr ees , val u e ) UTPF Upper-Tail Snedecorâs F Probability given numerator degrees of freedom and denominator degrees of freedom (of the F distribution), evaluated at value . Returns the probability that a Snedecor 's F random variable is greater than value. UTPF ( numerator , denominat or , va lu e ) UTPN Upper-Tail Normal Probability given mean and variance , evaluated at value. Returns the probability that a normal random variable is greater than value for a normal distribution. Note: The variance is the square of the standard deviation . UTPN ( mean , va ria nc e, valu e) UTPT Upper-Tail Studentâs t-Probability given degrees of freedom, evaluated at value. Returns the probability that the Student's t- random variable is greater than value. UTPT ( degr ees , val u e ) Real-number functions Some real-number functions can also take complex arguments. CEILING Smallest integer greater than or equal to value . CEILING ( val ue ) HP 3 9gs Engl ish. book Pa ge 13 We dnes day, Dec embe r 7, 2005 11 : 24 PM
13-14 Using mathe matical functions Examples CEILING(3.2) r eturns 4 CEILING(-3.2) r eturns -3 DEG â RAD Degrees to radians. Converts value from Degrees angle format to Radians angle format. DEG â RAD ( val ue ) Example DEG âRAD( 180) r eturns 3.14159265 359 , the va lu e of Ï . FLOOR Greatest integer less than or equal to value . FLOOR ( val ue ) Example FLOOR(-3.2) r eturns -4 FNROOT Function root-finder (lik e the Solve aplet). Finds the valu e for the given variable at which expression most nearly evaluates to zero. Uses guess as initial estimate. FNROOT ( e xpr essi on , var iable , gues s ) Example FNROOT(M*9.8/600-1,M,1) r eturns 61.2244897959 . FRAC Fractional part. FRAC ( val u e) Example FRAC (23.2) r eturns .2 HMS â Hours-minutes-seconds to deci mal. Converts a number or expression in H.MMSSs format (time or angle that can include fractions of a second) to x.x format (number of hours or degrees with a decimal fraction). HMS â ( H.M MSSs ) Example HMS â (8.30) r etur ns 8.5 â HMS Decimal to hours-minutes-seco nds. Converts a number or expression in x.x format (number of hours or degrees HP 3 9gs Engl ish. book Pa ge 14 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Using mathemati cal functions 13-15 with a decimal fraction) to H.MMSSs forma t (tim e or angle up to fractions of a second). â HMS ( x.x) Example â HMS(8.5) r eturns 8.3 INT Integer part. INT ( val ue ) Example INT(23.2) r eturns 23 MANT Mantissa (significant digits) of value . MANT ( valu e) Example MANT(21.2E34) r eturns 2.12 MAX Maximum. The greater of two values. MAX ( val ue 1 , va lu e2) Example MAX(210,25) r eturns 210 MIN Minimum. The lesser of two values. MIN ( val ue 1 , va lu e2) Example MIN(210,25) re t u rn s 25 MOD Modulo. The remai nder of value1 / value2. va lu e 1 MOD va l ue 2 Example 9 MOD 4 r eturns 1 % x percent of y ; that is, x /100* y . % ( x , y) Example % (20,50) r eturns 10 %CHANGE Percent change from x to y , that is, 100( yâx )/ x . % CHANGE( x , y) HP 3 9gs Engl ish. book Pa ge 15 We dnes day, Dec embe r 7, 2005 11 : 24 PM
13-16 Using mathe matical functions Example % CHANGE(20,50) r eturns 150 %TOTAL Percent total : (100) y/ x . What percentage of x , is y . % TOTAL( x , y) Example % TOTAL(20,50) r eturns 250 RAD â DEG Radians to degrees . Converts value from radians to degrees. RAD â DEG ( va lu e ) Example RAD âDEG( Ï) r eturns 180 ROUND Rounds value to decimal places . Accepts complex numbers. ROUND ( val ue , places) Round can also round to a number of significant digits as showed in example 2. Examples ROUND(7.8676,2) r eturns 7.87 ROUND (0.0036757,-3) r eturns 0. 00368 SIGN Sign of value . If positive, the result is 1. If negative, â1. If zero, result is zero. For a complex number, this is the unit vector in the direction of the number. SIGN ( val u e) SIGN (( x, y)) Examples SIGN (â2) re tu r n s â1 SIGN((3,4)) r eturns (.6,.8) TRUNCATE Truncates value to dec imal places . Accepts complex numbers. TRUNCATE ( valu e , places ) Example TRUNCATE(2.3678,2) r eturns 2.36 HP 3 9gs Engl ish. book Pa ge 16 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Using mathemati cal functions 13-17 XPON Exponent of value . XPON ( valu e) Example XPON(123.4) r eturns 2 Two-variable statistics These are functions for use with two-variable statistics. See âTwo-variableâ on pa ge 10-15. Symbolic functions The symbolic functions are used for symbolic manipulations of expression s. The variables can be formal or numeric, but the re sult is usually in symbolic form (not a number). You will find the symbols for the symbolic functions = and | ( where ) in the CHARS menu ( CHARS ) as well as the MATH menu. = ( equals ) Sets an equality for an equatio n. This is not a logical operator and does not store values. (See âTest functionsâ on page 13-18.) exp re ss io n 1 = e xpre ssion2 ISOLATE Isola tes the first occurrence of va riable in expression= 0 and returns a new expression, where variable=newexpression. The result is a general solution that represents multiple solutions by including the (formal) variables S1 to represent any sign and n1 to represent any integer. ISOLATE( expression , var iable ) Examples ISOLATE(2*X 8,X) ret u rn s -4 ISOLATE(A B*X/C,X) r eturns - (A*C/B) LINEAR? Tests whether expression is linear for the specified variable . Retur ns 0 (false) or 1 (true). LINEAR?( expression , var iable ) Example LINEAR?((X^2-1)/(X 1),X) r eturns 0 HP 3 9gs Engl ish. book Pa ge 17 We dnes day, Dec embe r 7, 2005 11 : 24 PM
13-18 Using mathe matical functions QUAD Solves quadratic expression= 0 for variab le and returns a new expression, where variable = newexpression. The result is a general solution th at represents both positive and negative solutions by in cluding the formal variable S1 to represent any sign: or â . QUAD( ex pre ss i on , variab l e ) Example QUAD((X -1) 2 -7,X) r eturns (2 s1*5.29150262213)/2 QUOTE Encloses an expression that should not be evaluated numerically. QUOTE( ex pre ss io n ) Examples QUOTE(SIN(45)) F1(X) stor es the e xpre ssion S IN(4 5) r ather than the value of SIN( 45 ) . Another meth od is to enclo se the e xpr essi on in single quotes. Fo r ex a m p l e, X^3 2*X F1(X) puts the e xpressi on X^3 2*X into F1(X) in the F uncti on apl et . | ( where ) Evaluates expression where each given variable is set to the given value . Defines numeric evaluation of a symbolic expression. e xpressi on |( var iable1=v alue1, var iable2=v alue2 ,... ) Example 3*(X 1)|(X=3) r eturns 12 . Test functions The test functions are logical operators that always return either a 1 ( true ) or a 0 ( false ). < Less than. Returns 1 if true, 0 if false. va lu e 1 < va lu e2 ⤠Less than or equal to. Returns 1 if true, 0 if false. va lu e 1 ⤠va lu e2 HP 3 9gs Engl ish. book Pa ge 18 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Using mathemati cal functions 13-19 = = Equals (logical test). Returns 1 if true, 0 if false. va lu e 1 ==va l ue 2 â Not equal to. Returns 1 if true, 0 if false. va lu e 1 â va l ue 2 > Greater than. Returns 1 if true, 0 i f false. va lu e 1 > va l ue 2 ⥠Greater than or equal to. Returns 1 if true, 0 if false. va lu e 1 ⥠va l ue 2 AND Compares value1 and value2 . Returns 1 if they are both non-zero, otherwise returns 0. va lu e 1 AND va l ue 2 IFTE If expression is true, do the trueclause ; if no t, do the falseclause. IFTE( e xpre ssion , true cla use , fals ecla use ) Example IFTE(X>0,X 2 ,X 3 ) NOT Returns 1 if value is zero , otherwise returns 0. NOT val ue OR Returns 1 if either value1 or value2 is n on-zero, otherwise returns 0. va lu e 1 OR va l ue 2 XOR Exclusive OR. Returns 1 if ei ther value1 or value2 âbut not both of themâis non-zero, otherwise r eturns 0. va lu e 1 XOR va l ue 2 Trigonometry functions The trigonometry functions can also take complex numbers as arguments. For SIN, COS, TAN, ASIN, ACOS, and ATAN, see the Keyboard category . ACOT Arc cotangent. ACOT ( valu e ) HP 3 9gs Engl ish. book Pa ge 19 We dnes day, Dec embe r 7, 2005 11 : 24 PM
13-20 Using mathe matical functions ACSC Arc cosecant. ACSC ( val u e) ASEC Arc secant. ASEC ( val u e) COT Cotangent: cos x /sinx . COT ( val u e) CSC Cosecant: 1/sin x CSC ( val u e) SEC Secant: 1/cos x . SEC ( val u e) Symbolic calculations The HP 39gs has the ability to perform symbo lic calculations, for example, symbolic integration and differentiation. You can perform symbolic calculations in HOME and in the Function aplet. In HOME When you perform calculation s that contain normal variables, the calcul ator substitutes values for any variables. For example, if you enter A B on the c ommand line and press , the calculator retrieves the values for A and B from memory and substitutes them in the calculation. Using formal variables To perform symbolic calculati ons, for example symbolic differentiations and integrations, you need to use formal names. The HP 39gs has six formal names available for use in symbolic calculations. Th ese are S0 to S5. When you perform a calculation that contai ns a formal name, the HP 39gs does not carry out any substitutions. You can mix formal names an d real variables. Evaluati ng (A B S1) 2 will evaluate A B , but not S1 . If you need to evaluate an expression that contains formal names numerically, you use the | ( where ) command, listed in the Math menu under the Symbolic categor y. For example to evaluate (S1*S2) 2 when S1=2 and S2=4 , you would enter the calculation as follows: HP 3 9gs Engl ish. book Pa ge 20 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Using mathemati cal functions 13-21 (The | symbol is in the CHARS menu: press CHARS . The = sign is listed in the MATH menu under Symbolic functions.) Symbolic calculations in the Function aplet You can perform symbolic operations i n the Function apletâs Symbolic view. For example, to find the derivative of a function in the Function apletâs Symbolic view, you define two functions and define the second function as a derivative of the first function. You then evaluate the second function. See âTo find derivatives in the Function apletâs Symbolic viewâ on p age 13-22 for an example. Finding derivatives The HP 39gs can perform symbo lic differentiation on some functions. There are two ways of using the HP 39gs to find derivatives. ⢠Y ou can perfor m differ entiatio ns in HOME b y using the fo rmal v ari ables , S1 to S5 . ⢠Y ou can perfor m differ entiati ons of f unctio ns of X in the F unction aplet . To find derivatives in HOME To find the derivative of the function in HO ME, use a formal variable in place of X. If you use X, the differentiation function substi tutes the value that X holds, and returns a numeric result. For example, consider the function: 1. Enter the diff er entiati on func tion o nto the command line , subs tituting S1 in place of X . S1 S1 2 dx x ( 2 ) sin ( 2 x () ) cos HP 3 9gs Engl ish. book Pa ge 21 We dnes day, Dec embe r 7, 2005 11 : 24 PM
13-22 Using mathe matical functions S1 2 . E valuate the f uncti on . 3 . Show the r esult . To find derivatives in the Function apletâs Symbolic view To find the derivative of the fu nction in the Function apletâs Symbolic view, you define two functions and define the second function as a derivati ve of the first function. For example, to differentiate : 1. Access the F unction a pletâs S y mbolic v ie w and def ine F1. 2 2. D e f i n e F 2 ( X ) as the der i vati ve of F(1). F1 3 . Select F 2( X ) and eva l ua t e it. x 2 () sin 2 x cos HP 3 9gs Engl ish. book Pa ge 22 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Using mathemati cal functions 13-23 4. Pr ess to display the r esult . Note: Us e the arr ow k ey s to v ie w the entir e functi on . | Y ou coul d also j us t def ine . To find the indefinite integral using formal variables F or ex ample, to f ind t he indefinite integral of use: 1. Enter the f uncti on . 0 S1 3 X 5 X 2 . Show the r esult f orm at . 3 . Pr ess to close the sho w w indo w . 4. Cop y the result and eva lu a te. Th us , substit uting X f or S1, it can be seen that: F 1 x () xx 2 () 2 x () co s sin () d = 3 x 2 5 â x d â« ( ) â« â X X S , 5 3 , 1 , 0 2 3 x 2 5 â x 5 x â3 x 3 3 ---- - X â â X () -------------- - ââ ââ ââ ââ ââ = d â« HP 3 9gs Engl ish. book Pa ge 23 We dnes day, Dec embe r 7, 2005 11 : 24 PM
13-24 Using mathe matical functions This result is de rived from substituting X = S1 and X = 0 into the original expression found in step 1. However, substituting X = 0 will not always evaluate to zero and may result in an unwanted constant. To see this, consider: The âextraâ constant of 6.4 results from the substitution of into ( x â2 ) 5 /5 , and should be disregarded if an indefinite integral is required. Program constants and physical constants When y ou pr ess , thr ee menus of func tions and constants become a vailable: ⢠the math functi ons menu (w hic h appears b y def ault) ⢠the pr ogr am constants menu , and ⢠the ph ysi cal constants menu . The math functions menu is described extensively earlier in this chapter. Program constants The program constants are numbers that have been assigned to various calculator settings to enable you to test for or specify such a setting in a program. For example, the various display formats are assigned the following numbers: 1 Standar d 2 F ix ed 3 Sc ientif ic 4 Engineering 5 Fraction 6 Mixed fraction In a program, you could store the constant number of a particular format into a variable and then subseque ntly test for that particular format. x 2 â () 4 x x ( 2 ) 5 â 5 ------------------- = d â« x 0 = HP 3 9gs Engl ish. book Pa ge 24 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Using mathemati cal functions 13-25 To access the menu of program constants: 1. Pr ess . 2. P r e s s . 3 . Use the ar r o w k e y s to na v igate thr ough the options . 4. Clic k and then to di spla y the number assigned to th e option you selected in th e pr ev ious step. The use of program constants i s illustrated in more detail in âProgrammingâ on page 18-1 Physical constants There are 29 physical cons tantsâfrom the fields of chemistry, physics and q uantum mechanicsâthat y ou can use in calculations. A list of all these constants can be found in âPh ysical Constantsâ on page R-16. To access the menu of physical constants: 1. Pr ess . 2. P r e s s . 3 . Use the ar r o w k e y s to na v igate thr ough the options . 4. T o see the s y mbol and va lue of a selected constan t , pr ess . (Clic k to close the infor mation w indo w that appears .) T he follo w ing e x ample sho ws the inf ormatio n av ailable about the spee d of li ght (one of the ph y sics constants) . 5 . T o us e the selected constant in a calculati on , pres s . The consta nt appears at the positio n of the c urso r on the edit line . HP 3 9gs Engl ish. book Pa ge 25 We dnes day, Dec embe r 7, 2005 11 : 24 PM
13-26 Using mathe matical functions Example Suppose you want to know the potential energy of a mass of 5 units according to the equation . 1. Enter 5 2 . Pr ess and then p r ess . 3 . Select light s... f r om the Phy sic s menu . 4. Pr ess . The menu c lose s and the v alue of the selec ted constant is cop ied to the edit line . 5 . Complete the equat ion as y ou w ould normally and pr ess to get the r esult . Em c 2 = HP 3 9gs Engl ish. book Pa ge 26 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Variables an d memory manageme nt 14-1 14 V ariables and memory manag ement Introduction The HP 39gs has approximately 200K of user memory. The calculator uses this memory to store variables, perform computations, and store history. A v a r i a b l e i s a n o b j e c t t h a t y o u c r e a t e i n m e m o r y t o h o l d data. The hp 39gs has two types of variables, home variables and aplet variables. ⢠Home variables are avai lable in all aplets. For example, you can store real numbers in variables A to Z and complex numbers in variables Z0 to Z9. These can be numbers you have entered, or the results of calculations. Th ese variables are available within all aplets and within any programs. ⢠Aplet variables apply only to a single aplet. Aplets have specific vari ables allocated to them which vary from aplet to aplet. You use the calculatorâs memory to store the following objects: ⢠copies of aplets with specific configurations ⢠new aplets that you download ⢠aplet variables ⢠home variables ⢠variables created thr ough a catalog or edito r, for example a matrix or a text note ⢠programs that you create. You can use the Memory Manager ( MEMORY ) to view the amount of memory av ailable. The catalog views, which are accessible via the Memory Manager, can be used to transfer variables such as lists or matrices between calculators. HP 3 9gs Engl ish. book Pa ge 1 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
14-2 Variables and m emory management Storing and recalling variables You can store numbers or expressi ons from a previous input or result into variables. Numeric Precision A number stored in a variable is always stored as a 12- digit mantissa with a 3-digit exponent. Numeric precision in the display, however, de pends on the display mode (Standard, Fixed, Scientific, Engineering, or Fraction). A displayed number has only the precision that is displayed. If you copy it from the HOME view display history, you obtain only the precision displayed, not the full internal precision. On the other hand, the variable Ans always contains the most recent result to full precis ion. To store a value 1. On the command line, enter the value or the calc ulation for the r esult yo u wi s h to s t ore . 2. P r e s s 3 . Ente r a name fo r the va riab l e. 4. Pr ess . To store the result s of a calculation If the value you want to s tore is in the HOME view display history, for example the results of a previous calculation, you need to copy it to the co mmand line, then store it. 1. P er f or m the calc ulation f or the r esult y ou want t o st or e . 3 86 3 2 . Mov e the highli ght to the r esult y ou w ish to st or e . 3 . Pr ess to copy the r esult to the command line . 4. Pr ess . HP 3 9gs Engl ish. book Pa ge 2 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Variables an d memory manageme nt 14-3 5 . Enter a name for the v ari able . A 6 . Pres s to stor e the re sult . The results of a calculation can also be stored directly to a variable. For example: 2 5 3 B To recall a value To recall a var iableâs value , type the name of the variable and press . A To use variables in calculations You can use variables in calculations. The calculator substitutes the variableâs value in the calculation: 65 A To clear a variable You can use the CLRVAR command to clear a specified variable. Fo r example, if you have stored {1 ,2,3,4} in variabl e L1, entering CLRVAR L1 w ill clear L1. (Y ou can find the CLRVAR command b y pr essing and c hoosing the PROMPT category of commands.) HP 3 9gs Engl ish. book Pa ge 3 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
14-4 Variables and m emory management The VARS menu You use the VARS menu to access all variables in the calculator. The VARS menu is organi sed by category. For each variable category in the left column, there is a list of variables in the right colu mn. You select a variable category and then select a variable in the category. 1. Open the V ARS menu . 2 . Use the arr o w k e y s or pr ess the alpha k ey o f the f irst letter in the category to select a v ari able category . Fo r ex a m p l e, t o s e l e c t the Matr i x category , pr ess . Note: In this instance , ther e is no need to pr ess the ALP HA ke y . 3 . Mo v e the highli ght to the v ar iable s column. 4. Use the arr ow k ey s to selec t the var iable that y ou w ant . F or ex ample , to select M2 , pr ess . HP 3 9gs Engl ish. book Pa ge 4 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Variables an d memory manageme nt 14-5 5 . Ch oose w h ether to place the var ia ble name or the v ari able v alue on the command line . â Pres s to indicate that y ou w a nt the v ari able âs contents t o appear on the command line . â Pr ess to indicate that y ou w ant the v ari able âs name to a ppear on the command line . 6 . Pr ess to place the va lue or name on the command line . The s elected ob jec t appears on the command line . Note: T he V AR S menu can also be used to en ter the names or va lues of var iables into pr ogr ams. Example This example demonstrates how to use the VARS menu to add the contents of two list variables, and to store the result in another list vari able. 1. Display the L ist Catalog . LIST to select L1 2 . Enter the data f or L1. 88 90 89 65 70 3 . R etur n to the L ist Cat alog to c r eate L2 . LIST to select L2 HP 3 9gs Engl ish. book Pa ge 5 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
14-6 Variables and m emory management 4. Enter data for L2 . 55 48 86 90 77 5 . Pr ess to ac cess HO ME . 6 . Open the v ar iable men u and selec t L1. 7 . Cop y it to th e command line . Note: Because the option is hi ghlighted , the var iable âs name , r ather than its contents , is copied to the command line . 8. Insert the oper ator and s elect the L2 v ar ia ble fr om t h e Li s t va ri ab l e s. 9 . Stor e the answ er in the List cat alog L3 var iable . L3 Note: Y ou can also type list name s dir ectl y fr om the k ey board . HP 3 9gs Engl ish. book Pa ge 6 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Variables an d memory manageme nt 14-7 Home variables It is not possible to store data of one type in a variable of another type. For example, yo u use the Matrix catalog to create matrices. You can crea te up to ten matrices, and you can store these in variables M0 to M9. You cannot store matr ices in variab les other than M0 to M9. Cate- gory A v ai lable name s Complex Z0 to Z9 Fo r ex a m p l e, (1,2) Z0 or 2 3 i Z1. Y ou can enter a complex number by ty ping (r ,i) , wher e r repr esents the r eal par t , and i r e pr esents the imaginar y part. Graphic G0 to G9 SeeâGraphic commandsâ on page 18-21 for more information on storing graphi c objects via programming commands. See âTo store into a graphics variableâ on page 17-5 for more information on storing graphic object via the sketch view. Library Aplet library va riables can store aplets that you have created, either by saving a copy of a standard aplet, or downloading an aplet from another source. List L0 to L9 For example, {1,2,3} L1. Matrix M0 to M9 can store matri ces or vectors. For example, [[1,2],[3,4] ] M0. Modes Modes variables store the modes settings that you can configure using MODES . Notepad Notepad variables store notes. Program P rogram variables store programs. Real A to Z and θ. Fo r ex a m p l e, 7 . 45 A . HP 3 9gs Engl ish. book Pa ge 7 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
14-8 Variables and m emory management Aplet variables Most aplet variables stor e values t hat are uniqu e to a particular aplet. These includ e symbolic expressions and equations (see below), settings for the Plot and Numeric views, and the results of some calculations such as roots and intersections. See the Reference Information chapter for more information about aplet variables. To access an aplet variable 1. Open the a plet that contains the v ar iab le y ou w ant to re c al l. 2 . Pr ess to display the V ARS menu . 3 . Use the arr o w k e y s to s elect a v ari able category in the left column, then pre ss to access the vari ables in the ri ght column . 4. Use the arr o w k e y s to se lect a v ar ia ble in the ri ght column. 5 . T o cop y the name of the v ar iable o nto the edit line , pr ess . ( is the defau lt setting .) Category Av ailable names Function F0 to F9 (Symbolic view). See âFunction aplet variablesâ on page R-7. Parametric X0, Y0 to X9, Y9 (Symbolic view). See âParametric a plet variablesâ on page R-8. Polar R0 to R9 (Symbolic view). See âPolar aplet variablesâ on page R-9. Sequence U0 to U9 (Symbolic view). See âSequence aplet variablesâ on page R-10. Solve E0 to E9 (Symbolic view). See âSolve aplet variablesâ on page R-11. Statistics C0 to C9 (Numeric view). See âStatistics aplet v ariablesâ on page R-12. HP 3 9gs Engl ish. book Pa ge 8 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Variables an d memory manageme nt 14-9 6 . T o cop y the v alue of the v ar iable in to the edit line , pr es s and pr ess . Memory Manager You can use the Memory Manager to determine the amount of available memory on the calculator. You can also use Memory Manager to organize memory. For example, if the available memory is low, you can use the Memory Manager to determine which aplets or variables consume large amounts of memo ry. You can make deletions to free up memory. Example 1. St art the Memory Manager . A list of var ia ble categor ies is displa yed . MEMORY F ree memory is display ed in the to p r ight cor ner and the body o f the scr een lists each catego r y , the memory it uses , and the per centage of the total memory it uses . 2 . Select the category w ith whi c h y ou w ant to w or k and pr ess . Memory Manager display s memory details of v aria bles w ithin the category . 3 . T o delet e var iables in a category: â Pr ess to delete the s elect ed v ari able . â Pres s CLEA R to dele te all var iables in the selec ted category . HP 3 9gs Engl ish. book Pa ge 9 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
HP 3 9gs Engl ish. book Pa ge 10 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Matrices 15-1 15 M atr ices Introduction You can perform matrix calc ulation s in HOME and in programs. The matrix and each row of a matrix appear in brackets, and the elements and rows are separated by commas. For example, the following matrix: is displayed in the history as: [[1,2,3],[4,5,6]] (If the Decimal Mark mode is set to Comma , then separate each element and each row with a period.) You can enter matrices directly in the command line, or create them in the matrix editor. Vectors Vectors are one-dimensional arrays. They are composed of just one row. A vector is represented with single brackets; for example, [1,2,3]. A vector c an be a real number vector or a complex number vector, for example [(1,2), (7,3)]. Matrices Matrices are two-dimensi onal arrays. They are composed of more than one row and more than one column. Two-dimensional matrices ar e represente d with nested brackets; for example, [[1,2,3],[4,5,6]]. You can create complex matrices, for example, [[(1,2), (3,4 )], [(4,5), (6,7)]]. Matrix Variables There are ten matrix variables available, named M0 to M9. You can use them in ca lculations in HOME or in a program. You can retrieve th e matrix names from the VARS menu, or just type th eir names from the keyboard. 123 456 HP 3 9gs Engl ish. book Pa ge 1 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
15-2 Matr ices Creating and storing matrices You can create, edit, delete, send, and receiv e matrices in the Matrix catalog. To open the Matrix catalog, press MATRIX . You can also create and store matricesânamed or unnamedâ-in HOME. For example, the command: POLYROOT([1,0,â1,0]) îM1 stores the root of the c omplex vector of length 3 into the M1 variable. M1 now contai ns the three roots of Matrix Catalog keys The table below lists the operations of the menu key s in the Matrix Catalog, as well as the use of Delete ( ) and Clear ( CLEAR ). x 3 x â0 = Key M e a n i n g Opens the highlighted matrix for editing. Prompts for a matrix type, then opens an empty matrix with the highlighted name. Transmits the highlighted matrix to another hp 39gs or a disk drive. See âSending and receiving apletsâ on page 19-4. Receiv es a matrix from anoth er hp 39gs or a disk drive. See âSending and receiving apletsâ on page 19-4. Clears the highlighted matrix. CLEAR Clears all matrices. or Moves to the end or the beginning of the catalog. HP 3 9gs Engl ish. book Pa ge 2 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Matrices 15-3 To create a ma trix in the Matrix Catalog 1. Pr ess MATRIX to open the Matr i x Ca talog . The Matri x catalog lists the 10 av ailable matr ix v ar iable s, M0 to M9 . 2 . Hi ghlight the matr ix v a r iable name you w ant to use and pres s . 3 . Select the type o f matr i x to c r eate. â For a v ec tor (one -dim ensional array) , sele ct Real vector or Complex vector . Certain oper atio ns ( , â , CROSS ) do n ot r eco gni z e a one -d ime nsi onal matr i x as a v ect or , so t his sele ction i s im por tant. â For a matrix (t w o -dimension al array) , sele ct Real matrix or Complex matrix . 4. F or each element in the matr i x , type a number or an e xpr ession , and pr es s . (The e xpr essi on ma y not cont ain sy mbolic v ar iable names .) For c om p l ex n u mb e rs , ente r eac h n umbe r in comple x fo rm; that is , (a, b) , wher e a is the real part and b is the imaginar y part . Y ou must inc lude the par entheses and the comma . 5 . Us e the c urs or k e y s to mo v e to a differ ent r ow or column . Y ou can change the dir ection o f the highli ght bar by pre ssing . The menu ke y toggles betw een the f ollo w ing thr ee options: â spec if ies that the c ursor mo ves t o the cell belo w the c u r r ent cell w hen y ou pre ss . â s pec if ies that the c ursor mo ves t o the cell to the ri ght of the c urr ent cell w hen y ou pr ess . â s pec ifi es that the c ursor st a y s in the c urr ent cell when y ou pr ess . 6 . When done , pr ess MATRIX to see the Matri x catalog , or pr ess to r eturn to HO ME . The matri x entr ie s ar e automati cally stor ed. HP 3 9gs Engl ish. book Pa ge 3 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
15-4 Matr ices A matrix is listed with two dimensions, even if it is 3Ã1. A vector is listed with the number of elements, such as 3. To transmit a matrix You can send matrices between c alculators just as you can send aplets, programs, lists, and notes. 1. Align the HP 3 9gs calculator s â infr ared ports (or connect the calc ulators using an appr opr iate cable) . 2 . Open the Matr ix catalogs on bo th calc ulator s. 3 . Hi ghlight the matri x to send . 4. Pr ess and ch oose the method of sending (infr ar ed or cable) . 5 . Pr ess on th e r ecei v ing cal c ulator and c hoose the method of r ecei v ing (infr ar ed or cable) . F or more infor matio n on sending and r ecei v ing file s, see âSending and rece i ving a plets â on page 19- 4. Working with matrices To edit a matrix In the Matrix catalog, highli ght the name of the matrix you want to edit and press . Matrix e dit keys The follow ing table lists the matrix edit key operations. Key M e a n i n g Copies the highlighted element to the edit line. Inserts a row of zeros above, or a column of zeros to the left, of the highlighted cell. (You are prompted to choose row or column.) A three-way toggle for cursor advancement in the Matrix editor. advances to the right, ¸ advances downward, and does not advance at all. Switches between larger and smaller font sizes. HP 3 9gs Engl ish. book Pa ge 4 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Matrices 15-5 To display a matrix ⢠In the Matri x catalog ( MATRIX ) , highlight the matri x name and pres s . ⢠In HOME , ente r the name of the matr i x v ari able and pr ess . To display one element In HOME, enter matrixname ( row,column ). For example, if M2 is [[3,4],[5,6]] , then M2(1,2) returns 4 . To create a ma trix in HOME 1. Ente r the matr i x in the edit line . Start and end the matri x and each r ow w i th square br ack ets (the s hifted and k e y s) . 2 . Separate each element and each r o w w ith a comma. Ex ample: [[1,2],[3,4]] . 3 . Pr ess to enter and displa y the matr i x . The left screen below shows the matrix [[2.5,729],[16,2]] being stored into M5. The screen on the right shows the vector [66,3 3,11] being stored into M6. Note that you can enter an expression (like 5/2) for an element of the matrix, and it will be evaluated. Deletes the highlighted cells, row, or column (you are prompted to make a choice). CLEAR Clears all elements from the matrix. Moves to the first row, last row, first column, or last column respectively. K ey Meaning (Conti nued) HP 3 9gs Engl ish. book Pa ge 5 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
15-6 Matr ices To store one element In HOME, enter, value matrixname ( row, column ). For example, to change the element in the first row and second column of M5 to 728, then display the resulting matrix: 728 M 512 M5 . An attempt to store an element to a row or column beyond the size of the matrix results in an error message. Matrix arithmetic You can use the arithmetic functions ( , â, Ã , / and powers) with matrix arguments. Division left-multiplies by the inverse of the divisor. You can enter the matrices themselv es or enter t he names of sto red matrix va riables. The matrices can be real or complex. For the next examples, store [[1,2],[3,4]] into M1 and [[5,6],[7,8]] into M2. Example 1. Cr eate the fi rst matr ix . MATRIX 1 2 3 4 2 . Create the se cond matr i x . MATRIX 5 6 7 8 HP 3 9gs Engl ish. book Pa ge 6 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Matrices 15-7 3 . Add the matr ices that yo u cre a t e d. M1 M2 To multiply and divide by a scalar For division by a scalar, enter the matrix first, then the operator, then the scalar. For multiplication, the order of the operands does not matter. The matrix and the scalar can be real or complex. For example, to divide the result of the previous example by 2, press the following keys: 2 To multiply two matrices To multiply the two matrices M1 and M2 that you created for the previous example, press the following keys: M1 M 2 To multiply a matrix by a vector, enter the matrix first, then the vector. The number of elements in the vector must equal the nu mber of columns in the matrix. To raise a matrix to a power You can raise a ma trix to any power as long as the power is an integer. The following example shows the re sult of raising matrix M1, created earlier, to the power of 5. M1 5 Note: You can also raise a matrix to a power without first storing it as a variable. Matrices can be raised to ne gative powers . In this case, the result is equivalent to 1/[matrix]^ABS(power). In the following example, M1 is raised to the power of â2. HP 3 9gs Engl ish. book Pa ge 7 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
15-8 Matr ices M1 2 To divide by a square matrix For division of a matrix or a vector by a square matrix, the number of rows of the dividend (or th e number of elements, if it is a vector) must equal the number of rows in the divisor. This operation is not a mathematical di vision: it is a left- multiplication by the inverse of th e divisor. M1/M2 is equivalent to M2 â1 * M1. To divide the two matrices M1 and M2 that you created for the previous example, press the following keys: M1 M2 To invert a matrix You can invert a square matrix in HOME by typing the matrix (or its variable name) and pressing x â1 . Or you can use the matri x INVERSE command. Enter INVERSE ( ma trixn ame ) in HOME and press . To negate each element You can change the sign of each element in a matrix by pressing before the matrix name. Solving systems of linear equations Example Solve the following linear system: 1. Open the Matr i x catalog a nd cr ea te a ve cto r . MATRIX 2 x 3 y 4 z 5 xy z â 7 4 xy â2 z 1 = = = HP 3 9gs Engl ish. book Pa ge 8 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Matrices 15-9 2 . Cr eate the vec tor of the constants in the linear sys t em . 5 7 1 3 . R etur n to the Matri x Cat al og. MATRIX In this e x ample , the ve ctor y ou cr eated is listed a s M1. 4. Cr eate a ne w matr i x . Sele ct Real matrix 5 . Enter the equati on coeff ic ients . 23 4 11 1 4 12 In this e x ample , the matri x y ou c r eated is listed as M2 . 6 . R etur n to HOME and ent er the calc ulatio n to left-multipl y the constants v ector b y the inv erse o f the coeff ic ien ts matr i x. M2 x â1 M1 The result is a vector of the solutio ns x = 2, y = 3 and z = â2. An alternative method, is to use the RREF function. See âRREFâ on page 15-12. HP 3 9gs Engl ish. book Pa ge 9 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
15-10 Matri ces Matrix functions and commands About functions ⢠Fu n c t i o n s c a n b e u s e d i n a ny a p l e t o r i n H O M E. T h e y ar e listed in the MA TH menu unde r the Matr i x categor y . T h e y can be used in mathematical e xpr essi ons âpr imar ily in HOMEâa s w ell as in pr ogr ams. ⢠F unctions al wa ys pr oduce and displa y a r esult . The y do not c hange any st or ed var iables , such as a matri x va riab l e. ⢠F unctions ha ve ar guments that ar e enclo sed in pare ntheses and separ ated b y commas; f or e x ample , CROSS ( vect or 1 , ve cto r 2 ) . The matr i x input can be either a matr i x v ari able name (such a s M1 ) or the actual matr i x data inside br ack ets. F or ex ample, CROSS(M1,[1,2]) . About commands Matrix commands are listed in the CMDS menu ( CMDS ), in the matrix category. See âMatrix commandsâ on page 18-24 for details of the matrix commands available for use in programming. Functions differ from co mmands in that a function can be used in an expression. Commands cannot be used in an expression. Argument conventions ⢠Fo r row # or column# , supply the n umber of the r ow (counting fr om the top, s tarting with 1) or the number of the column (counting fr om the left , starting w ith 1) . ⢠T he ar gument matr ix can r efer to either a v ector or a matr i x . Matrix functions COLNORM Column Norm. Finds the maxi mum value (over all columns) of the sums of the absolute values of all elements in a column. COLNORM ( matr ix ) HP 3 9gs Engl ish. book Pa ge 10 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Matrices 15-11 COND Condition Number. Finds the 1-norm (column norm) of a square matrix . COND ( matr i x ) CROSS Cross Product of vector1 with vector2 . CROSS ( vec to r 1 , ve ct or 2 ) DET Determinant of a square matrix . DET ( matr i x ) DOT Dot Product of two arrays, matrix1 matrix2 . DOT ( matr i x1, matr i x2 ) EIGENVAL Displays the eigenvalue s in vector form for matrix . EIGENVAL ( matri x ) EIGENVV Eigenvectors and Eige nvalues for a square matri x . Displays a list of two arra ys. The first contains the eigenvectors and the second contains the ei genvalues. EIGENVV ( matri x ) IDENMAT Identity matrix. Creates a square matrix of dimension size à size whose diagonal elements a re 1 and off- diagonal elements are zero. IDENMAT ( siz e ) INVERSE Inverts a square matrix (real or complex). INVERSE ( matri x ) LQ LQ Factor ization. Factors an m à n matrix into three matrices: {[[ m à n lowertrapezoidal ]],[[ n à n orthogona l ]], [[ m à m permutation ]]}. LQ ( matr i x ) LSQ Least Squares. Displays the minimum norm least squares matrix (or vector ). LSQ ( matr i x1, matr i x2 ) HP 3 9gs Engl ish. book Pa ge 11 We dnes day, Dec embe r 7, 2005 11 : 24 PM
15-12 Matri ces LU LU Decomposition. Factors a square matr ix into three matrices: {[[ lowertriangular ]],[[ uppertriangular]],[[ permutation ]]} The uppertriangular has ones on its diagonal. LU ( matr ix ) MAKEMAT Mak e Matrix. Creates a matrix of dimension rows à columns , using expression to calculate each ele ment. If expression contains the variables I and J, then the calculation for each element substitutes the current row number for I and the current column number for J. MAKEMAT ( ex p res s i on , rows, columns) Example MAKEMAT(0,3,3) r eturns a 3Ã3 z ero matr i x , [[0,0,0],[0,0,0],[0,0,0]] . QR QR Factorization. Factors an m à n matri x into three matrices: {[[ m Ãm orthogonal ]],[[m Ãn uppertrapezoidal ]],[[ n à n permutation ]]}. QR ( matr ix ) RANK Rank of a rectangular matrix . RANK ( matr i x ) ROWNORM Row Norm. Finds the maximum value (over all rows) for the sums of the absolute values of all elements in a row. ROWNORM ( matr i x ) RREF Reduced-Row Echelon Form. Changes a rectangular matrix to its reduced row-echelon for m. RREF ( matr i x ) SCHUR Schur Decomposition. Factors a square matrix into two matrices. If matrix is real, then the resu lt is {[[ orthogonal ]],[[ up per-quasi triangular ]]}. If matrix is complex, then the result is {[[ unitary ]],[[ upper-triangular ]]}. SCHUR ( matr i x ) SIZE Dimensions of matrix . Returned as a list: {rows,columns}. SIZE ( matr i x ) HP 3 9gs Engl ish. book Pa ge 12 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Matrices 15-13 SPECNORM Spectral Norm of matrix . SPECNORM ( matri x ) SPECRAD Spectral Radi us of a squa re matrix . SPECRAD ( matri x ) SVD Singular Value Decomp osition. Factors an m à n matrix into two matrices and a vector: {[[ m à m square orthogonal ]],[[ n à n square orthogonal ]], [ real ]}. SVD ( matr i x ) SVL Si ngular Values. Returns a vector containing the singular values of matrix. SVL ( matr i x ) TRACE Finds the trace of a square matrix. The trace is equal to the sum of the diagonal elements. (It is also equal to the sum of the eigenvalues.) TRACE ( matr i x ) TRN Transposes matr ix . For a complex matrix, TRN finds the conjugate transpose. TRN ( matr i x ) Examples Identity Matrix You can create an identity matrix with the IDENMAT function. For example, IDENMAT(2) creates the 2Ã2 identity matrix [[1,0],[0, 1]]. You can also create an identity matrix using the MAKEMAT ( make matrix ) function. For example, entering MAKEMAT(I¼J,4,4) creates a 4 à 4 matrix showing the numeral 1 for all elements except zeros on the diagonal. The logical operator ¼ returns 0 wh en I (the row number) and J (the column number) are equal, and returns 1 when they ar e not equal . HP 3 9gs Engl ish. book Pa ge 13 We dnes day, Dec embe r 7, 2005 11 : 24 PM
15-14 Matri ces Trans posi ng a Matrix The TRN function swaps the row-column and column-row elements of a matrix. For instance, e lement 1,2 (row 1, column 2) is swapped with element 2,1; element 2,3 is swapped with element 3,2; and so on. For examp le, TRN([[1,2],[3,4]]) creates the matrix [[1,3],[2,4]] . Reduced-Row Echelon Form The following set of equations can be written as the augmented matrix which can then stored as a real matrix in any matrix variable. M1 is used in this example. You can use the RREF function to change this to reduced row echelon form, storing it in any matrix variable. M2 is used in this example. The reduced row echelon matrix gives the solution to the linear equation in the fourth column. An advantage of using the RREF function is that it will also work with inconsistent matrices resulting from syst ems of equations which have no solution or infinite solutions. For example, the following set of equations has an infinite number of solutions: x 2 y â3 z 1 4 2 xy z â 3 4 x â 2 y â2 z 1 4 = = = 12 â3 1 4 21 1 â3 â 42 â2 1 4 34 Ã xy z â 5 2 xy â7 x 2 y â z 2 = = = HP 3 9gs Engl ish. book Pa ge 14 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Matrices 15-15 The final row of zeros in the reduced-row echelon form of the augmented matrix indicates an inconsistent system with infinite solutio ns. HP 3 9gs Engl ish. book Pa ge 15 We dnes day, Dec embe r 7, 2005 11 : 24 PM
HP 3 9gs Engl ish. book Pa ge 16 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Lists 16-1 16 L ists You can do list operations in HOME and in programs. A list consists of comma-separated real or complex numbers, expressions, or matr ices, all enclosed in braces . A list may, for example, contain a sequence of real numbers such as {1,2,3} . (If the Decimal Mark mode is set to Comma , then the separators are periods.) Lists represent a convenient way to group related objects. There are ten list variables available, named L0 to L9. You can use them in calculations or expressions in HOME or in a program. Retrieve the li st names from the VARS menu, or just type their names fro m the keyboard. You can create, edit, delete , send, and re ceive named lists in the List catalog ( LIST ). You can also create and store listsânamed or unnnamedâin HOME lists List variables are identical in behavio ur to the columns C1.C0 in the Statistics aplet. You can store a statistics column to a list (or vice versa) a nd use any of the list functions on the statistics columns, or the statistics functions, on the list variables. Create a list in the List Catalog 1. Open the List catalog. LIST . 2 . Highligh t the list name y ou want to assig n to the ne w list (L1, etc .) and pres s to display the List editor . HP 3 9gs Engl ish. book Pa ge 1 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
16-2 Lists 3 . E nter the values you want i n th e l ist, pressi ng after each one. V alue s can be r eal or comple x numbers (o r an expr ession) . If you enter a calc ulation , it is e valuated and the r esult is inserted in the list . 4. When done , pr ess LIST to see the List catalog, or pr ess to re turn to HO ME . List catalog ke ys The list catalog keys are: Key M e a n i n g Opens the highlighted list for editing. Transmits the highlighted list to another hp 39gs or a PC. See âSending and receiving apletsâ on page 19-4 for further information. Receives a list from another hp 39gs or a PC. See âSending and receiving apletsâ on page 19-4 for further information. Clears the highlighted list. CLEAR Clears all lists. or Moves to the end or the beginning of the catalog. HP 3 9gs Engl ish. book Pa ge 2 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Lists 16-3 List edit keys When you press to create or change a list, the following keys are available to you: Create a list in HOME 1. Enter the list on the edit line . Start and end the list w ith br aces (the shifted and ke ys) and separ ate each element with a comma. 2 . Pr ess to ev a luate and display the list. Immediatel y after typing in the list , y ou can sto r e it in a var iable by pr essing lis tname . The list v ar iable name s ar e L0 thr ough L9 . This example stores the list {2 5,14 7 , 8} in L1. Note: Y ou can omit the final br ace when enter ing a list . Key M e a n i n g Copies the highlighted list ite m into the edit line. Inserts a new value before the highlighted item. Deletes the highlighted item from the list. CLEAR Clears all elements from the list. or Moves to the end or the beginning of the list. HP 3 9gs Engl ish. book Pa ge 3 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
16-4 Lists Displaying and editing lists To display a list ⢠In the List cata log, hi ghlight the list name and pr ess . ⢠In HOME , ente r the name of the list and pr ess . To display one element In HOME, enter listname ( element# ). For example, if L2 is {3,4,5,6}, then L2(2) returns 4 . To edit a list 1. Open th e L ist catalog. LIST . 2 . Pr ess or to highlight the name of the list y ou w ant to edit (L1, etc.) and press to display the list contents. 3 . Pres s or to hig hlight the el ement yo u want to edit . In this e x ample , edit the third e lement s o that it has a value of 5 . 5 4. Pr ess . HP 3 9gs Engl ish. book Pa ge 4 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Lists 16-5 To insert an element in a list 1. Open the List catalog. LIST . 2. P r e s s o r t o highli ght the name of the list y ou wan t to edit (L1, etc .) and pre ss to displa y the list conten ts. New elements are inserted abov e the highlighted positi on . In this example, an element, with the value of 9, is inserted between the first and second elements in the list. 3 . Pr ess to the insertion position, then pr ess , and press 9. 4. Pr ess . To stor e one element In HOME, enter value listname ( element ) . For example, to store 148 as the second element in L1, type 148 L1(2) . HP 3 9gs Engl ish. book Pa ge 5 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
16-6 Lists Deleting lists To delete a list In the List catalog, highli ght the list name and press . You are prompted to confirm that you want to delete the contents of the highlighted list variable. Press to delete the contents. To delete all lists In the List catalog, press CLEAR . Transmitting lists You can send lists to calculators or PCs just as you c an aplets, programs, matrices, and notes. 1. Align the HP 3 9gs calculator s â infr ared ports (or connect the calc ulators using an appr opr iate cable) . 2 . Open the L ist catalogs on both calc ulator s. 3 . Hi ghlight the list to send . 4. Pr ess and ch oose the method of sending (infr ar ed or cable) . 5 . Pr ess on th e r ecei v ing cal c ulator and c hoose the method of r ecei v ing (infr ar ed or cable) . F or more infor matio n on sending and r ecei v ing file s, see âSending and rece i ving a plets â on page 19- 4. List functions List functions are found in the MATH menu. You c an use them in HOME, as well as in programs. You can type in the name of the function, or you can copy the name of the function from the List category of the MA TH menu. Press (the alpha L character key). This highlights the List category in the left column. Press to move the cursor to the right column which contain the List functions, select a function, and press . List functions have the following syntax: ⢠F unctions ha ve ar guments that ar e enclo sed in pare ntheses and separated b y commas. Example: HP 3 9gs Engl ish. book Pa ge 6 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Lists 16-7 CONCAT(L1,L2) . An ar gument can be either a list v ari able name (su ch as L1) or the actual list . F or e xample , REVERSE({1 ,2,3}) . ⢠If Dec i mal Mark in Modes is set to C omma, u se peri ods to separat e ar guments. F or e x ample , CONCAT(L1.L2) . Common operators like , â, Ã, and / c an take lists as arguments. I f there are t wo ar guments and both are lists, then the lists must have the same length, since the calculation pairs the elements . If there are two arguments and one is a real number, then the calculation pairs the number with each element of the list. Example 5 * {1,2,3} re t u rn s {5,10,15} . Besides the common operator s that can take numbers, matrices, or lists as arguments, ther e are commands that can only operate on lists. CONCAT Concatenates two lists into a new list. CONCAT( list1 , list2 ) Example CONCAT({1,2,3},{4}) ret u rn s {1,2,3,4} . Î LIST Creates a new list composed of the first differences, that is, the differences between the se quential elements in list1. The new list has one fewer elements than list1 . The first differences for {x 1 x 2 ... x n } are {x 2 âx 1 ... x n âx nâ1 } . Î LIST( list1 ) HP 3 9gs Engl ish. book Pa ge 7 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
16-8 Lists Example In HOME, store {3,5,8,12,17 ,23} in L5 and find the first differences for the list. { 3,5, 8,12 ,1 7 ,2 3 } L 5 L Select Î LIST L5 MAKELIST Calculates a sequence of elements for a new lis t. Evaluates expression with variable from begin to end values, taken at increment steps. MAKELIST( expression , va riab l e , begin , end , incr ement ) The MAKELIST function generates a series by automatically producing a list from the repeated evaluation of an expression. Example In HOME, generate a series of squares from 23 to 27. L Sele ct MAKELIST A A 2 3 27 1 Î LIST Calculates the product of all elements in list. Î LIST( list ) Example Î LIST({2,3,4}) re t u rn s 24 . POS Returns the position of an element within a list. The element can be a value, a variable, or an expression. If there is more than one instance of the element, the HP 3 9gs Engl ish. book Pa ge 8 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Lists 16-9 position of the first occurrence is retu rned. A value of 0 is returned if there is no occurrence of the specified element. POS( list , element ) Example POS ({3, 7, 12, 19},12) returns 3 REVERSE Creates a list by reversing the order of the elements in a list. REVERSE( list ) SIZE Calculates the number of elements in a list. SIZE( list ) Also works with matrices. Σ LIST Calculates the sum of all elements in list. Σ LIST( list ) Example Σ LIST({2,3,4}) ret u rn s 9 . SORT Sort s elements in a scending order. SORT( list ) Finding statistical values for list elements T o f i n d v a l u e s s u c h a s t h e mean, median, maximum, an d minimum values of the elements in a list, use the Statistics aplet. Example In this example, use the Statistics aplet to find the mean, median, maximum, and minimum values of the elements in the list, L1. 1. Cr eate L1 w ith values 8 8, 9 0, 8 9 , 6 5, 7 0, and 8 9 . { 8 8 90 89 65 7 0 89 } L1 HP 3 9gs Engl ish. book Pa ge 9 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
16-10 Lists 2 . In HOME , st or e L1 into C1. Y ou w ill then be able to see the list data in the Numer ic vi e w of the Statis tics aplet . L1 C1 3 . S tart the Statis tic s aplet , and select 1-v ar ia ble mode (pr ess , i f necess ary , to displa y ) . Sele ct Statistics Note: Y our list values ar e no w in column 1 (C1) . 4. In the S ymboli c v ie w , def ine H1 (fo r ex ample) as C1 (sample ) and 1 (fr equency). 5 . Go to the Numer ic v ie w to displa y calc ulated statisti cs . See âOne -v ar iable â on page 10 -14 for the mea ning of each com puted statis tic . HP 3 9gs Engl ish. book Pa ge 10 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Notes and sketches 17-1 17 Notes and sk etc hes Introduction The HP 39gs has text and pi cture editors for entering notes and sketche s. ⢠E ach a plet has its o wn independent Note v iew and Sk etch vi e w . Not es and sk etc hes that y ou cr eate in these vi e ws ar e assoc iated w ith t he aplet. When y ou sa v e the aplet , or send it to another calc ulator , the notes and sketc hes are sa ved or sent as well . ⢠Th e Notepad is a collection o f notes independent of all aplets. T hese notes can also be sent to another calc ulato r v ia the No tepad C atalog . Aplet note view You can attach text to an aplet in its Note view. To write a note in Note view 1. In an aplet , pr ess NOTE f or the Note v ie w . 2 . Use the not e editing k e y s sho wn in the ta ble in the fo llo w i ng sec tion . 3 . Set A lpha lock ( ) for quic k entry of letters. F or lo wer case Alpha lock , pr ess . 4. While Alpha loc k is on: â T o type a single letter of the opposit e case , pre ss letter . â T o type a single n on-alpha ch ar acte r (suc h as 5 or [ ) , pr es s f i r st . (This turns off A lpha lo ck fo r o ne cha ract er .) Y our w or k is automati call y sav e d . Pr ess an y vi e w ke y ( , , , ) or to e xi t the Notes v ie w . HP 3 9gs Engl ish. book Pa ge 1 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
17-2 Notes and sketches Note edit keys Key M e a n i n g Space key for text entry. Displays next page of a multi-pa ge note. Alpha-lock for letter entry. Lower-case alpha-loc k for letter entry. Backspaces cursor and deletes character. Deletes current character. Starts a new line. CLEAR Erases the entire note. Menu for entering variable names, and contents of variab les. Menu for entering math operations, and constants. CMDS Menu for entering program commands. CHARS Displays special characters. To type one, highlight it and press . To copy a chara cter without closing the CHARS screen, press . HP 3 9gs Engl ish. book Pa ge 2 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Notes and sketches 17-3 Aplet sketch view You can attach pictures to an aplet in its Sketch view ( SKETCH ). Y our wor k is aut omaticall y sa v ed w ith the aplet . Press an y other vi e w ke y or to e x it the Sk etch v ie w Sketch keys To dr aw a li ne 1. In an aplet , pr ess SKETCH f or the Sketc h v ie w . 2 . In Sk etch v iew , pr ess and mo ve the c ursor to w her e y ou w ant to start the line 3 . Pr ess . This turns on line- dr aw ing . 4. Mo v e the c urso r in any dir ectio n to the end poin t of the line b y pr essing the , , , k ey s. 5 . Pr ess to finish th e line . Key M e a n i n g Stores the specified portion of the current sketch to a graphics variable (G1 through G0). Adds a new, blank page to the current sketch set. Displays next sketch in the sketch set. Animates if held down. Opens the edit line to type a text label. Displays the menu-key labels for drawing. Deletes the current sketch. CLEAR Erases the entire sketch set. Toggles menu key labels on and off. If menu key labels are hidden, or any menu key, redisplays the menu key labels. H P 3 9 gs E n gl i s h . bo o k P a ge 3 W ed n es d a y , D ec e m b e r 7, 2 005 11: 24 P M
17-4 Notes and sketches To draw a box 1. In Sk etch v ie w , pres s and mov e the c ursor t o wher e you w ant any corner of the bo x to be. 2. P r e s s . 3 . Mo v e the cur sor to mar k the opposite cor ner for the bo x . Y ou can adj ust the si ze of the bo x by mo v ing the cu rs o r . 4. Pr ess to f inish the bo x . To draw a circle 1. In Sket ch v ie w , press and mo v e the c ursor t o wher e you want the center of the c i r cle to be . 2 . Pres s . This tur ns on c irc le dr aw ing. 3 . Mo v e the curs or the distance of the radius . 4. Pr ess to dr aw the c irc le . DRAW keys Key M e a n i n g Dot on. Turns pixels o n as the cursor moves. Dot off. Turns pixels o ff as the cursor moves. Draws a line from the cursorâs starting position to the cursorâs current position. Press when you have finished. You can draw a line at any angle. Draws a box from the cursorâs starting position to the cursorâs current position. Press when you have finished. Draws a circle with the cursorâs starting position as the center. The radius is the distance between the cursorâs starting and ending position. Press to draw the circle. HP 3 9gs Engl ish. book Pa ge 4 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Notes and sketches 17-5 To label parts of a sketch 1. Pr ess and type the te xt on the edit line . T o lock the Alpha shift on , pre ss (for upper case) or (for lo w er cas e) . T o mak e the label a smalle r c har acte r si z e , turn o ff befo r e pres sing . ( is a toggle betw een small and lar ge f ont si z e) . The smaller c har acter si z e cannot displa y lo w er case letters . 2. P r e s s . 3 . P osition the label w here y ou want it b y pr essing the , , , ke ys . 4. Pr ess again to affi x the label. 5. P re s s to c o n t i n u e dr aw ing, or pre ss to e xit the Sk etch v ie w . To crea te a set of sketches You can create a set of up to ten sketches. This allows for simple animatio n. ⢠After making a sk etc h , pre ss to add a ne w , blank page. Y ou can no w mak e a new sk etch , whic h becomes part of the c urr ent se t of sk etches . ⢠T o v ie w the next sk etch in an e x isting set , pr ess . Hold do wn f or ani mati on . ⢠T o r emov e t he c urr ent pag e in the c urr ent sk etch ser ies , pre ss . To store into a graphics variable You can define a portion of a s ketch inside a box, and then store that graphic into a graphics variable. 1. In the Sk etch v ie w , display the sk etc h y ou want t o copy (stor e i nto a v ariable). 2. P r e s s . 3 . Highligh t the var iable name yo u w ant to us e and pr ess . 4. Dr aw a bo x ar ound the por ti on y ou w ant to cop y : mo ve the c ursor to one cor ner , press , then mov e the curs or to the opp osite corner , a nd pre ss . HP 3 9gs Engl ish. book Pa ge 5 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
17-6 Notes and sketches To import a graphics variable You can copy the contents of a graphics variable into the Sketch view of an aplet. 1. Open the Sketch v iew of the aplet ( SKETCH ). T he graphi c w ill be copied her e. 2 . Pr ess , . 3 . Highlight Graphic , then pr ess and highligh t the name of the v ari able ( G1 , etc .) . 4. Pr es s to r ecall the co ntents of the gr aphics va riab l e. 5 . Mov e t he box to w here y o u w ould like to copy the gr aphi c, the n pr es s . The notepad Subject to available memory , you can store as many notes as you want in the Notepad ( NOTEPAD ). These notes are independent of any aplet. The Notepad catalog lists the existing entries by name. It does not include notes that were created in apletsâ Note view s , but these can be imported. See âTo import a noteâ on page 17-8 . To create a note in the Notepad 1. Displa y the Notepad catalog. NOTEPAD 2 . Cr eate a new not e . 3 . Ente r a name fo r y our note. MYNO TE HP 3 9gs Engl ish. book Pa ge 6 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Notes and sketches 17-7 4. W r ite y our note . See âNote e dit ke ys â on page 17 - 2 for mor e infor mation on the entry and editing of notes. 5 . When yo u are f inis hed , press or an aplet ke y to e x it Notepad . Y our wor k is automaticall y sav ed. Notepad Catalog keys Key M e a n i n g Opens the selected note for editing. Begins a new note, and asks for a name. Transmits the selected note to another HP 39 gs or PC. Receives a note being transmitted from another HP 39gs or PC. Deletes the selected note . CLEAR Deletes all notes in the catalog. HP 3 9gs Engl ish. book Pa ge 7 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
17-8 Notes and sketches To import a note You can import a no te from the Notepad into an apletâs Note view, and vice versa. Supp ose you want to copy a note named âAssignmentsâ fr om the Notepad into the Function Note view: 1. In the F unction aplet , display the Not e v ie w ( NOTE ). 2 . Pr ess , highlight Notepad in the left column, then hi ghlight the name â Assi gnments â in the r ight co lumn . 3 . Pr ess to copy the cont ents of â Assignments â to the F unction Not e v ie w . Note: T o r ecall the name in st ead of the contents , pr ess inst ead of . Suppose you want to copy the Note view from the current aplet into the note, Assignments, in the Notepad. 1. In the Notepad ( NOTEPAD ), open the note , â Assignments â . 2 . Pr ess , hig hlight Note in the left column , then pr ess and highligh t NoteText in the ri ght column. 3 . Pres s to r ecall the conte nts of the Not e v ie w into the note â Assignments â . HP 3 9gs Engl ish. book Pa ge 8 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Programming 18-1 18 Pr ogr amming Introduction This chapter describes how to pro gram using the hp 39gs. In this chapter youâll learn about: ⢠using the Pr ogram catalog to c r eate and edit pr ogr ams ⢠pr ogr amming commands ⢠stor ing and retr ie v ing var iables in pr ograms ⢠pr ogr amming var iables. HINT More information on programming, including examples and special tools, ca n be found at HPâs calculators web site: http://www.hp.com /calculators The Contents of a Program An HP 39gs program contains a sequence of numbers, mathematical expressions, and commands that execute automatically to perform a task. These items are separated by a colon ( : ). Commands that take multiple arguments have those arguments separated by a semicolon ( ; ). For example, PIXON xposition ; yposition: Structured Programming Inside a program you can use branching structures to control the execution flow. You can take advantage of structured programming by creating building-bloc k programs. Each building -block program stands aloneâand it can be c alled from other programs. Note: If a program has a space in it s name then you have to put quotes around it when you want to run it . HP 3 9gs Engl ish. book Pa ge 1 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
18-2 Programming Example RUN GETVALUE: RUN CALCULATE: RUN " SHOW ANSWER" : This program is separated into three main tasks, each an individual program. Within each progr am, the task can be simpleâor it can be di vided further into other programs that perform smaller tasks. Program catalog The Program catalog is wher e you create, edit, delete, send, receive, or run progra ms. This section describes how to ⢠open the Pr ogr am catalog ⢠cr eate a ne w pr ogr am ⢠enter commands f r om the pr o gr am commands menu ⢠enter f uncti ons fr om the MA TH men u ⢠edit a pr ogram ⢠run and debug a pr ogram ⢠stop a pr ogram ⢠copy a pr ogram ⢠send and r ecei ve a pr ogram ⢠delete a pr ogr am or its contents ⢠c ustomi z e an aplet . Open Program Catalog 1. Pr ess PROGR M . T he Pr ogram C atalog displa y s a list of pr ogram names . The Pr ogr am Catalog contains a built-in entr y called Editline . Editline cont ains the last e xpr essio n that yo u enter ed fr om the edit line in HOME , or the last data y ou ent er ed in an inpu t fo rm . (If you pr ess fr om HOME w ithout enter ing any dat a , the HP 3 9gs runs the cont ents of Editline .) Bef or e starting to w ork w ith progr ams, y ou should tak e a fe w minutes to become f a miliar w ith the Pr ogr am catalog menu k e y s. Y ou can use an y of the follo wing k ey s (both menu and k ey board), to per for m tasks in the Pr ogram catalog . HP 3 9gs Engl ish. book Pa ge 2 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Programming 18-3 Program catalog k eys The program catalog keys are: Key M e a n i n g Opens the highlighted program for editing. Prompts for a new program name, then opens an empty program. Transmits the highlighted program to another HP 39gs or to a disk drive. Receives the highlighted program from another HP 39gs or from a disk drive. Runs the highlighted program. or Moves to the beginning or end of the Program catalog. Deletes the highlighted program. CLEAR Deletes all programs in the program catalog. HP 3 9gs Engl ish. book Pa ge 3 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
18-4 Programming Creating and editing programs Create a new program 1. Pr ess PROGR M to open the Pr ogr am catalog . 2. P r e s s . The HP 3 9gs pr ompts yo u fo r a n a m e. A pr ogr am name can contain spec ial char acters , such as a space . Ho we ve r , if y ou use spec ial char acters and then run the pr ogr am b y typing it in HOME , y ou must enc lose the pr ogr am name in double quotes ( " " ) . Don't use the " s ymbol w ithin y our pr ogr am name. 3 . T ype y our progr am name , then pr ess . When y ou pr ess , the Pr ogr am E ditor opens. 4. Enter y our pr ogr am. W hen done , star t an y other acti vity . Y our wor k is sa ve d auto maticall y . Enter commands Un til you become familiar with the HP 39gs commands, the easiest way to enter comma nds is to select them from the Commands menu from the Program editor. You can also type in commands using alpha c haracters. 1. F r om the Pr ogra m edito r , pr es s CMDS to open the Pr ogr am Commands men u . CMDS HP 3 9gs Engl ish. book Pa ge 4 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Programming 18-5 2 . On the left, u se or to highligh t a command category , then pr ess to ac cess the commands in the category . Select the command that y ou w ant . 3 . Pr ess to paste the command into the pr ogram editor . Edit a program 1. Pres s PR OGRM to open the Pr ogram catalog. 2 . Use the arr o w k e y s to hi ghlight the pr ogram y ou wa nt to edit, and pr ess . T he HP 39gs opens the Pr ogr am E ditor . The name of y our progr am appears in the title bar of the displa y . Y ou can us e the fo llo w i ng k ey s to edit yo ur pr ogr am . HP 3 9gs Engl ish. book Pa ge 5 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
18-6 Programming Editing keys The editing keys are: Key M e a n i n g Inserts the character at the editing point. Inserts space into text. Display s previous page of the program. Displays next page of the program. Moves up or down one line. Moves right or left one character. Alpha-lock for letter entry. Press A...Z to lock lower case. Backspaces cursor and deletes character. Deletes current character. Starts a new line. CLEAR Erases the entire program. Displays menus for selecting variable names, contents of variables, math functions, and program constants. CMDS Displays menus for selecting program conmmands. CHARS Displays all char acters. To type one, highlight it and press . To enter several characters in a row, use the menu key while in the CHARS menu. HP 3 9gs Engl ish. book Pa ge 6 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Programming 18-7 Using programs Run a program From HOME, type RUN program_name. or From the Program catalog, highlight the program you want to run and press Regardless of where you star t the program, all programs run in HOME. What you see will differ slightly depending on where you started the program. If you start the program from HOME, the HP 39gs displays the contents of Ans (Home variable containing the last result), when the program has finished. If you start the program from the Program catalog, the hp39gs returns you to the Program catalog when the program ends. Debug a program If you run a program that contains errors, the program will stop and you will see an error message. To debug the program: 1. Pr ess to edit the pr ogr am. T he insert c ursor a ppears in the pr ogra m at the poin t w her e the err or occ urr ed. 2 . Edit the pr ogram t o fi x the err or . 3 . R u n the pr ogram . 4. R epeat the pr ocess un til y ou corr ect all er r ors . Stop a program You c an stop the running of a program at any time by pressing CANCEL (the key). Note: You may have to press it a couple of times. HP 3 9gs Engl ish. book Pa ge 7 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
18-8 Programming Copy a program You can use the following procedure if you want to make a copy of y our work before editingâor if you want to use one program as a template for another. 1. Pr ess PROGR M to open the Pr ogr am catalog . 2. P r e s s . 3 . T ype a ne w f ile name, then c hoose . T he Progr am Edito r opens with a ne w pr ogr am . 4. Pr ess to open the var iables menu . 5 . Pr ess to quickly sc r oll to Pr ogram . 6 . Pr ess , then highlight the pr ogr am y ou w ant to copy . 7 . Pres s , then pr ess . T he conte nts of the hi ghligh ted pr ogr am ar e copi ed into the c u r r ent pr ogram at the c urs or location . HINT If you use a programming routine often, save the routine under a different program name, then use the above method to copy it into your programs. Transmit a program You can send programs to, and rec eive programs from, other calculators just as you can send and receive aplets, matrices, lists, and notes. After aligning the calculatorsâ infrared port s, open the Program catalogs on both calculators. Highlight the program to send, then press on the sending calculator and on the receiving calculator. You can also send programs to, and receive programs from, a remote storage devi ce (aplet di sk drive or computer). This takes pla ce via a cable connection and requires an aplet disk driv e or specialized software running on a PC (such as a connectivi ty kit). HP 3 9gs Engl ish. book Pa ge 8 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Programming 18-9 Delete a program To delete a program: 1. Pr ess PROGRM to open the Progr am catalog. 2 . Highligh t a pr ogr am to delet e , then pr ess . Delete all programs You can delete all programs at once. 1. In the Pr ogr am catalog , pres s CLEAR . 2. P r e s s . Delete the contents of a program You can clear t he contents of a program withou t deleting the program name. 1. Pr ess PROGRM to open the Progr am catalog. 2 . Hi ghligh t a pr ogr am, then pr ess . 3. P re s s CLEAR , then pr ess . 4. T he conten ts of the pr ogr am ar e deleted , but the pr ogr am name r emai ns . Customizing an aplet You can customize a n aplet and develop a set of programs to work with the aplet. Use the SETVIEWS command to create a custom VI EWS menu which links specially wr itten programs to the new aplet. A useful method for customizing an aplet is illu strated below: 1. Dec ide on the built-in aplet that y ou want to c ustomi ze . Fo r ex a mple y ou coul d c ustomi ze the F unction aplet or the S tatistic s aplet . T he c us tomi z ed aplet inher its all the prope rties of the built-in aplet . Sa v e the cu stomi z ed aplet w ith a unique name . 2 . C ust omi z e the new a plet if y ou need to , for e x ample b y pr esetting ax es or angle mea sur es . 3 . De v elop the pr ogr ams to w or k w ith y our c us tomi z ed aplet . When yo u dev elop the apletâs pr ograms , use the standar d aplet naming conv ention . This allo ws y ou to k eep trac k of the pr ograms in the Pr ogr am catalog th at belong to ea c h aplet. See â Aplet naming con ven tion â on page 18-10. HP 3 9gs Engl ish. book Pa ge 9 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
18-10 Programming 4. Dev elop a progr am that uses the SE T VIEW S command to modify the apletâs VIEW S menu . The menu opti ons pr o v ide links to ass oc iated pr ograms . Y ou can spec i fy an y other progr ams that you w ant tr ansfe rr ed with the aplet . See âSETVIEW Sâ on page 18-14 for inf ormati on on the command . 5 . Ensur e that the cu stomi z ed aplet is selec ted , then run the menu conf igur atio n pr ogr am to conf igur e the apletâs VIEW S menu . 6 . T es t the cu st omi z ed aplet and debug the ass oc iat ed pr ogr ams. (R efer to âDebug a pr ogr am â on page 16 - 7) . Aplet naming convention To assist users in kee ping tr ack of a plets and associated programs, use the following naming co nvention when setting up an apletâs programs: ⢠St art all pr ogram name s w ith an abbr e v iati on of the aplet name . W e will u se AP L in this ex ample. ⢠Name pr o gr ams called b y menu entr ies in the VIEW S menu number , after the entry , fo r ex ample: â APL .ME1 f or the pr o gr am called by menu opti on 1 â APL .ME2 f or the pr o gr am called by menu opti on 2 ⢠Name the pr ogram that conf igur es the new VIE W S menu option APL .S V where S V stands for SETVIEWS . For example, a customized aplet called âDifferentiationâ might call programs called DIFF.ME1, DIFF.ME2, and DIFF. SV. Example This example aplet is designed to demonstr ate the process of customizing an aplet. The new aplet is based on the Function aplet. Note: This aplet is not intended to serve a serious use, merely to illu strate the process. HP 3 9gs Engl ish. book Pa ge 10 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Programming 18-11 Save the aplet 1. Open the F uncti on aplet and sa ve it as âEXP ERIMENT â . The ne w aplet appear s in the Aplet library . Select Function EXP ERIMENT 2 . Cr eate a pr ogr am called EXP .ME1 with contents as show n. T his pr ogr am conf igur es the plot r anges, then r uns a pr ogr am that allo ws y ou to s et the angle f ormat . 3 . Cr eate a pr ogr am called EXP .ME2 with contents as show n. T his pr ogr am sets the numer ic v iew opti ons fo r the aplet , and r uns the pr ogr am that y ou can us e to conf igur e the angle mode . 4. Cr eate a progr am called EXP .ANG wh ic h the pr e v io us tw o pr ogr ams call . 5 . Cr eate a pr ogr am called EXP .S w hich r uns w hen you start th e aplet , as show n. T his pr ogr am sets the angle mode to degrees , and sets u p the initial f uncti on that the aplet plots . Configuring the Setviews menu option programs In this secti on w e will begin b y confi gur ing the VIEW S menu b y using the SETVI EW S command. W e w ill then c r eate the âhelper â pr ogr ams called b y the VIEW S menu whi ch w ill do the actual w ork . HP 3 9gs Engl ish. book Pa ge 11 We dnes day, Dec embe r 7, 2005 11 : 24 PM
18-12 Programming 6 . Open the Pr ogram cat alog and cr eate a progr am named âEXP .S Vâ . Include the f ollo w ing code in the pr ogr am. E a c h entry line after the command SE T VIEW S is a tri o that consists of a VIEW S menu te xt li ne (a space indicate s none), a progr am name , and a number that def ines the v ie w to go to afte r the pr ogr am has r un its course . All pr ogr ams listed her e will tr ansfer w ith an aplet w hen the a plet is tr ansfer r ed . SETVIEWS â â â â ; â â â â ; 18; Sets the f i r st menu opti on to be â Auto scale â . This is the fo urth standar d F uncti on aplet v ie w menu opti on and the 18 â Auto scale â , spec ifi es that it is to be inc luded in the ne w menu . The empty quotes w ill ensur e that the old name of â A uto scale â appears on the ne w menu . See âSETVIEWSâ o n page 18-14. â â My Entry1â â ;â â EXP.ME1â â ;1; Sets the seco nd menu option . This optio n runs pr ogram EXP .ME1, then r eturns to view 1 , Pl ot vi ew . â â My Entry2â â ;â â EXP.ME2â â ;3; Sets the third men u option . This option runs the pr ogra m EXP .ME2 , then r eturns to v ie w 3, the NUM v ie w . â â â â ;â â EXP.SVâ â ;0; This line spec ifi es that the pr ogram to s et the V ie w menu (this pr ogr am) is tr ansfe rr ed with the a plet . T he space char acter between the f irst set of quotes i n the tr io sp ec if ie s that no men u option appears f or the entry . Y ou do not ne ed to tr ansfe r this progr am w ith the aplet , but it allo ws user s to modif y the apletâs men u if the y wan t to . HP 3 9gs Engl ish. book Pa ge 12 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Programming 18-13 â â â â ;â â EXP.ANGâ â ;0 ; The pr o gr am EXP .ANG is a small routine that is called by other pr ogr ams that the aplet us es . This e ntry spec ifi es that the pr ogr am EXP.ANG is transfer r ed w hen the aplet is tr ansfer r ed, bu t the space in the fir st quotes en sur es that no entry appears on the menu . â â Startâ â ;â â EXP.Sâ â ;7: T his spec ifi es the S tart menu option . The pr ogr am that is ass oc iated w ith this entry , EXP.S, runs a utomati call y when y ou start the aple t . Beca use this menu opti on spec ifi es v ie w 7 , the VIEW S menu opens when y ou star t the apl et . Y ou onl y need to run this pr ogr am once to conf igur e y our apletâs V IEW S menu . Onc e the apletâ s VIEW S menu is conf igured , it remains that w a y until y ou run SETVIEW S again. Y ou do not need to inc lude this pr ogr a m f or y our aplet to w ork , but it is use ful to spec ify that the pr ogr am is atta c hed to the aplet , and transmitted w hen the aplet is transmitted . 7 . Re turn to the pr ogram catalog. T he progr ams that y ou c r eated sh ould appear as f ollow s: 8. Y ou must now th e pr ogr am EXP . S V to ex ecute t he SETVIEW S command and cr eate th e modified VIEW S menu . Check that the name of the ne w aplet is hig hlighted in the A plet vi ew . 9 . Y ou can no w r etur n to the Aplet libr ary and pre ss to run y our new a plet . Programming commands This section describes th e commands for programming with hp 39GS. You can enter these commands in your program by typing them or by accessing them from the Commands menu. HP 3 9gs Engl ish. book Pa ge 13 We dnes day, Dec embe r 7, 2005 11 : 24 PM
18-14 Programming Aplet commands CHECK Checks (selects) the correspon ding function in the current aplet. For example, Check 3 would check F3 if the current aplet is Function. T hen a checkmark would appear next to F3 in Symbolic view, F3 would be plotted in Plot view, and evaluated in Numeric view. CHECK n : SELECT Selects the named aplet and ma kes it the current aplet. Note: Quotes are needed if th e name contains spaces or other special characters. SELECT apletname : SETVIEWS The SETVIEWS command is used to define entries in the VIEWS menu for aplets that you customize. See âCustomizing an ap letâ on page 18-9 for an example of using the SETVIEWS command. When you use the SETVIEWS command, the apletâs standard VIEWS menu is deleted and the customized menu is used in its place. You only need to apply the command to an aplet once. The VIEWS menu changes remain unless you apply the command again. Typically, you develop a program that uses the SETVIEWS command only. The command contains a trio of arguments for each menu option to create, or program to attach. Keep the following points in mind when using this command: ⢠The SE T VIEW S command deletes an apletâs standar d V ie w s menu opti ons . If y ou wan t to us e an y of the standar d opti ons on y our r econf igur ed VI EW S menu , y ou must inc lude th em in the confi guratio n. ⢠When y ou in v ok e the SETVIEW S command, the changes to an apletâs VIEW S menu remain w ith the aplet . Y ou need to in vok e the comman d on the a plet again to change the VIEW S menu . ⢠All the pr ograms that ar e called fr om the VI EW S menu ar e tr ansfe rr ed when the a plet is tr ansferr ed, f or ex amp le to anot her cal c ulator or to a PC. ⢠As part of the VIEW S menu conf igur ation , y ou can spec i fy pr ogr ams that you w ant tr ansfer r ed w ith the aplet , but ar e not called as menu optio ns. F or e xam ple , these can be su b-pr ogr ams that menu HP 3 9gs Engl ish. book Pa ge 14 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Programming 18-15 options u se , or the pr ogr am that def ines the a pletâs VIEW S menu . ⢠Y ou can inclu de a âStart â optio n in the VIEW S men u to spec if y a pr ogr am that y ou w ant to run auto maticall y when the aplet s tarts. This pr ogram typically sets up the apletâ s initial confi guration . T he S T AR T option on the men u is also usef ul for r esetting the aplet . Command syntax The syntax for the command is as follows: SETVIEWS " Pr ompt1 " ;" Pr ogr amName1 " ; ViewN um be r1 ; " Pr ompt2 " ;" Pr ogr amName2 " ; ViewN um be r2 : (Y ou can repeat as man y Prompt/ProgramName/ ViewNumber tri os of ar guments as y ou lik e .) Within each Prompt/ProgramName/ViewNumber trio, you separate each item with a semi-colon. Prompt Prompt is the text that is displayed for the corresponding entry in the Views menu. Enclose the prompt text in double quotes. Associating programs with your aplet If Prompt consists of a single space, then no entry appears in the view menu. The program specified in the ProgramName item is associated with the aplet and transferred whenever the aplet is transmitted. Typically, you do this if you want to transfer the Setviews program with the aplet, or you want to transfer a sub-program that other menu programs use. Auto-run programs If the Prompt item is âStartâ, then the ProgramName program runs whenever y ou start the aplet. This is useful for setting up a program to co nfigure the aplet. Users can select the Start item from the VIEWS menu to reset the aplet if they change conf igurations. You can also define a menu item called âResetâ which is auto-run if the user choo ses the button in the APLET view. HP 3 9gs Engl ish. book Pa ge 15 We dnes day, Dec embe r 7, 2005 11 : 24 PM
18-16 Programming ProgramName ProgramName is the name of the program that runs when the corresponding menu entry is selected. All pr ograms that are identified in the apletâs SETV IEWS command are transferred when the aplet is transmitted. ViewNumber V iewNumber is the number of a view to start after the program finishes runn ing. For example, if you want the menu option to display the Pl ot view when the associated program finishes, you would spec ify 1 as the ViewNumber value. Including standard menu options To include one of an apletâs standard VIEWS menu options in your customized menu, set up the arguments trio as follows: ⢠T he firs t ar gument spec ifi es the menu item name: â Leav e the argument empt y to use the stand ar d V ie w s menu name fo r the item, or â Enter a menu item name to r eplace the standar d name . ⢠The second argument spec ifi es the pr ogr am to run: â Lea v e the ar gument em pty to r un the standar d menu option . â Insert a progr am name to run the pr ogram be for e the standar d menu optio n is e xec uted. ⢠T he thir d ar gument s pec if ies the v ie w and the menu number f or the item . Deter mine the menu number fr om the Vi ew n umbers ta ble belo w . Note: SE TVIEW S w ith no ar guments r esets the v ie w s to def ault of the base aplet . HP 3 9gs Engl ish. book Pa ge 16 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Programming 18-17 View numbers The Function aplet views are numbered as follows: View numbers from 15 on will vary according to the parent aplet. The list shown above is for the Function aplet. Whatever the normal VIEWS menu for the parent aplet, the first entry will become number 1 5, the second number 16 and so on. UNCHECK Unchecks (unselects) the corresponding functio n in the current aplet. For example, Uncheck 3 would unc heck F3 if the current aplet is Function. UNCHECK n : Branch commands Branch commands let a program make a deci sion based on the result of one or more tests. Unlike the ot her programming commands, the branch commands work in logical groups. Therefore, the commands are described together rather than each independently. IF...THEN...END Executes a sequence of commands in the true-clause only if the test-clause evaluate s to true. Its syntax is: IF test-clause THEN true-clause END 0 1 2 3 4 5 6 7 8 9 10 HOME Plot Symbolic Numeric Plot-Setup Symbolic-Setup Numeric-Setup Views Note Sketch view Aplet Catalog 11 12 13 14 15 16 17 18 19 20 21 List Catalog Matrix Catalog Notepad Catalog Program Catalog Plot-Detail Plot-Table Overlay Plot Auto scale Decimal Integer Trig HP 3 9gs Engl ish. book Pa ge 17 We dnes day, Dec embe r 7, 2005 11 : 24 PM
18-18 Programming Example 1 î A : IF A==1 THEN MSGBOX " A EQUALS 1" : END: IF... THEN... ELSE... END Executes the true-clause sequence of commands if the test- clause is true, or the false-clause se quence of commands if the test-clause is false. IF test-clause THEN true-clause ELSE fals e-clause END Example 1 î A : IF A==1 THEN MSGBOX "A EQUALS 1" : ELSE MSGBOX "A IS NOT EQUAL TO 1" : END: CASE...END Executes a series of test-clause commands that execute the appropriate true-c lause sequence of c ommands. Its syntax is: CASE IF test-clause 1 THEN true -c laus e 1 END IF test-clause 2 THEN true -c laus e 2 END . . . IF test-clause n THEN tr ue -clau se n END END: When CASE is execute d, test-clause 1 is evaluated. If the test is true, true-clause 1 is executed, and execution skips to END. If test-clause 1 if false, execution proceeds to test- clause 2 . Execution with the CASE structur e continues until a true-clause is executed (o r until all the tes t-clauses evaluate to false). IFERR... THEN... ELSE⦠END... Many conditions are automati cally recognized by the HP 39gs as error conditions and are automatically treated as errors in programs. HP 3 9gs Engl ish. book Pa ge 18 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Programming 18-19 IFERR...THEN...ELSEâ¦END allows a program to intercept error conditions that otherwise would cause the program to abort. Its syntax is: IFERR tr ap-cla us e THEN clause _1 ELSE clause _2 END : Example IFERR 60/X î Y: THEN MSGBOX "Error: X is zero.": ELSE MSGBOX "Value is "Y: END: RUN Runs the named program. If your program name c ontains special characters, such as a space, then you must enclose the fi le name in double quotes (" "). RUN " pr ogram name " : or RUN pr ogr amname : STOP Stops the current pr ogram. STOP : Drawing commands The drawing commands act on the display. The scale of the display depends on the current aplet's Xmin, Xmax, Ymin, and Ymax values. The following examples assume the hp 39gs default settings with t he Function aplet as the current aplet. ARC Draws a circular arc, of give n radius, whose centre is at (x,y) The arc is drawn from start_angle_measurement , to end_angle_measurement . ARC x;y; radius ; start_angle_measurement ; end_angle_measurement : HP 3 9gs Engl ish. book Pa ge 19 We dnes day, Dec embe r 7, 2005 11 : 24 PM
18-20 Programming Example ARC 0;0;2;0;2 Ï : FREEZE: Dr a w s a c irc le center ed at (0, 0) of r adius 2 . T he FREEZE command causes the c ir cle to r emain di spla ye d on t he sc reen until y ou pr ess a k ey . BOX Draws a box with diagonally opposite corners ( x1,y1 ) and ( x2,y2 ). BOX x1 ; y1; x2; y2: Example BOX -1;-1;1;1: FREEZE: Dr a w s a bo x , lo w er corner at (â1,â1) , upper corner at (1,1) ERASE Clears the display ERASE: FREEZE Halts the program, freezing the cu rrent display. Execution resumes when any key is pressed. LINE Dr aws a line from (x1, y1) to ( x2, y2 ) . LINE x1; y1; x2 ; y2: PIXOFF Turns off the pixel at the specified coordinates (x,y) . PIXOFF x;y : PIXON Turns on the pixel at the specified coordinates (x,y) . PIXON x;y : TLINE Toggles the pixels along the line from (x1, y1) to ( x2, y2) on and off. Any pixel that was turned off, is turned on; any pixel that was turned on, is turned off. TLINE can be used to erase a line. TLINE x1 ; y1 ; x2 ; y2: HP 3 9gs Engl ish. book Pa ge 20 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Programming 18-21 Example TLINE 0;0;3;3: Er ase s pr e v iou sly dr a wn 4 5 degr ee line fr om (0, 0) to (3, 3) , or dr aw s that line if it doesnât alr eady e xist . Graphic commands The graphic commands use th e graphics variables G0 through G9âor the Page variable from Sketchâas graphicname arguments. The position argument takes the form ( x,y ). Position coordi nates depend on the current apletâs scale, which is specified by Xmin, Xmax, Ymin, and Ymax. The upp er left corn er of the target graphic ( graphic2 ) is at (Xmin,Ymax). You can capture the current display and store it in G0 by simultaneously pressing . DISPLAY â Stores the curr ent display in graphicname . DISPLAY â gr aphi cname : â DISPLAY Displays graph ic from graphicname in the display. â DISPLAY gr aphi cname : â GROB Creates a graphic from ex pression , using font_size , and stores the resulting graphic in graphicname . Font sizes are 1, 2, or 3. If the fontsize argument is 0, the HP 39gs creates a graphic display li ke that created by the SHOW operation. â GROB gr aphicname ; ex p ress io n ; fon ts iz e : GROBNOT Replaces graphic in graphicname with bitwise-inverted graphic. GROBNOT gr aphicname : GROBOR Using the logical OR, superimposes graphicname2 onto graphicname1 . The upper left corner of graphicname2 is placed at position . GROBOR gr aphic name1 ; ( po sition) ; gr aphi cname2 : Example GROBOR G0; (1,1); G1 : HP 3 9gs Engl ish. book Pa ge 21 We dnes day, Dec embe r 7, 2005 11 : 24 PM
18-22 Programming will superimpose G1 onto G0 starting a position (1,1), where the position is given in terms of the current axes settings, not as a pixel position. GROBXOR Using the logical XOR, su perimposes graphicname2 onto graphicname1 . The upper left corner of graphicname2 is placed at position . GROBXOR gr aphi cname1 ; ( position) ; gr aphicname2 : MAKEGROB Creates graphic with given width, heig ht, and hexadecimal data, and stores it in graphicname . MAKEGROB gr aphicname ; wi dt h ; he ight ; he xdata : PLOT â Stores the Plot view display as a graphic in graphicname . PLOT â graphi cnam e : PLOT â and DISPLAY â can be used to transfer a copy of the current PLOT view into the sketch view of the aplet for later use and editing. Example 1 î PageNum: PLOT â Page: â DISPLAY Page: FREEZE: This program stores the current PLOT view to the first page in the sketch view of the current aplet and then displays the sketch as a gr aphi c object u ntil any key is pressed. â PLOT Puts graph from graphicname into the Plot view display. â PLOT graphi cnam e : REPLACE Replaces portion of graphic in graphicname1 with graphicname2 , s tarting at position . REPLACE also works for lists and matrices. REPLACE gr aphi cname1 ; ( posi tion ) ; gr aphicname2 : SUB Extracts a portion of the named graphic (or list or matrix), and stores it in a new variable, name . The portion is specified by position and positions. SUB name ; graphi cname ; ( positi on ) ; ( positions ) : HP 3 9gs Engl ish. book Pa ge 22 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Programming 18-23 ZEROGROB Creates a blank graphic with given width and height , and stores i t in graphicname . ZEROGROB gr aphicname ; wi dt h ; hei ght : Loop commands Loop hp allow a program to execute a routine repeatedly. The HP 39gs has three loop structures. The example programs below illustrate each of these structures incrementing the variable A from 1 to 12. DOâ¦UNTIL â¦END Do ... Until ... End is a loop command that executes the loop-clause repeatedly until test-clause returns a true (nonzero) result. Because the test is executed after the loop-clause, the loop-clause is always executed at least once. Its syntax is: DO loop-cla use UNTIL test-clause END 1 î A: DO A 1 î A DISP 3;A: UNTIL A = = 12 END: WHILE⦠REPEAT⦠END While ... Repeat ... End is a loop command that repeatedly evaluates test-clause and exe cutes loop-clause sequence if the test is true. Because the test-clause is executed before the loop-clause, the lo op-clause is not executed if the test is initially false. Its syntax is: WHILE test-clause REPEAT loop-c lause END 1 î A: WHILE A < 12 REPEAT A 1 î A DISP 3;A: END: FORâ¦TOâ¦STEP ...END FOR name = start -expr essi on TO end-expr ession [STEP incr ement ]; loop-cla use END FOR A=1 TO 12 STEP 1; DISP 3;A: END: HP 3 9gs Engl ish. book Pa ge 23 We dnes day, Dec embe r 7, 2005 11 : 24 PM
18-24 Programming Note that the STEP parameter is optional. If it is omitted, a step value of 1 is assumed. BREAK Terminates loop. BREAK: Matrix commands The matrix commands take variables M0âM9 as arguments. ADDCOL Add Column. Inserts values into a column before column_number in the specified matrix . You enter the values as a vector. The values must be separated by commas and the number of valu es must be the same as the number of rows in the matrix name . ADDCOL name ;[ val u e 1 ,...,value n ]; column_number : ADDROW Add Row. Inserts values into a row before row_number in the specified matrix. You enter the values as a vector. The values mu st be sepa rated by commas and the number of values must be the same as the number of columns in the matrix name . ADDROW name ;[ va l u e 1 ,..., va lu e n ]; r o w_nu mber : DELCOL Delete Column. Deletes the specified column from the specified matrix . DELCOL name ; column_number : DELROW Delete Row. Deletes the spe cified row from the specified matrix. DELROW name ; row _ n u m b e r : EDITMAT Starts the Matrix Editor and displays the s pecified matrix. If used in programming, return s to the program when user presses . EDITMAT name : HP 3 9gs Engl ish. book Pa ge 24 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Programming 18-25 RANDMAT Creates random matrix with a specified number of rows and columns and stores the result in name ( name must be M0...M9 ). The entries will be integers ranging from â9 to 9. RANDMAT name ; rows ; c olumns : REDIM Redimensions the specified matrix or vector to si ze . For a matrix, size is a list of two integers {n1,n2} . For a vector, size is a list co ntaining one integer {n} . REDIM name ; si z e : REPLACE Replaces portion of a matrix or vector stored in name with an object starting at position start . start for a matr ix is a list containing two numbers; for a vector, it is a single number. Replace also works with lists and graphics. REPLACE name ; star t ; objec t : SCALE Multiplies the specified row_number of the specified matrix by value . SCALE name ; val ue ; rown u m b er : SCALEADD Multiplies the row of the matrix nam e by value , then adds this result to the second specified row. SCALEADD name ; val u e ; row 1 ; row 2 : SUB Extracts a sub-objectâ a portion of a list, matrix, or graphic fro m object âand stores it into name . start and end are each specified using a list with two numbers for a matrix, a number for vector or lists, or an ordered pair, ( X,Y ), for graphic s. SUB name ; object ; sta rt ; end : SWAPCOL Swaps Columns. Exch anges column1 and column2 of the specified matrix . SWAPCOL name ; column1 ; column2 : SWAPROW Swap Rows. Exc hanges row1 and row2 in the specified matrix . SWAPROW name ; row 1 ; row2 : HP 3 9gs Engl ish. book Pa ge 25 We dnes day, Dec embe r 7, 2005 11 : 24 PM
18-26 Programming Print commands These commands print to an HP infrared printer, for example the HP 82240B printer. PRDISPLAY Prints the contents of the display. PRDISPLAY: PRHISTORY Prints all objects in the history. PRHISTORY: PRVAR Prints name and co ntents of variablename . PRVAR va ri ablename : You can also use the PRVAR comman d to print the contents of a program or a note. PRVAR pr ogr amname ;PROG: PRVAR not ename ; NOTE: Prompt commands BEEP Beeps at the frequency and for the time you specify. BEEP frequen cy ; seconds : CHOOSE Creates a choose box, which is a bo x containing a list of options from which the user chooses one. Each option is numbered, 1 through n . The result of the choose command is to store the number of the option chosen in a variable. The syntax is CHOOSE variable_name ; t itle ; option 1 ; option 2 ; ... optio n n : where variable_name is the number of the option that will be highlighted by default whenever the choose box is displayed, title is the text displayed in the title bar of the choose box, an d option 1 ...option n are the options listed in the choose box. HP 3 9gs Engl ish. book Pa ge 26 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Programming 18-27 Example 3 î A:CHOOSE A; "COMIC STRIPS"; "DILBERT"; "CALVIN&HOBBES"; "BLONDIE": CLRVAR Clears the specified va riable. The syntax is: CLR V AR v ari able : Example If you have stored {1,2,3,4} in variable L1, entering CLVAR L1 w ill clear L1. DISP Displays textitem in a row of the display at the line_number . A text item consists of any number of expressions and quoted strings of text. The expressions are evaluated and turned into strings. Lines are numbered from the top of the screen, 1 being the top and 7 being the bottom. DISP line_nu mber ; te x titem : Example DISP 3;"A is" 2 2 Res u lt : A is 4 (display ed on line 3) DISPXY Dis plays object at position ( x_pos , y_pos ) in size font . The syntax is: DISPXY x_po s ; y_po s ; fo nt ; object : The value of object can be a text string, a variable, o r a combination of both. x_pos and y_pos are r elati ve to the c urr ent settings of Xmin, Xmax , Ymin and Ymax (whi c h y ou set in th e PL O T SETUP vie w) . T he value of fo nt is either 1 (small) or 2 (lar ge). HP 3 9gs Engl ish. book Pa ge 27 We dnes day, Dec embe r 7, 2005 11 : 24 PM
18-28 Programming Example DISPXY â3.5;1.5;2;"HELLO WORLD": DISPTIME Displays the current date and time. DISPTIME To set the date and time, simply store the correct settings in the date and time variables. Use the following formats: M.DDYYYY for the date and H.MMSS for the time. Examples 5.152000 î DATE( sets the date to May 15, 2000) . 10.1500 î TIME (sets the time to 10:15 am). EDITMAT Matrix Editor. Opens the Matr ix editor for the specified matrix. Returns to the program when user presses EDITMAT matr ixname : The EDITMAT command can also be used to create matrices. 1. Pr ess CMDS 2. P r e s s M 1, and the n pr ess . T he Matri x catalog opens w ith M1 a vailable f or editing . EDITMAT matrixname is an alternative to opening the matrix editor with matrixname . FREEZE This command prevents the display from being updated after the program runs. This allows you to view the graphics created by the program. Cancel FREEZE by pressing any key. FREEZE: HP 3 9gs Engl ish. book Pa ge 28 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Programming 18-29 GETKEY Waits for a key, then st ores the key code rc.p in name, where r is row number, c is column number, and p is key- plane number. The key-planes numbers are: 1 for unshifted; 2 for shifted; 4 for alpha-shifted; and 5 for both alpha-shifted and shifted . GETKEY name : INPUT Creates an input form with a title bar and one field. The field has a label and a default value. There is text help at the bottom of the form. The user enters a value and presses the menu key. The value that the user enters is stored in the vari able name . The title , label , and help items are text strings and need to be enclosed in double quotes. Use CHARS to type the quote marks " ". INPUT name ; title , label ; help ; de fa ult : Example INPUT R; "Circular Area"; "Radius"; "Enter Number";1: MSGBOX Displays a message box cont aining textitem. A text item consists of any number of expressions and quoted strings of text. The expressions are evaluated and turned into strings of text. For examp le, "AREA IS:" 2 2 becomes ARE A IS: 4 . Use CHARS to type the quote marks " ". MSGBOX te xtitem : Example 1 î A: MSGBOX "AREA IS: " Ï*A^2: You can also use the NoteText variable to provide text arguments. This can be used to insert line breaks. For example, press NOTE and ty pe AREA IS . The position line MSGBOX NoteText " " Ï*A^ 2: will display the same message box as the previous example . HP 3 9gs Engl ish. book Pa ge 29 We dnes day, Dec embe r 7, 2005 11 : 24 PM
18-30 Programming PROMPT Displays an input box with name as the title, and prompts for a value for name . name can be a variable such as Aâ¦Z, θ , L1â¦l9, C1â¦C9 or Z1â¦Z9. PROMPT name : WAIT Halts program execution for the specified number of seconds. WAIT sec onds : Stat-One and Stat-Two commands The following commands are used for analyzing one- variable and two-variable statistic al data. Stat-One commands DO1VSTATS Calculates STATS using dat asetname and stores the results in the corresponding variables: N Σ , Tot Σ , Mean Σ , PVar Σ , SVar Σ , PSDev, SSDev, Min Σ , Q1, Median, Q3, and Max Σ . Datasetname can be H1, H2, ..., or H5. Datasetname must include at least two data points. DO1VSTATS datas etname : SETFREQ Sets datasetname frequency a ccording to column or value. Datasetname can be H1, H2,..., or H5, column can be C0âC9 and value can be any positive integer. SETFREQ data setname ; colum n : or SETFREQ def inition ; va l u e : SETSAMPLE Sets datasetname sample according to column. Datasetname can be H1âH5, and column can be COâC9. SETSAMPLE datas etname ; column : Stat-Two commands DO2VSTATS Calculates STATS using dat asetname and stores the results in corresponding variables: MeanX, Σ X, Σ X2, MeanY, Σ Y, ΣY2, Σ XY, Corr, PCov, SCo v, and RELERR. HP 3 9gs Engl ish. book Pa ge 30 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Programming 18-31 Datasetname can be SI, S2,..., or S5 . Datasetname must include at least two pairs of data points. DO2VSTATS datasetname : SETDEPEND Sets datasetname dependent column . Datasetname can be S1, S2, â¦, or S5 and column can be C0âC9. SETDEPEND datasetname ; column : SETINDEP Sets datasetname independent column . Datasetname can be S1, S2,â¦, or S5 and co lumn can be C0âC9. SETINDEP datasetname ; column : Storing and retrieving variables in programs The hp 39gs has both Home variables and Aplet variables. Home variables ar e used for real numbers, complex numbers, graphics, lists, and matrices. Home variables keep the same values in HOME and in aplets. Aplet variables are those whose values depend on the current aplet. The aplet variab les are used in programming to emulate the definitions and settings you make when working with aplets interactively. You use the Variable menu ( ) to retrieve either Home variables or aplet vari ables. Se e âThe VARS menuâ on page 14-4. Not all variables are availa ble in every aplet. S1fitâS5fit, for example, are only available in the St at is tic s a pl et . U nde r e ac h va ri ab le nam e i s a li st of th e aplets where the variable can be used. HP 3 9gs Engl ish. book Pa ge 31 We dnes day, Dec embe r 7, 2005 11 : 24 PM
18-32 Programming Plot-view variables Area Function Contains the last value found by the Area function in Plot- FCN menu. Axes All Aplets Turns axes on or off. From Plot Setup, check (o r uncheck) AXES . or In a program, type: 1 î Axes âto turn axes on (def ault) . 0 î Axes âto turn ax es off . Connect Function Parametric Polar Solve Statistics Draws lines between successively plotted points. From Plot Setup, check (o r uncheck) CONNECT . or In a program, type 1 î Connect â to connect plotted points (def ault , e x cept in St atistic s w her e the def ault is off). 0 î Connect â not to connect plotted po ints . Coord Function Parametric Polar Sequence Solve Statistics Turns the coordinate-display mode in Plo t view on or off. From Plot view, use the Menu mean key to toggle coordinate display on an off. In a program, type 1 î Coord âto tur n coor dinate displa y on (def ault). 0 î Coord âto turn coor din ate displa y off . Extremum Function Contains the last value foun d by the Extremum operation in the Plot-FCN menu. FastRes Function Solve Toggles resolution between plotting in every other column (faster), or plotting in every column (more detail). From Plot Setup, choose Faster or More Detail. or In a program, type 1 î FastRes âfor f aster . 0 î FastRes âfor mor e detail (def ault) . HP 3 9gs Engl ish. book Pa ge 32 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Programming 18-33 Grid All Aplets Turns the background grid in Plot view o n or off. From Plot setup, check (or uncheck) GRID . or In a program, type 1 î Grid to tur n the gr id on . 0 î Grid to tur n the gri d off (def ault). Hmin/Hmax Statistics Defines minimum and maximum values for histogram bars. From Plot Setup for one-variable statistics, set values for HRNG . or In a program, type î Hmin î Hmax wh ere Hwidth Statistics Sets the width of histogram bars. From Plot Setup in 1VAR stats set a value for Hwidth or In a program, type n î Hwidth Indep All Aplets Defines the value of the independent variable used in tracing mode. In a program, type n î Indep InvCross All Aplets Toggles between solid crosshai rs or inverted crosshairs. (Inverted is useful if the background is solid). From Plot Setup, check (or uncheck) InvCross or In a program, type: 1 î InvCross âto in v ert the cr osshair s. 0 î InvCross âf or soli d cr osshair s (default). n 1 n 2 n 2 n 1 > HP 3 9gs Engl ish. book Pa ge 33 We dnes day, Dec embe r 7, 2005 11 : 24 PM
18-34 Programming Isect Function Contains the last value found by the Intersection function in the Plot-FCN menu. Labels All Aplets Draws labels in Plot view showing X and Y ranges. From Plot Setup, check (o r uncheck) Labels or In a program, type 1 î Labels âto turn labels on . 0 î Labels âto turn labels o ff (def ault) . Nmin / Nmax Sequence Defines the minimum and maxi mum independent variable values. Appears as the NRNG fi elds in the Plot Setup input form. From Plot Setup, enter values for NRNG . or In a program, type î Nmin î Nmax whe re Recenter All Aplets Recenters at the crosshairs locations when zooming. From Plot-Zoom-Set Factors, check (or un check) Recenter or In a program, type 1 î Recenter â to tur n r ecent er on (def ault). 0 î Recenter âto tur n r ecenter o ff . Root Function Contains the last value found by the Root function in the Plot-FCN menu. n 1 n 2 n 2 n 1 > HP 3 9gs Engl ish. book Pa ge 34 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Programming 18-35 S1markâS5mark Statistics Sets the mark to use for scatter plots. From Plot Setup for two-variable statistics, S1mark- S5mark , then choose a mark. or In a program, type n î S1mark wh ere n is 1,2,3,...5 SeqPlot Sequence Enables you to choose types of sequence plot: Stairstep or Cobweb. From Plot Setup, select SeqPlot , then choose Stairstep or Cobwe b . or In a program, type 1 î SeqPlot âfor Stairstep. 2 î SeqPlot âfor Cobweb. Simult Function Parametric Polar Sequence Enables you to choose between simultaneous and sequential graphing of all selected expressions . From Plot Setup, check (or uncheck) _ SIMULT or In a program, type 1 î Simult âf or simultaneou s gr aphing (def ault). 0 î Simult âf or seq uenti al gr aphing . Slope Function Contains the last value found by the Slope function in the Plot-FCN menu. StatPlot Statistics Enables you to choose types of 1-variable statistics plot between Histogram or Box-and-Whisker. From Plot Setup, select StatPlot , then choose Histogram or BoxWh isker . or In a program, type 1 î StatPlot âfor Histogram. 2 î StatPlot âfor Box-and-Whisker. HP 3 9gs Engl ish. book Pa ge 35 We dnes day, Dec embe r 7, 2005 11 : 24 PM
18-36 Programming Umin/Umax Polar Sets the minimum and maxi mum independent values. Appears as the URNG field in the Plot Setup input form. From the Plot Setup input form, enter values for URNG . or In a program, type î Umin î Umax wher e Ustep Polar Sets the step size for an independent v ariable. From the Plot Setup input form, enter values for USTEP . or In a program, type n î Ustep wher e Tmin / Tmax Parametric Sets the minimum and maxi mum independent variable values. Appears as the TRN G field in the Plot Setup input form. From Plot Setup, enter values for TRNG . or In a pr ogr am, type î Tmin î Tmax wher e Tracing All Aplets Turns the tracing mode on or off in Plot view. In a program, type 1 î Tracing âto tur n T r ac ing mode on (def ault) . 0 î Tracing âto tur n T r ac ing mode off . n 1 n 2 n 2 n 1 > n 0 > n 1 n 2 n 2 n 1 > HP 3 9gs Engl ish. book Pa ge 36 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Programming 18-37 Tstep Parametric Sets the step size for the independent variable. From the Plot Setup input form, enter values for TSTEP . or In a program, type n î Tstep wh ere Xcross All Aplets Sets the horizontal coordinate of the c rosshairs. Only works with TRACE off. In a program, type n î Xcross Ycross All Aplets Sets the vertical coordinate of the crosshairs. Only works with TRACE off. In a program, type n î Ycross Xtick All Aplets Sets the distance between tick marks for the horizontal axis. From the Plot Setup input form, enter a value for Xtick . or In a program, type n î Xtick wh ere Ytick All Aplets Sets the distance between tick marks for the vertical axis. From the Plot Setup input form, enter a value for Ytick . or In a program, type n î Ytick wh ere Xmin / Xmax All Aplets Sets the minimum and maximum horizontal values of the plot screen. Appears as the XRNG fields (horizontal range) in the Plot Setup input form. From Plot Setup, enter values for XR NG . or In a program, type n 0 > n 0 > n 0 > HP 3 9gs Engl ish. book Pa ge 37 We dnes day, Dec embe r 7, 2005 11 : 24 PM
18-38 Programming î Xmin î Xmax whe re Ymin / Ymax All Aplets Sets the minimum and maximum vertical values of the plot screen. Appears as the YRNG fields (vertical range) in the Plot Setup input form. From Plot Setup, enter the values for YRNG . or In a program, type î Ymin î Ymax whe re Xzoom All Aplets Sets the horizontal zoom factor. From Plot-ZOOM-Set Factors, enter the value for XZOOM . or In a program, type n î XZOOM wher e The default value is 4. Yzoom All Aplets Sets the vertical zoom factor. From Plot-ZOOM-Set Factors, enter the value for YZOOM . or In a program, type n î YZOOM The default value is 4. n 1 n 2 n 2 n 1 > n 1 n 2 n 2 n 1 > n 0 > HP 3 9gs Engl ish. book Pa ge 38 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Programming 18-39 Symbolic-view variables Angle All Aplets Sets the angle mode. From Symbolic Setup, choose Degrees , Radia ns , or Grads for angle measure. or In a program, type 1 î Angle âfor De grees. 2 î Angle âfor Radian s. 3 î Angle âfor Grads. F1...F9, F0 Function Can contain any expression. Independent variable is X . Example 'SIN( X)' î F1( X ) You must put single quotes around an expression to keep it from being evaluated before it is stored. Use CHARS to type the single quote mark. X1, Y1...X9,Y9 X0,Y0 Parametric Can contain any expression. Independent variable is T. Example 'SIN(4*T)' î Y1(T):'2*SIN(6*T)' î X1(T) R1...R9, R0 Polar Can contain any expression. Independent variable is θ . Example '2*SIN(2* θ)' î R1( θ ) U1...U9, U0 Sequence Can contain any expression. Independent variable is N. Example RECURSE (U,U(N-1)*N,1,2) î U1(N) E1...E9, E0 Solve Can contain any equa tion or expression. Independent variable is selected by high lighting it in Numeric View. Example 'X Y*X-2=Y' î E1 HP 3 9gs Engl ish. book Pa ge 39 We dnes day, Dec embe r 7, 2005 11 : 24 PM
18-40 Programming S1fit...S5fit Statistics Sets the type of fit to be used by the FIT operation in drawing the regression line. From Symbolic Setup view, specify the fit in the field for S1FIT, S2FIT, etc. or In a program, store one of the fo llowing constant numbers or names into a variable S1fit , S2fit , etc. 1 Linear 2 LogFit 3 ExpFit 4 Power 5 QuadFit 6 Cubic 7 Logist 8 ExpFit 9 TrigFit 10 User Defined Example Cubic î S2fit or 6 î S2fit HP 3 9gs Engl ish. book Pa ge 40 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Programming 18-41 Numeric-view variables The following aplet variabl es control the Numeric view . The value of the variable appl ies to the current aplet only. C1...C9, C0 Statistics C0 through C9 , for column s of data. Can contain lists. Enter da ta in the N umeric view or In a program, type LIST î C n wh ere n = 0, 1, 2, 3 ... 9 Digits All Aplets Number of decimal places to use for Number format in the HOME view and for labeling axes in the Plot view. From the Modes view, enter a value in the second field of Number Format . or In a program, type n î Digits wh ere Format All Aplets Defines the number display format to use for numeric format in the HOME view and for labeling axes in the Plot view. From the Modes view, choose Standard , Fixed , Scientific , Engineering, Fraction or Mixed Fraction in the Number Format field. or In a program, store the constant number (or its name) into the vari able Format . 1 Standard 2 Fixed 3 Sci 4 Eng 5 Fraction 6 MixFraction 0 n 11 << HP 3 9gs Engl ish. book Pa ge 41 We dnes day, Dec embe r 7, 2005 11 : 24 PM
18-42 Programming Note that if Fraction or M ixed Fraction is chosen, the setting will be ignored when labeling axes in Plot view. A setting of Scientific will be used instead. Example Scientific î Format or 3 î Format NumCol All Aplets except Statistics aplet Sets the column to be highlighted in Numeric view. In a program, type n î NumCol where n can be 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 . NumFont Function Parametric Polar Sequence Statistics Enables you to choose the font size in Numeric view. Does not appear in the Num Setup input form. Corresponds to the key in Numeric view. In a program, type 0 î NumFont fo r small (defa ult) . 1 î NumFont for big. NumIndep Function Parametric Polar Sequence Specifies the list of indepe ndent valu es to be used by Build Your Own Table. In a program, type LIST î NumIndep NumRow All Aplets except Statistics aplet Sets the row to be highlighted in Numeric view. In a program, type n î NumRow wher e NumStart Function Parametric Polar Sequence Sets the starting value for a table in Numeric view. From Num Setup, enter a value for NUMSTART . or In a program, type n î NumStart n 0 > HP 3 9gs Engl ish. book Pa ge 42 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Programming 18-43 NumStep Function Parametric Polar Sequence Sets the step size (increment value) for an independent varia ble in N umeri c view. From Num Setup, enter a value for NU MSTEP . or In a program, type n î NumStep wh ere NumType Function Parametric Polar Sequence Sets the table format. From Num Setup, choose Automatic or Build You r Own . or In a program, type 0 î NumType f or Build Y our Ow n . 1 î NumType for A utomatic (d ef ault ) . NumZoom Function Parametric Polar Sequence Sets the zoom factor in the Numeric view. From Num Setup, type in a value for NUMZOOM . or In a program, type n î NumZoom wh ere StatMode Statistics Enables you to choose between 1-variable and 2- variable statistics in the Statistics aplet. Does not appear in the Plot Setup input form. Corresponds to the and menu keys in Numeric View. In a program, store the constant name (or its number) into the variab le StatMode. 1VAR = 1 , 2VAR = 2. Example 1VAR î StatMode or 1 î StatMode n 0 > n 0 > HP 3 9gs Engl ish. book Pa ge 43 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Note variables The following aplet variable is available in Note view. NoteText All Aplets Use NoteText to recall text previously entered in Note view. Sketch variables The following aplet variables are available in Sk etch view. Page All Aplets Sets a page in a sketch set. The graphics can be viewed one at a time using the and keys. The Page var iable refers to the cu rrently displayed page of a sketch set. In a program, type gr aphi cname î Page PageNum All Aplets Sets a number for referring to a particular page of the sketch set (in Sketch view). In a program, type the page that is shown when SKETCH is pressed. n î PageNum HP 3 9gs Engl ish. book Pa ge 44 We dnes day, Dec embe r 7, 2005 11 : 24 PM
Extending aplets 19-1 19 Extending aplets Aplets are the application environments where you explore different cla sses of mathematical operations. You can extend the capabili ty of the HP 39gs in the following ways: ⢠Cr eate ne w aplets , based on e x isting aplets , w ith spec ifi c conf igur ations suc h as angle measur e, gr aphical or tabular settings, and annotations. ⢠T r ansmit aplets between HP 3 9gs calculator s v ia an infr a re d link. ⢠Do wnload e-lessons (teac hing aplets ) fr om He wlett-P ac k ar dâs Calc ulator w eb site. ⢠Pr ogr am new aplets . See c hapter 18, âPr ogramming â, for further details. Creating new aplets based on existing aplets You can create a new aplet ba sed on an existing aplet. To create a new aplet, save an existing aplet under a new name, then modify the aplet to add the configurations and the functionality that you want. Information that defines an a plet is saved automatically as it is entered into the calculator. To keep as much memory available for storage as possible, delete any aplets you no longer need. Example This e xample demonstrates how to create a new aplet by saving a copy of the bu ilt-in Solve aplet. The new aplet is saved under the name âTRIANGLESâ contains the formulas commonly used in calculation s involving right-angled triangles. HP 3 9gs Engl ish. book Pa ge 1 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
19-2 Exten ding aplet s 1. Open the Solv e aplet and save it under the n e w name . Solve | T R I A N G L E S 2 . En te r t he fou r formu l as : θ O H θ A H θ OA AB C 3 . Dec ide whether y ou want the a plet to oper ate in Degr ees , R adians , or Gr ads. MODES Degrees 4. V ie w the Aplet L ibr ary . T he âT RIANGLE Sâ aplet is listed in t he Aplet L ibrary . T he Solv e aplet can no w be r eset and used f or other pr oblems. HP 3 9gs Engl ish. book Pa ge 2 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Extending aplets 19-3 Using a customized aplet To use the âT rianglesâ aplet, simply s elect the appropriate formula, change to the Numeric view and solve for the missing variable. Find the length of a ladder leaning against a vertical wall if it forms an angle of 35 o with the horizontal and extends 5 metres up the wall. 1. Selec t the aplet. TRIANGLES 2 . Ch oose the sine f or mula in E1. 3 . Change to the Numer ic vi ew a n d e n t e r t he kno w n values . 35 5 4. Sol ve f or the missing va lu e. T he length of the ladder is appr o x imately 8.7 2 metr es Resetting an aplet Resetting an aplet clears all data and resets all default settings. To reset an aplet, open the Library, select the aplet and press . You can only r eset an aplet that is based on a built-i n aplet if the programmer who created it has provided a Reset option. HP 3 9gs Engl ish. book Pa ge 3 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
19-4 Exten ding aplet s Annotating an aplet with notes The Note view ( NOTE ) attaches a note to the current aplet. See Chapter 17, âNotes and sketc hesâ. Annotating an aplet with sketches The Sketch view ( SKETCH ) attaches a picture to the current aplet. See chapter 17, âNotes and sketchesâ. HINT Notes and s k et c hes th at y ou atta c h to an aplet becom e part of the aplet. W hen yo u transfer the aplet to another calculator , the associ ated note a nd sketc h are tr ansferr e d as well. Downloading e-lessons from the web In addition to the standard aplets that come with the calculator, you can download aplets from the world wide web. For example, Hewlett-Packardâs Calculators web site contains aplets that de monstrate certain mathematical concepts. Note that you need the Graphing Calculator Connectivity Kit in order to load aplets from a PC. Hewlett-Packardâs Calculators web site can be found at: http://www.hp.com/calculators Sending and receiving aplets A convenient way to distribute or share problems in class and to turn in homework is to transmit (copy) aplets d i r e c t l y f r o m o n e H P 3 9 g s t o a n o t h e r . T h i s c a n t a k e p l a c e via the infrared port or via a suitable cable. (You can use a serial cable with a 4-pin mini-USB connector, which plugs into the RS232 port on the calculator. The serial cable is available as a separate accessory.) You can also send aplets to, and receive aplets from, a PC. This requires special softwa re running on the PC (such as the PC Connectivity Kit). A USB cable with a 5-pin mini- USB connector is provided with the hp39gs for connecting with a PC. It plugs into the USB port on the calculator. HP 3 9gs Engl ish. book Pa ge 4 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
Extending aplets 19-5 To transmit an aplet 1. Co nnect the P C or a plet disk dr i v e to the calc ulator by cable or align the tw o calc ulators â infr ar ed ports by matc hing up the tr iangle marks on the r ims of the calc ulators . P lace the calculato rs no mor e than 4 inches (10 cm) apar t. 2 . Sending calc ulator : Open the L ibrary , highlight the aplet to s end, and pr ess . â Th e S END TO men u appears w ith th e f ollo w ing optio ns: HP39G (IRDA) = to send vi a high-speed infr ared HP39/40 (USB) = to send vi a the USB port HP39/40 (SER) = to send via the R S2 3 2 serial port USB DISK DRIVE = to send to a disk dri ve v ia the USB port SER. DISK DRIVE = to send to a disk dr iv e vi a the R S 232 s e r i a l p o r t Note : c hoos e a disk dri ve optio n if you ar e using the hp3 9gs connecti vity kit to tr ansfer the ap let . Hi ghlight y our selecti on and pres s . â If transmitting to a disk dr iv e , y ou ha ve the optio ns of se nding to the c ur r ent (de fault) directory or to anot her director y . 3 . R ecei ving calc ulator : Open the aplet library and pr ess . â Th e RECEIVE FROM menu appear s w ith the fo llo w i ng optio ns: HP39G (IRDA) = to r ecei v e v ia hi gh-speed infr ar ed HP39G = to r ecei ve v ia low-s peed infr ared HP39/40 (USB) = to r ecei v e v ia the U SB por t HP39/40 (SER) = to rece i ve v ia the R S2 3 2 seri al port USB DISK DRIVE = to recei ve fr om a disk dr i ve v ia the USB po r t SER. DISK DRIVE = to r ece i v e fr om a disk dri ve vi a the R S 232 s e r i a l p o r t HP 3 9gs Engl ish. book Pa ge 5 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
19-6 Exten ding aplet s Note : ch oose a disk dri ve option if y ou are using the hp3 9gs connecti vity kit to tr ansfer the a plet . Hi ghlight y our selec tion and pr ess . The T r ansmit annu nc iatorâ âi s display e d until tr ansmis sion is co mplet e . If you are using the PC Connectivity Kit to download aplets from a PC, you will see a list of aplets in the PCâs current directory. Chec k as ma ny item s as you wou ld like to receive. Sorting items in the aplet library menu list Once you have entered information into an aplet, you have defined a new version of an aplet. The information is automatically saved under the cur rent aplet name, such as âFunction.â To create additio nal aplets of the same type, you must give the current aplet a new name. The advantage of storing an ap let is to allow you to keep a copy of a working environment for later use. The aplet library is where you g o to manage your aplets. Press . Highlight (using the arrow keys) the name of the aplet you want to act on. To sort the aplet list In the aplet library, press . Select the sorting scheme and press . ⢠Chronologically pr od uces a c hr onological order based on the dat e an aplet w as last used . (The last- used aplet ap pears firs t, and so on .) ⢠Alphabetically pr o duces an alphabetical or der b y aplet name . To delete an aplet You cannot delete a built-in aplet. You can only clear its data and reset its default settings. To delete a customized aplet, open the aplet library, highlight the aplet to be deleted, and press . To delete all custom aplets, press CLEAR . HP 3 9gs Engl ish. book Pa ge 6 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
R-1 R Re fer ence inf ormation Glossary aplet A small application, limited to one topic. The built-in aplet types are Function, Parametric , Polar, Sequence, Solve, Statistics, Inference, Finance, Trig Explorer, Quad Explorer, Linear Solver and Triangle Solve. An aplet can be filled with the data and solutions for a specific problem. It is reusable (like a program, but easier to use) and it records all your settings and definitions. command An operation for use in programs. Commands can store results in variables, but do no t display results. Arguments are separated by semi- colons, such as DISP expression ; line# . expression A number, variable, or algebraic expression (numbers plus functions) that produces a value. function An operation, possibly with arguments, that returns a result. It does not store results in variables. The arguments must be enclosed in parentheses and separated with commas (or periods in Comma mode), such as CROSS ( matrix1,matrix2 ). HOME T he basic starting point of the calculator. Go to HOME to do calculatio ns. Library For aplet management: to start, save, reset, send and receive aplets. HP 3 9gs Engl ish. book Pa ge 1 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
R-2 list A set of values separated by commas (periods if the Decimal Mark mode is set to Comma ) and enclosed in braces. Lists are commonly used to enter statistical data and to evaluate a function with multiple values. Created and manipulate d by the List editor and catalog. matrix A two-dimensional ar ray of values separated by commas (periods if the Decimal Mark mode is set to Comma ) and enclosed in nested brackets. Created and manipulated by the Matrix catalog and editor. Vectors are also handled by the Matrix catalog and editor. menu A choice of options given in the display. It can appear as a list or as a set of menu-key labels across the bottom of the display. menu keys The top row of keys. Th eir operations depend on the current context. The labels along the bottom of the display show the current meanings. note Text that you write in the Notepad or in the Note view for a specific aplet. program A reusable set of instructions that you record using the Program editor. sketch A drawing that you make in the Sketch view for a specific aplet. variable The name of a number, list, matrix, note, or graphic that is stored in memory. Use to store and use to retrieve. vector A one-dimensional ar ray of values separated by commas (periods if the Decimal Mark mode is set to Comma ) and enclosed in single brackets. Created and manipulated by the Matrix catalog and editor. HP 3 9gs Engl ish. book Pa ge 2 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
R-3 Resetting the HP 39gs If the calculator âlocks upâ and seems to be stuc k, you must reset it. This is much like resetting a PC. It cancels certain operations, restores ce rtain conditio ns, and clears temporary memory locations. However, it does not clear stored data (variables, ap let databases, programs) unless you use the proced ure, âTo e rase all memor y and reset defaultsâ. To reset using the keyboard Press and hold the key and the thir d menu key simultaneously, then release them. If the c alculator does not respond t o the above key sequence, then: 1. T ur n the calc ulator o v er and locate the small hole in the bac k of the calc ulator . 2 . Insert the end of a straightened metal paper c lip into the hole as f a r as it w i ll go . Hold it ther e fo r 1 second , then r emo v e it . 3 . Pre ss If necessary , pr es s and the f irst and last men u k e y s simultaneou sly . (Note: This w ill era se y our calc ulator memory .) To erase all memory and reset defaults If the calculator does not respond to the above resetting procedures, you might need to re start it by erasing all of memory. You will lose everything you have stored. All factory-default settings are restored. 1. Pr ess and h old the k e y , the firs t menu k ey , and the last menu ke y simultaneously . 2 . R eleas e all k e y s in the re ver se or der . Note: T o cancel this pr ocess, r elease only the top-r ow k e ys , then pr ess the thir d menu k ey . views T he possible contexts for an aplet: Plot, Plot Setup, Numeric, Numeric Setup, Symbolic, Symbolic Setup, Sketch, Note, and special views like split screens. Refe renc eInf o.fm Pa ge 3 Fri day, Dec embe r 16 , 20 05 1 0:00 AM
R-4 If the calculator does not turn on If the HP 39gs does not turn on follow the steps below until the calculator turns on. You may find that the calculator turns on before you have completed the procedure. If the calculator still does not turn on, please contact Customer Support for further information. 1. Pr ess and hold the ke y for 10 seconds. 2 . Pr ess and hold the k e y and the thir d menu k ey simultaneou sl y . R elease the thir d menu k ey , then r elease t he ke y . 3 . Pr ess and h old the k ey , the first men u k e y , an d the si xth menu k ey simultaneo usly . Rele ase the si xth menu k ey , then r elease the fir st men u k e y , and then r elease t he ke y . 4. L ocate the small hole in the bac k of the calc ulator . Insert the end of a straightened metal paper clip into the hole as f ar as it w ill go . Hold it there f or 1 second , then r emov e it . Pre ss the k ey . 5 . Remo ve the batter ie s (see âBatter ies â on page R - 4) , pr ess and hold the ke y f or 10 seconds, and then put the bat ter ies back in. Pr ess the k e y . Operating details Operating temperature: 0 ° to 45 ° C (32 ° to 113 ° F). Storage temperature: â20 ° to 65 ° C (â 4 ° to 149 ° F). Operating and storage humidity: 90% relative humidity at 40 ° C (104 °F) maximum. Avoid getting the calculator wet. Battery operates at 6.0V dc, 80mA maximum. Batteries The calculator uses 4 AAA(LR03) batteries as main power and a CR2032 li thium battery for memory ba ckup. Before using the calculator , please install the batteries according to the following procedure. Refe renc eInf o.fm Pa ge 4 Fri day, Dec embe r 16 , 20 05 1 0:00 AM
R-5 To install the main batteries a. Slide up the battery compartment cove r as illustrated. b. Insert 4 new AAA (LR03) batteries into the main compartment. Make sure each battery is inserted in the indicated direction. To install the backup battery a. Press down the holder. Push the plate to the shown direction and lift it. b. Insert a new CR2032 lithium battery. Make sure its positive ( ) side is facing up. c. Replace the plate and push it to the origin al place. After installing the batteries, press to turn the power on. Warning: It is recommended that you replace this battery every 5 years. When the low battery ico n is disp layed, you need to replace the batte ries as soon as possible. However, avoid removing th e backup battery and ma in batteries at the same time to avoid data lost. Refe renc eInf o.fm Pa ge 5 Fri day, Dec embe r 16 , 20 05 1 0:00 AM
R-6 Variables Home variables The home variables are: Categor y Available name Complex Z1... Z9, Z0 Graphic G1 ... G9, G0 Library Function Parametric Polar Sequence Solve Statistics User-named List L1 ... L9 , L0 Matrix M1 ... M9 , M0 Modes Ans Date HAngle HDigits HFormat Ierr Time Notepad User-named Program Editline User-named Real A...Z, θ HP 3 9gs Engl ish. book Pa ge 6 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
R-7 Function aplet variables The function aplet variables a re: Category Av ailable name Plot Axes Connect Coord FastRes Grid Indep InvCross Labels Recenter Simult Tracing Xcross Ycross Xtick Ytick Xmin Xmax Ymin Ymax Xzoom Yxoom Plot-FCN Area Extremum Isect Root Slope Symbolic Angle F1 F2 F3 F4 F5 F6 F7 F8 F9 F0 Nume ric Digits Format NumCol NumFont NumIndep NumRow NumStart NumStep NumType NumZoom Note N oteText Sketc h Page PageNum HP 3 9gs Engl ish. book Pa ge 7 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
R-8 Parametric aplet variables The parametric aplet variables are: Categor y Available name Plot Axes Connect Coord Grid Indep InvCross Labels Recenter Simult Tmin Tmax Tracing Tstep Xcross Ycross Xtick Ytick Xmin Xmax Ymin Ymax Xzoom Yzoom Symbolic Angle X1 Y1 X2 Y2 X3 Y3 X4 Y4 X5 Y5 X6 Y6 X7 Y7 X8 Y8 X9 Y9 X0 Y0 Numeric Digits Format NumCol NumFont NumIndep NumRow NumStart NumStep NumType NumZoom Note NoteText Sketch Page PageNum HP 3 9gs Engl ish. book Pa ge 8 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
R-9 Polar aplet variables The polar aplet variables are: Category Av ailable names Plot Axes Connect Coord Grid Indep InvCross Labels Recenter Simult Umin Umax θ step Tracing Xcross Ycross Xtick Ytick Xmin Xmax Ymin Ymax Xzoom Yxoom Symbolic Angle R1 R2 R3 R4 R5 R6 R7 R8 R9 R0 Nume ric Digits Format NumCol NumFont NumIndep NumRow NumStart NumStep NumType NumZoom Note N oteText Sketc h Page PageNum HP 3 9gs Engl ish. book Pa ge 9 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
R-10 Sequence aplet variables The sequence aplet variables are: Categor y Available name Plot Axes Coord Grid Indep InvCross Labels Nmin Nmax Recenter SeqPlot Simult Tracing Xcross Ycross Xtick Ytick Xmin Xmax Ymin Ymax Xzoom Yzoom Symbolic Angle U1 U2 U3 U4 U5 U6 U7 U8 U9 U0 Numeric Digits Format NumCol NumFont NumIndep NumRow NumStart NumStep NumType NumZoom Note NoteText Sketch Page PageNum HP 3 9gs Engl ish. book Pa ge 10 We dnes day, Dec embe r 7, 2005 11 : 24 PM
R-11 Solve aplet variables The solve aplet variables are: Category Av ailable name Plot Axes Connect Coord FastRes Grid Indep InvCross Labels Recenter Tracing Xcross Ycross Xtick Ytick Xmin Xmax Ymin Ymax Xzoom Yxoom Symbolic Angle E1 E2 E3 E4 E5 E6 E7 E8 E9 E0 Nume ric Digits Format NumCol NumRow Note N oteText Sketc h Page PageNum HP 3 9gs Engl ish. book Pa ge 11 We dnes day, Dec embe r 7, 2005 11 : 24 PM
R-12 Statistics aplet variables The statistics aplet variables are: Categor y Available name Plot Axes Connect Coord Grid Hmin Hmax Hwidth Indep InvCross Labels Recenter S1mark S2mark S3mark S4mark S5mark StatPlot Tracing Xcross Ycross Xtick Ytick Xmin Xmax Ymin Ymax Xzoom Yxoom Symbolic Angle S1fit S2fit S3fit S4fit S5fit Numeric C0,...C9 Digits Format NumCol NumFont NumRow StatMode Stat-One Max Σ Mean Σ Median Min Σ N Σ Q1 Q3 PSDev SSDev PVar Σ SVar Σ Tot Σ Stat-Two Corr Cov Fit MeanX MeanY RelErr Σ X Σ X2 Σ XY Σ Y Σ Y2 Note NoteText Sketch Page PageNum HP 3 9gs Engl ish. book Pa ge 12 We dnes day, Dec embe r 7, 2005 11 : 24 PM
R-13 MATH menu categories Math functions The math functions are: Category Av ailable name Calculus TAYLOR Complex ARG CONJ IM RE Constant e i MAXREAL MINREAL Ï Hyper b. ACOSH ASINH ATANH COSH SINH TANH ALOG EXP EXPM1 LNP1 List CONCAT Î LIST MAKELIST Ï LIST POS REVERSE SIZE Σ LIST SORT Loop ITERATE RECURSE Σ â â« HP 3 9gs Engl ish. book Pa ge 13 We dnes day, Dec embe r 7, 2005 11 : 24 PM
R-14 Matrix COLNORM COND CROSS DET DOT EIGENVAL EIGENVV IDENMAT INVERSE LQ LSQ LU MAKEMAT QR RANK ROWNORM RREF SCHUR SIZE SPECNORM SPECRAD SVD SVL TRACE TRN Polynom. POLYCOEF POLYEVAL POLYFORM POLYROOT Prob. COMB ! PERM RANDOM UTPC UTPF UTPN UTPT Real CEILING DEG âRAD FLOOR FNROOT FRAC HMS â â HMS INT MANT MAX MIN MOD % %CHANGE %TOTAL RAD âDEG ROUND SIGN TRUNCATE XPON Stat-Two PREDX PREDY Symbolic = ISOLATE LINEAR? QUAD QUOTE | Category Av ailable name (Continued) HP 3 9gs Engl ish. book Pa ge 14 We dnes day, Dec embe r 7, 2005 11 : 24 PM
R-15 Program constants The program constants are: Tests < ⤠= = â > ⥠AND IFTE NOT OR XOR Trig ACOT ACSC ASEC COT CSC SEC Category Av ailabl e name (Continued) Category Av ailable name Angle Degrees Grads Radians Format Standard Fixed Sci Eng Fraction SeqPlot Cobweb Stairstep S1...5fit Linear LogFit ExpFit Power Trigonometric QuadFit Cubic Logist User Exponent StatMode Stat1Var Stat2Var StatPlot Hist BoxW HP 3 9gs Engl ish. book Pa ge 15 We dnes day, Dec embe r 7, 2005 11 : 24 PM
R-16 Physical Constants The physical constants are: Categor y Available Na me Chemist ⢠Avogadro (A vogadr o âs Number , NA) ⢠Boltz . (Boltmann, k) ⢠mol. vo... (molar v olume , Vm) ⢠univ gas (uni v ers al gas , R) ⢠std temp (standard temper ature , St d T ) ⢠std pres (standar d pr essur e, St d P ) Phyics ⢠StefBolt (S tef a n-Boltzmann, Ï ) â¢l ight s... (speed of ligh t , c) ⢠permitti (per mittiv it y , ε 0) ⢠permeab (permeab ilit y , μ 0) ⢠acce gr... (acceleration of gr av it y , g) ⢠gravita... (gr av itation , G) Quantum ⢠Plankâs (P lank âs constant , h) ⢠Diracâs (Dir acâs, hbar ) ⢠e charge (electr onic c har ge , q) ⢠e mass (electr on mass, me) ⢠q/me ra... (q/me r atio , qme) ⢠proton m (pr oton mass , mp) ⢠mp/me r... (mp/me r atio , mpme) ⢠fine str (f ine stru ctur e, α ) ⢠mag flux (magnetic f lu x , Ï ) ⢠Faraday (F arada y , F) ⢠Rydberg (Ry dberg , ) ⢠Bohr rad (Bohr r adius , a0) ⢠Bohr mag (Bohr magneton , μ B) ⢠nuc. mag (nuc lear magneton , μ N) ⢠photon... (photon w ave length, λ ) ⢠photon... (photon f r equenc y , f0) ⢠Compt w... (Compton w av elength, λ c) R â HP 3 9gs Engl ish. book Pa ge 16 We dnes day, Dec embe r 7, 2005 11 : 24 PM
R-17 Program commands The program commands are: Category Command Aplet CHECK SELECT SETVIEWS UNCHECK Branch IF THEN ELSE END CASE IFERR RUN STOP Drawing ARC BOX ERASE FREEZE LINE PIXOFF PIXON TLINE Graphic DISPLAY â â DISPLAY â GROB GROBNOT GROBOR GROBXOR MAKEGROB PLOT â â PLOT REPLACE SUB ZEROGROB Loop FOR = TO STEP END DO UNTIL END WHILE REPEAT END BREAK Matrix ADDCOL ADDROW DELCOL DELROW EDITMAT RANDMAT REDIM REPLACE SCALE SCALEADD SUB SWAPCOL SWAPROW Print PRDISPLAY PRHISTORY PRVAR Prompt BEEP CHOOSE CLRVAR DISP DISPXY DISPTIME EDITMAT FREEZE GETKEY INPUT MSGBOX PROMPT WAIT Stat-One D O1VSTATS RANDSEED SETFREQ SETSAMPLE HP 3 9gs Engl ish. book Pa ge 17 We dnes day, Dec embe r 7, 2005 11 : 24 PM
R-18 Status messages Stat-Two DO2VSTATS SETDEPEND SETINDEP Category Command (Continued) Messag e M eaning Bad Argument Type Incorrect input for this operation. Bad Argument Value The value is out of range for this operation. Infinite Result Math exception, such as 1/0. Insufficient Memory You must recover some memory to continue operation. Delete one or more matrices, lists, notes, or programs (using catalogs), or custom (not built- in) aplets (using MEMORY ). Insufficient Statistics Data Not enough data points for the calculation. For two-variable statistics there must be two columns of data, and each column must have at least four numbers. Invalid Dimension Array argumen t had wrong dimensions. Invalid Statistics Data Need two columns with equal numbers of data values. HP 3 9gs Engl ish. book Pa ge 18 We dnes day, Dec embe r 7, 2005 11 : 24 PM
R-19 Invalid Syntax The function or command you entered does not include the proper arguments or order of arguments. The delimiters (parentheses, commas, periods, and semi-colons) must also be correct. Look up the function name in the index to find its proper syntax. Name Conflict The | (where) function attempted to assign a value to the variable of integration or summation index. No Eq uati ons Checked You must e nter and chec k an equation (Symbolic view) before evaluating this function. (OFF SCREEN) Function value, root, extremum, or intersection is not visible in the current screen. Receive Error Pro blem with data reception from another calculator. Re- send the data. Too Few Arguments The command requires more arguments than you supplied . Undefined Name The global variable named does not exist. Undefined Result The calculation has a mathematically undefined result (such as 0/0). Out of Memory You must recover a lot of memory to continue operation. Delete one or more matrices, lists, notes, or programs (using catalogs), or custom (not built- in) aplets (using MEMORY ). Message Meaning (Continued) HP 3 9gs Engl ish. book Pa ge 19 We dnes day, Dec embe r 7, 2005 11 : 24 PM
HP 3 9gs Engl ish. book Pa ge 20 We dnes day, Dec embe r 7, 2005 11 : 24 PM
W-1 L imited W arr anty HP 39gs Graphing Calculator; Warranty peri od: 12 months 1. HP war r ants to you , the end- us er cu stomer , t hat HP har dw are , acc es sor ies and su pplies w i ll be fr ee fr om def ects in mater ials and w ork manship after the date of pur chase , for the peri od spec if ied abo v e . If HP r ecei ves notice of such defects during t he war r ant y peri od, HP w ill, at its option , e ither re pair or re place pr oducts w hic h pr o v e to be defecti v e . R eplacement pr oducts ma y be either ne w or like -ne w . 2 . HP w arr ants to y ou that HP softwar e will no t fail to e x ecu te its pr ogramming ins truc tio ns after the date o f pur chase , for the per iod spec ifi ed abo v e , due to def ects in mater ial and w orkmanship w hen pr operl y installed and used . If HP recei ves noti ce of suc h def ects dur ing the w arr anty per iod , HP will r eplace softwar e media whic h does not ex ecute its pr ogr amming instruc tions due to suc h defe cts. 3 . HP does no t war r ant that the oper ation of HP pr oducts w ill be uninter rupted or er r or fr ee. If HP is unable , w ithi n a r easonable time , to r epair or r eplace an y produc t to a condition as w a r r anted, y ou will be entitled to a r ef und of the pur c hase pr ice upon pr om pt r etur n of the pr oduct w ith proo f of pur chas e . 4. HP pr oducts may con tain r emanuf a ctur ed par ts equi v alent to ne w in perfor mance or ma y hav e been sub jec t to inc iden tal us e . 5 . W arr ant y does not apply to def ects r esulting from (a) impr oper or inadequate maintenance or calibr ation, (b) soft w are , inter f acing , par ts or suppl ies not suppli ed by HP , (c) unauthori z ed modificati on or mi suse, ( d) op eratio n out sid e of t he pub lis he d en vir onmental spec ificati ons f or the pr oduct , or (e) impr oper site pr eparation o r maintenance . HP 3 9gs Engl ish. book Pa ge 1 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
W-2 6 . HP MAKE S NO O THER E XPRE S S W ARRANTY OR CONDI T ION WHET HER WRI TTEN OR OR AL . T O THE EXTENT ALL O WED B Y L OCAL LA W , ANY IMP LIED W ARRANTY OR CONDI TION OF MERCHANT ABILITY , S A T ISF A CT OR Y QU ALITY , OR FI TNE SS F OR A P AR TICUL AR P URP OSE I S LIMITED T O THE DUR A TION OF THE EXP RE S S W A RRANTY SET F OR TH ABO VE . Some countr ies , st ates or pr o v inces do not allo w limitations o n the dur ation o f an implied warr ant y , so th e abo v e limitation or e x clu sio n might n ot appl y to y ou . T his w ar r anty gi ve s y ou spec if ic legal r ights and y ou might also hav e other r igh ts that vary fr om country to country , st ate to state , or pro vince to pr ov ince . 7 . T O THE EXTENT ALL O WED B Y L OCAL L A W , THE REMEDIE S IN THIS W ARRANTY S T A TEMENT ARE Y OUR S OLE AND EX CL USIVE REMEDIE S. EX CEPT AS INDICA TED ABO VE , IN NO EVENT WILL HP OR I T S S UPP LI ER S BE LIABLE FOR L O S S OF DA T A OR F OR DIRE CT , SPE CIAL , INCIDENT AL, C ONSE QUENT IAL (INCL UDING L OS T PR OFIT OR D A T A) , OR O THER D AMA GE , WHETHER B ASED IN CONTRA CT , T OR T , OR O THERWI SE . Some countr ies , States or pro vinces do not allo w the ex clusi on or limitati on of inc idental or conseq uenti al damages, so the abo ve limit ation or e x clu sion ma y not appl y to y ou . 8. The onl y war r anties for HP pr oducts and serv ices ar e set forth in the e x pr ess w arr anty statements accompany ing such pr oducts and serv ices . HP shall not be lia ble for t echni cal or editor ial err ors or omissions contain ed herein . FOR CONSUMER TRANSACTIONS IN AUSTRALIA AND NEW ZEALAND: THE WARRANTY TERMS CONTAINED IN THIS STATEMENT, EXCEPT TO THE EXTENT LAWFULLY PERMITTED, DO NOT EXCLUDE, RESTRICT OR MODIFY AND ARE IN ADDI TION TO THE MANDATORY STATUTORY RIGHTS A PPLICABLE TO THE SALE OF THIS PRODUCT T O YOU. HP 3 9gs Engl ish. book Pa ge 2 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
W-3 Service Europe Countr y : T elephone numbers Au str ia 43-1-3 60 2 77120 3 Belgium 3 2 - 2 - 712 6 219 D e n m a r k 45 - 8 - 2 332 84 4 Ea s te r n Eu ro p e countr ies 4 20-5- 414 2 2 5 2 3 Fi n l a n d 35 - 896 40 0 09 F r ance 3 3-1- 4 99 39 006 German y 4 9-6 9-9 5 30 7103 Gr eece 4 20 -5-414 2 2 5 2 3 Holland 3 1- 2 -06 54 5 301 Italy 3 9-0 2 - 7 5419 7 8 2 No r wa y 4 7 - 63 84 9 309 P ortugal 3 51- 2 29 5 7 0 200 Spain 34 -915-64 20 9 5 S weden 4 6 -8519 9 206 5 Sw i t ze r l a n d 4 1 - 1 - 43953 58 (German) 41- 2 2 -8 2 7 8 7 80 (F renc h) 3 9-02 - 7 5419 7 8 2 (Italian) T ur ke y 4 20 -5-414 2 2 5 2 3 UK 44 - 20 7 - 4 5 80161 Cz ech R epubli c 4 20 -5- 414 2 2 5 2 3 South A fr ica 2 7 -11- 2 3 7 6 200 Lu xembour g 3 2 - 2 - 712 6 219 Other Eur opean countr ies 4 20-5- 414 2 2 5 2 3 Asia P ac ific Country : T elephone numbers A ust r alia 61-3-9 8 41-5 211 Singapor e 61-3-9 841-5 211 HP 3 9gs Engl ish. book Pa ge 3 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
W-4 P lease logon to http://www .hp.com f or t he lat est se r v ice and supp ort info rmati on .h L.Ame r ic a Country: Telephone numbers Ar gentina 0 - 810 -5 5 5-5 5 20 Bra zil Sao P aulo 3 7 4 7 - 7 7 9 9; RO T C 0 -800 -15 77 51 M e xi c o M x C i t y 5258 - 9 922; RO T C 01-800 - 4 7 2 -66 84 Ven e z u e l a 0 80 0 - 4 7 46 - 8368 Chi le 800 - 3 609 99 C o l u m b i a 9 - 8 0 0 - 1 1 4726 P eru 0 - 800 -10111 Central Ame rica & Caribb ean 1-800 - 71 1- 2 88 4 Guatemala 1-800 -99 9-51 0 5 Pu e r t o R i c o 1 - 877- 232- 0 5 89 Cos ta R ica 0 -800 -011 -0 5 2 4 N.Americ a Country : T elephon e numbers U . S. 1800-HP INVENT Ca n ad a (9 05) 20 6 - 4663 o r 800 - HP INVENT RO TC = Rest of th e co unt r y HP 3 9gs Engl ish. book Pa ge 4 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
W-5 Regulatory infor mation Federal Communications Commission Noti ce This equipment has been tested and found to comply with the limits for a Class B digital dev ice, pursuant to Part 15 of the FCC Rules. These limi ts are designed to provide reasonable protection agains t harmful interference in a residential installation. This equipment generates, uses, and can radiate ra dio frequency energy and, if not installed and used in accord ance with the instructions, may cause harmful interferenc e to radio communications. However, there is no guarante e that interference will not occur in a particula r installa tion. If this equipment does cause harmful interference to radio or television reception, which can be determined by turning the equipment off and on, the user is encouraged to try to correct the inter ference by one or more of the follo wing measures: ⢠Reorient or relocate the receiving antenna. ⢠Increase the separation be tween the equipment and the receiver. ⢠Connect the equipment into an outlet on a circuit different from that to which the receiver is connected. ⢠Consult the dealer or an exp erienced radio or television technician for help. Modifications The FCC requires the user to be notified that any changes or modifications made to this device that are not expressly approved by Hewlett-Packard Company may void the user's authority to operate the equipment. Cables Connecti ons to this device mu st be made with shielded cables with metallic RFI/EMI connector hoods to maintain compliance with FCC rules and regulations. Declaration of Conformity for Products Marked with FCC Logo, United States Only This device complies with Pa rt 15 of the FCC Rules. Operation is subject to the following two condi tions: (1) this device may not cause harmful interference, and (2) this device must accept any interference received, including interference that may cause undesired operation. For questions regarding your product, contact: Hewlett-Packard Company P. O. Box 692000, Mail Stop 530113 HP 3 9gs Engl ish. book Pa ge 5 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
W-6 Houston, Texas 77269-2000 Or, call 1-800-474-6836 For questions regarding this FCC declarati on, contact: Hewlett-Packard Company P. O. Box 692000, Mai l Stop 510101 Houston, Texas 77269-2000 Or, call 1-281-514-3333 To identify this produc t, refer to the part, series, or model number found on the product. Canadian Notice This Class B digital apparatus meets all requ irements of the Canadian Interference-Causing Equipment Regulations. Avis Canadien Cet ap pareil numé ri que de la classe B r especte toutes l es e x igences du Règlement sur le matériel br ouil leur du Can ad a . European Union Regulatory Notice This product complies with the following EU Directives: ⢠Low Voltage Directive 73/23/EEC ⢠EMC Directive 89/336/EEC Compliance with these direct ives implies conformity to applicable h armonized European standa rds (European Norms) which are listed on the EU Declaration of Conformity issued by Hewlett- Packard for this product or product family. This compliance is indicated by the following conformity marking placed on the product: Japanese Notice ã ã®è£ ç½®ã¯ã æ å ±å¦çè£ ç½®çé»æ³¢é害èªä¸»è¦å¶å è°ä¼ ï¼VCCIï¼ ã®åº æºã« åº ã¥ ã 㯠㩠㹠B æ å ±æè¡è£ ç½® 㧠ã ã ã ã®è£ ç½®ã¯ã 家åºç°å¢ 㧠使ç¨ã ã ã 㨠ã ç®ç 㨠ã 㦠ã ã¾ ã ãã ã ã® è£ ç½®ã 㩠㸠㪠ã ã 㬠ã 㸠㧠㳠å ä¿¡æ© ã« è¿æ¥ ã ã¦ ä½¿ç¨ ã ã ã 㨠ã å ä¿¡ é 害ãå¼ãèµ· ã ã ã 㨠ã ã ã ã¾ã ã å ã æ± ã 説ææ¸ ã« å¾ ã£ ã¦ æ£ ã ã å ã æ± ã ã ã 㦠ã ã ã ãã Th is markin g is v alid f or non- T ele- com prodcts and E U harmoniz ed T elecom product s (e.g . Bluetooth). xxxx* Th is mark ing is v alid f or E U non- harmoni zed T elecom pr oducts. *Notified body number (used only if applicable - r efer to the product label) HP 3 9gs Engl ish. book Pa ge 6 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
W-7 Korean Notice Disposal of Waste Equipment by Users in Private Household in the European Union This symbol on the product or on its packaging indicates that this product must not be disposed of with your other household waste. Instead, it is your responsibility to dispose of your waste equipment by handing it over to a designated collection point for the recycling of waste electrical and electronic equipment. The separate collection and recycling of your waste equipment at the time of disposal will help to conserve natural resources and ensure that it is recycled in a manner that protects human health and the environment. For more information about where you can drop off your waste equi pment for recycling, please contact your local city office, yo ur household waste disposal service or the sh op where you purchased the product. HP 3 9gs Engl ish. book Pa ge 7 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
HP 3 9gs Engl ish. book Pa ge 8 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
I-1 Index A absolute value 13-5 add 13-3 algebraic entry 1-19 alpha characters typing 1-6 alphabetical so rting 19-6 angle measure 1-10 in statistics 10-12 setting 1-11 animation 17-5 creating 17 -5 annunciators 1-3 Ans (last answer) 1-24 antilogarithm 13-4, 13-9 aplet attaching notes 19-4 clearing 19-3 copying 19-4 definition of R-1 deleting 19-6 Function 13-21 Inference 11-1 key 1-4 library 19-6 Linear Solver 8-1 opening 1-16 Parametric 4-1 Polar 5-1 receiving 19-5 resetting 19-3 sending 19-4 , 19-5 Sketch view 17-1 Solve 7-1 sorting 19-6 statistics 10-1 transmitting 19-5 Triangle Solver 9-1 aplet commands CHECK 18-14 SELECT 18-14 SETVIEWS 18-17 UNCHECK 18-17 aplet variables definition 14 -1 , 14-8 in Plot view 18-32 new 14-1 aplet views canceling operations in 1-1 changing 1-19 note 1-18 Numeric view 1-17 Plot view 1-16 sketch 1-18 split-screen 1-17 Symbolic view 1-16 arc cosecant 13-20 arc cosine 13-4 arc cotangent 13-19 arc secant 13-20 arc sine 13-4 arc tangent 13-5 area graphical 3-10 interactive 3-10 variable 18-32 arguments with matrices 15-10 attaching a note to an aplet 17-1 a sketch to an aplet 17-3 auto scale 2-14 axes plotting 2-7 variable 18-32 B bad argument R-18 bad guesses error message 7-7 batteries R-4 box-and-whisker plot 10-16 branch commands CASE...END 18-18 IF...THEN...ELSE...END 18-18 IFERR...THEN...ELSE 18-18 branch structures 18-1 7 build your own table 2-19 HP 3 9gs Engl ish. book Pa ge 1 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
I-2 C calculus operat ions 13-7 catalogs 1-30 chronological sorting 19-6 circle dra wing 17-4 clearing aplet 19-3 character s 1-22 display 1-22 display history 1-25 edit line 1-22 lists 16-6 plot 2-7 cobweb graph 6-1 coeffi cients polynomial 13-11 columns changing position 18-25 combinations 13-12 commands aplet 18-14 branch 18-17 definition of R-1 drawing 18-19 graphic 18-21 loop 18-23 print 18-26 program 18-4, R-17 stat-one 18-30 stat-two 18-30 with matrices 15-1 0 complex number functions 13-5, 13-16 conjugate 13-7 imaginary pa rt 13-7 real p art 13-7 complex numbers 1-29 entering 1-29 math functions 13-7 storing 1-29 confide nce in tervals 11-15 conjugate 13-7 connecting data points 10-1 9 variable 18-32 via infrar ed 19-5 via serial cable 19-5 via USB cable 19-5 connectivity kit 19-4 constant? error message 7-7 constants e 13-8 i 13-8 maximum real number 13-8 minimum real number 13-8 physical 1-8, 13-25, R-16 program R-15, R-16 contrast decreasing disp lay 1-2 increasing display 1-2 conversi ons 13-8 coordinate display 2-9 copying display 1-22 graphics 17-6 notes 17-8 programs 18-8 correlation coefficient 10-17 CORR 10-17 statistical 10-15 cosecant 13-20 cosine 13-4 inverse hyperbolic 13-9 cotangent 13-2 0 covariance statistical 10-15 creating aplet 19-1 lists 16-1 matrices 15-3 notes in Notepad 17-6 programs 18-4 sketches 17-3 critical value(s) displayed 11-4 cross product vector 15-11 curve fitting 10-12, 10-17 D data set definition 10-8 date, setting 18-28 debugging programs 18-7 decimal changing format 1-10 scaling 2-14, 2-15 decreasing display contrast 1-2 HP 3 9gs Engl ish. book Pa ge 2 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
I-3 definite integral 13-6 deleting aplet 19-6 lists 16-6 matrices 15-5 programs 18-9 statistical data 10-11 delimiters, programming 18-1 derivatives definition of 13-6 in Function aplet 13-22 in Home 13-21 determinant square matrix 15-11 differentiation 13-6 display 18-21 adjusting contrast 1-2 annunciator line 1-2 capture 18-21 clearing 1-2 date and time 18-28 element 15-5 elements 16-4 engineering 1-10 fixed 1-10 fraction 1-10 history 1-22 line 1-23 matrices 15-5 parts of 1-2 printing contents 18-26 rescaling 2-13 scientific 1-10 scrolling through history 1-25 soft key labels 1-2 standard 1-10 divide 13-3 drawing circles 17-4 keys 17-4 lines and boxes 17-3 drawing commands ARC 18-19 BOX 18-20 ERASE 18-20 FREEZE 18-20 LINE 18-20 PIXOFF 18-20 PIXON 18-20 TLINE 18-20 E e 13-8 edit line 1-2 editing matrices 15-4 notes 17-2 programs 18-5 Editline Program catalog 18-2 editors 1-30 eigenvalues 15-11 eigenvectors 15-11 element storing 15-6 E-lessons 1-12 engineering number format 1-11 equals for equations 13-17 logical test 13-19 equations solving 7- 1 erasing a line in Sketch view 18-20 error messages bad guesses 7-7 constant? 7-7 exclusive OR 13-1 9 exiting views 1-19 exponent fit 10-13 minus 1 13-10 of value 13-17 raisin g to 13-5 expression defining 2-1, R-1 entering in HOME 1-19 evaluating in aplets 2-3 literal 13-18 plot 3-3 extremum 3-10 F factorial 13-12 FastRes variable 18-32 fit a curve to 2VAR da ta 10-17 choosing 10-12 defining your own 10-13 fixed number format 1-10 HP 3 9gs Engl ish. book Pa ge 3 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
I-4 font size change 3-8, 17-5 forecasting 10-20 fraction number format 1-11 full-precision display 1-10 function analyze graph with FCN tools 3-4 definition 2-2, R-1 entering 1-19 gamma 13-12 intersection point 3-5 math menu R-13 slope 3-5 syntax 13-2 tracing 2-8 Function aplet 2-20, 3-1 function variables area 18-32 axes 18-32 connect 18-32 fastres 18-32 grid 18-33 in menu map R-7 indep 18-3 3 isect 18-34 labels 18-34 Recent er 18-3 4 root 18-34 ycross 18-37 G glossary R-1 graph analyzing statistical data in 10 -19 auto scale 2-14 box-and-whisker 10-16 capture cu rrent display 18-21 cobweb 6-1 compar ing 2-5 connected points 10-17 defining the independent variable 18-36 drawing axes 2-7 expressions 3-3 grid points 2-7 histogr am 10-15 in Solve aplet 7-7 one-var iable stat istics 10-18 overlayin g 2-15 scatter 10-15, 10-17 split-sc reen view 2-14 splitting into plot and close-up 2-13 splitting into plot and table 2-13 stairsteps 6-1 statistical data 10-15 t values 2-6 tickmarks 2-6 tracing 2-8 two-variable statistics 10-18 Graphic commands â GROB 18-21 DISPLAY â 18-21 GROBNOT 18-21 GROBOR 18-21 GROBXOR 18-22 MAKEGROB 18-22 PLOT â 18-22 REPLACE 18-22 SUB 18-22 ZEROGROB 18-23 graphics copying 17-6 copying into Sketch view 17-6 storing and recalling 17-6 , 18-21 H histogram 10-15 adjusting 10-16 range 10-18 setting min/max values for bars 18-33 width 10-18 history 1-2, 18-26 Home 1-1 calculating in 1-19 display 1-2 evaluating expressions 2-4 reusing lines 1-23 variables 14-1, 14-7, R-6 horizontal zoom 18-38 hyperbolic maths functions 13-10 hyperbolic trigonometry ACOSH 13-9 ALOG 13-9 ASINH 13-9 ATANH 13-9 COSH 13-9 EXP 13-10 HP 3 9gs Engl ish. book Pa ge 4 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
I-5 EXPM1 13-10 LNP1 13-10 SINH 13-9 TANH 13-9 hypothesis alternative 11-2 inference tests 11-8 null 11-2 tests 11-2 I i 13-8 implied multiplication 1-20 importing graphics 17-6 notes 17-8 increasing display contrast 1-2 indefinite integral using symbolic variables 13-23 independent values adding to table 2-18 independent variable defined for Tracing mode 18-33 inference confidence intervals 11-15 hypothesis tests 11-8 One-Proportion Z-Interval 11-17 One-Sample Z-Interval 11-15 One-Sample Z-Test 11-8 Two-Proportion Z-Interval 11-1 7 Two-Proportion Z-Test 11-11 Two-Sample T-Inte rval 11-19 Two-Sample Z-Interval 11-16 infinite result R-18 infrared transmission of aplets 19-5 initia l guess 7-5 input forms resetting default values 1-9 setting Modes 1-11 insufficient memory R-18 insufficient statistics data R-18 integer rank matrix 15-12 integer scaling 2-14, 2-15 integral definite 13-6 indefinite 13-23 integration 13-6 interpreting intermediate guesses 7-7 intersect ion 3-11 invalid dimension R-18 statistics data R-18 syntax R-19 inverse hyperbolic cosi ne 13-9 inverse hy perbolic functions 13-1 0 inverse hyperbolic sine 13-9 inverse hyperbolic tangent 13-9 inverting matrices 15-8 isect v ariable 18-34 K keyboard editing keys 1-5 entry k eys 1-5 inactive keys 1-8 list keys 16-2 math functions 1-7 menu keys 1-4 Notepad keys 17-8 shifted keystrokes 1-6 L labeling axes 2-7 parts of a sketc h 17-5 letters, typing 1-6 library, managing aplets in 19-6 linear fit 10-13 Linear Solver aplet 8-1 list arithmetic with 16-7 calculate sequence of e lements 16-8 calculating product of 16-8 composed from differences 16-7 concatenating 16-7 counting elements in 16-9 creating 16-1, 16-3, 16 -4 , 16- 5 deleting 16-6 deleting list items 16-3 displaying 16-4 displaying list elements 16-4 editing 16-3 finding statistical values in list ele- ments 16-9 HP 3 9gs Engl ish. book Pa ge 5 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
I-6 generate a series 16-8 list function syntax 16-6 list variables 16-1 returning position of element in 16-8 revers ing orde r in 16-9 sending and receiving 16-6 sorting elements 16-9 storing elements 16- 1 , 16-4 , 16-5 storing one element 16-6 logarithm 13-4 logarithmic fit 10-13 functions 13-3 logical operators AND 13-19 equals (logical test) 13-19 greater than 13-19 greater than or equal to 13-19 IFTE 13-19 less than 13-18 less than or equal to 13-18 NOT 13-19 not equal to 13-1 9 OR 13-19 XOR 13-19 logistic fit 10-13 loop commands BREA K 18-24 DO...UNTIL...END 18-23 FOR I= 18-24 WHILE...REPEAT...END 18-23 loop func tions ITERATE 13-10 RECUR SE 13-10 summation 13-11 low battery 1-1 lowercase letters 1-6 M mantissa 13-15 math functions complex number 13-7 hyperbolic 13-10 in menu map R-13 keyboard 13-3 logical operators 13-18 menu 1-7 polynomial 13-11 probability 13-12 real-number 13-13 symbolic 13-17 trigonometry 13-19 MATH menu 13-1 math operations 1-19 enclosing arguments 1-21 in scientific notation 1-20 negative numbers in 1-20 matrices adding rows 18-24 addition a nd subtraction 15-6 arguments 15-10 arithmetic operations in 15-6 assembly from vectors 15-1 changing row position 18-25 column norm 15-10 comma 16-7 commands 15-10 condition number 15-11 create identity 15-13 creating 15-3 creating in Home 15-5 deleting 15-5 deleting columns 18-24 deleting rows 18-24 determinant 15-11 display eigenvalues 15-11 displaying 15-5 displaying matrix elements 15-5 dividing by a square matrix 15-8 dot product 15-11 editing 15-4 extracting a portion 18-25 finding the trace of a square ma- trix 15-13 inverting 15-8 matrix calculations 15-1 multiplying and dividing by scalar 15-7 multiplying by vector 15-7 multiplying row by value and add- ing result to second row 18-25 multiplying row number by value 18-25 negating elements 15-8 opening Matrix Editor 18-28 raised to a power 15-7 redimension 18-25 replacing portion of matrix or vec- tor 18-25 sending or receiving 15-4 HP 3 9gs Engl ish. book Pa ge 6 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
I-7 singular value decomposition 15-13 singular values 15-13 size 15-12 spectral norm 15-13 spectral radius 15-13 start Matrix Editor 18-24 storing elements 15-3, 15-5 storing matrix elements 15-6 swap column 18-25 swap row 18-25 transposing 15-13, 15-14 variables 15-1 matrix functions 15-10 COLNORM 15-10 COND 15-11 CROSS 15-11 DET 15-11 DOT 15-11 EIGENVAL 15-11 EIGENVV 15-11 IDENMAT 15-11 INVERSE 15-11 LQ 15-11 LSQ 15-11 LU 15-12 MAKEMAT 15-12 QR 15-12 RANK 15-12 ROWNORM 15-12 RREF 15-12 SCHUR 15-12 SIZE 15-12 SPECNORM 15-13 SPECRAD 15-13 SVD 15-13 SVL 15-13 TRACE 15-13 TRN 15-13 maximum real number 1-22, 13-8 memory R-18 clearing all R-3 organizing 14-9 out of R-19 saving 1-25, 19-1 viewing 14-1 menu lists searching 1-8 minimum real number 13-8 mixed fraction format 1-11 modes angle measure 1-10 decimal mark 1-11 number format 1-10 multiple solutions plotting to find 7-7 multiplication 13-3 implied 1-20 N name c onfli ct R-19 naming programs 18-4 natural exponential 13-3, 13-10 natural log plus 1 13-10 natural logarithm 13-3 negation 13-5 negative numbers 1-20 no equations checked R-19 Normal Z-distribution, confidence i n- tervals 11-15 note copying 17-8 editing 17-2 importing 17-8 printing 18-26 viewing 17-1 writing 17-1 Notepad 17-1 catalog keys 17-7 creating notes 17-6 writing in 17-6 nrng 2-6 n th root 13-6 null hypothesis 11-2 number format engine ering 1-11 fixed 1-10 fraction 1-11 in Solve aplet 7-5 mixed fraction 1-11 scientific 1-10 Standard 1-10 numeric prec ision 14-9 Numeric view adding values 2-18 automatic 2-16 build your ow n table 2-19 display defining function for col- umn 2-17 HP 3 9gs Engl ish. book Pa ge 7 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
I-8 recalc ulating 2-18 setup 2-16, 2-19 O off automatic 1-1 power 1-1 on/cancel 1-1 One-Proportion Z-Interval 11- 17 One-Sample T-Interval 11-18 One-Sample T-Test 11-12 One-Sample Z-Interval 11-15 One-Sample Z-Test 11-8 order of precedence 1-21 overlaying plots 2-15 , 4-3 P Ï 13-8 paired columns 10-11 parametric variables axes 18-32 connect 18-32 grid 18-33 in menu map R-8 indep 18-3 3 labels 18-34 recent er 18-3 4 ycross 18-37 parentheses to close arguments 1-21 to specify order of operation 1-21 pause 18-30 permutations 13-12 pictures attaching in Sketch view 17-3 plot analyzing statistical data in 10 -19 auto scale 2-14 box-and-whisker 10-16 cobweb 6-1 compar ing 2-5 connected points 10-17, 10-19 decimal scaling 2-14 defining the independent variable 18-36 drawing axes 2-7 expressions 3-3 grid points 2-7 histogr am 10-15 in Solve aplet 7-7 integer scaling 2-14 one-variable statistics 10-18 overlay plot 2-13 overlaying 2-15, 4-3 scaling 2-13 scatter 10-15, 10 -17 sequence 2-6 setting up 2-5, 3-2 split-sc reen view 2-14 splitting 2-14 splitting into plot and close-up 2-13 splitting into plot and table 2-13 stairsteps 6-1 statistical data 10-15 statistics parameters 10-18 t values 2-6 tickmarks 2-6 to capture current display 18-21 tracing 2-8 trigonometric scaling 2-14 two-variable statistics 10-18 plotting resolution and tracing 2-8 plot-view variables area 18-32 connect 18-32 fastres 18-32 function 18-32 grid 18-33 hmin/hmax 18-33 hwidth 18-33 isect 18-34 labels 18-34 recenter 18-34 root 18-34 s1mark-s5mark 18-35 statplot 18-35 tracing 18-33 umin/umax 18-36 ustep 18-36 polar variables axes 18-32 connect 18-32 grid 18-33 in menu map R-9 indep 18-33 labels 18-34 recenter 18-34 ycross 18-37 HP 3 9gs Engl ish. book Pa ge 8 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
I-9 polynomial coefficients 13-11 evaluation 13-11 form 13-11 roots 13-12 Taylor 13-7 polynomial functions POLYCOEF 13-11 POLYEVAL 13-11 POLYF ORM 13-11 POLYROOT 13-12 ports 19-5 position argument 18 -21 power (x raised to y) 13-5 preced ence 1-22 predicted values statistical 10-20 print contents of display 18-26 name and contents of variable 18-26 object in history 18-26 variables 18-26 probability functions ! 13-12 COMB 13-12 RANDOM 13-13 UTPC 13-13 UTPF 13-13 UTPN 13-13 UTPT 13-13 program commands 18-4 copying 18-8 creating 18-4 debugging 18-7 deleting 18-9 delimiters 18-1 editing 18-5 naming 18-4 pausing 18-30 printing 18-26 sending and receiving 18-8 structured 18-1 prompt commands beep 18-26 create choose box 18-26 create input form 18-29 display item 18-27 display message box 18-29 halt program execution 18-30 insert line breaks 18-29 prevent screen display being up- dated 18-28 set date and time 18-28 store ke ycode 18-29 Q quadratic extre mum 3-6 fit 10-13 function 3-4 quotes in program names 18-4 R random numbers 13-13 real number maximum 13-8 minimum 13-8 real p art 13-7 real-number functions 13-13 % 13-15 %CHANGE 13-15 %TOTAL 13-16 CEILING 13-13 DEGtoRAD 13-14 FNROOT 13-14 HMSto 13-14 INT 13-15 MANT 13-15 MAX 13-15 MIN 13-15 MOD 13-15 RADtoDEG 13-16 ROUND 13-16 SIGN 13-16 TRUNCATE 13-16 XPON 13-17 recalc ulation fo r table 2-18 receive error R-19 receiv ing aplet 19-5 lists 16-6 matrices 15-4 programs 18-8 redra wing table of numbers 2-17 reduced row eche lon 15-12 HP 3 9gs Engl ish. book Pa ge 9 Wed nesd ay, Dece mber 7, 2 005 11: 2 4 P M
I-10 regression analysis 10-17 fit models 10-13 formula 10-12 user-defined fit 10-13 relative error statistical 10-18 resetting aplet 19-3 calculator R-3 memory R-3 result copying to edit line 1-22 reusing 1-22 root interac tive 3-10 n th 13-6 variable 18-34 root-finding displaying 7-7 interac tive 3-9 operat ions 3-10 variables 3-10 S S1mark-S5mark variables 18-35 scaling automatic 2-14 decimal 2-10, 2-14 integer 2-10, 2-14, 2-15 options 2-13 resetting 2-13 trigonometric 2-14 scatter plot 10-15, 10 -17 connected 10-17 , 10-1 9 SCHUR decomposition 15-12 scientific number format 1-10, 1-20 scrolling in Trace mode 2-8 searching menu lists 1-8 speed searches 1-8 secant 13-20 sending aplets 19-4 lists 16-6 programs 18-8 sequence definition 2-2 sequence variables Axes 18-32 Grid 18-33 in menu map R-10 Indep 18-33 Labels 18-34 Recenter 18-34 Ycross 18-37 serial port connectivity 19-5 setting date 18-28 time 18-28 sign reversal 7-6 sine 13-4 inverse hyperbolic 13-9 singular value decomposition matrix 15-13 singular values matrix 15-13 sketches creating 17-5 creating a blank graphic 18-23 creating a set of 17-5 erasing a line 18-20 labeling 17-5 opening view 17-3 sets 17-5 storing in graphics variable 17-5 slope 3-10 soft key labels 1-2 solve error messages 7-7 initial guesses 7-5 interpreting intermediate guesses 7-7 interpreting results 7-6 plotting to find guesses 7-7 setting number format 7-5 solve variables axes 18-32 connect 18-32 fastres 18-32 grid 18-33 in menu map R-11 indep 18-33 labels 18-34 recenter 18-34 ycross 18-37 sorting 19-6 aplets in alphab etic order 19-6 HP 3 9gs Engl ish. book Pa ge 10 We dnes day, Dec embe r 7, 2005 11 : 24 PM
I-11 aplets in chronological order 19-6 elements in a list 16-9 spectral norm 15-1 3 spectral radius 15-13 square root 13-5 stack history printing 18-26 stairsteps graph 6-1 standard number format 1-10 statistics analysis 10-1 analyzing plots 10-19 angle mode 10-12 calculate one-variable 18-30 calculate two-variable 18-30 data set variables 18-41 data structure 18-41 define one-variable sample 18-30 define two-va riable data setâs de- pendent column 18-31 define two-variable data setâs in- dependent column 18 -31 defining a fit 10-12 defining a regression model 10-12 deleting data 10-11 editing data 10-10 frequency 18-30 inserting data 10-11 plot type 10-18 plotting data 10-15 predicted values 10-20 regression curve (fit) models 10-12 saving data 10-10 sorting data 10-11 specifying angle setting 10-12 toggling between one-variable and two-variable 10-12 tracing plots 10-19 troubleshooting with plots 10-19 zooming in plots 10-19 statistics variables Axes 18-32 Connect 18-32 Grid 18-33 Hmin/Hmax 18-33 Hwidth 18-33 in menu map R-12 Indep 18-33 Labels 18-34 Recenter 18-34 S1mark-S5mark 18-35 Ycross 18-37 step size of independent variabl e 18-37 storing list elements 16-1, 16-4, 16-5 , 16-6 matrix elements 15-3 , 15-5, 15-6 results of calculation 14-2 value 14-2 strings literal in symbolic operations 13-18 subtract 13-3 summation function 13-11 symbolic calculations in Function aplet 13-21 defining expressions 2-1 differentiation 13-21 displaying definitions 3-8 evaluating variab les in view 2-3 setup view for statistics 10-12 symbolic functions | (where) 13-18 equal s 13-17 ISOLATE 13-17 LINEAR? 13-17 QUAD 13-18 QUOTE 13-18 Symbolic view defining expressions 3-2 syntax 13-2 syntax errors 18-7 T table navigate around 3-8 numeric values 3-7 numeric view setup 2-16 tangent 13-4 inverse hyperbolic 13-9 Taylor polynomial 13-7 θ rng 2-6 θ step 2-6 tickmarks for plotting 2-6 time 13-1 4 HP 3 9gs Engl ish. book Pa ge 11 We dnes day, Dec embe r 7, 2005 11 : 24 PM
I-12 setting 18-28 time, converting 13-14 times sign 1-20 tmax 18-36 tmin 18-36 too few arguments R-19 tracing functions 2-8 more than one curve 2-8 not matching plot 2-8 plots 2-8 transmitting lists 16-6 matrices 15-4 programs 18-8 transposing a matrix 15-13 Triangle Solver aplet 9-1 trigono metric fit 10-13 functions 13-19 scaling 2-10, 2-14, 2-1 5 trigonometry functions ACOT 13-19 ACSC 13-20 ASEC 13-20 COT 13-20 CSC 13-20 SEC 13-20 trng 2-6 truncating values to decimal places 13-16 tstep 2-6, 18-37 Two-Pr oportion Z- Interval 11 -17 Two-Pr oportion Z- Test 11-11 Two-Sample T-Inte rval 11-19 Two-Sample T-tes t 11-14 Two-Sample Z-Interval 11-16 typing letters 1-6 U undefined name R-19 result R-19 un-zoom 2-11 upper-tail chi-squared probability 13-13 upper-tail normal probability 13-13 upper-tail Snedecorâs F 13-1 3 upper-tail studentâs t-probability 13-13 USB connectivity 19-5 user defined regression fit 10-13 V value recall 14-3 storing 14-2 variables aplet 14-1 categories 14-7 clearing 14-3 definition 14-1, 14-7, R-2 in equations 7-10 in Symbolic view 2-3 independent 18-36 local 14-1 previous result (Ans) 1-23 printing 18-26 root 18-34 root-finding 3-10 step size of independent 18-37 types 14-1, 14-7 use in calculations 14-3 VARS menu 14-4 , 14-5 vectors column 15-1 cross product 15-11 definition of R-2 views 1-18 configuration 1-18 definition of R-3 W warning symbol 1-8 where command ( | ) 13-18 X Xcross variab le 18-3 7 xrng 2-6 Y Ycross variable 18-37 yrng 2-6 HP 3 9gs Engl ish. book Pa ge 12 We dnes day, Dec embe r 7, 2005 11 : 24 PM
I-13 Z Z-Interval 11-15 zoom 2-17 axes 2-12 box 2-9 center 2-9 examples of 2-11 factors 2-13 in 2-9 options 2-9, 3-8 options within a table 2-17 out 2-9 redrawing table of numbers op- tions 2-17 square 2-10 un-zoom 2-11 within Numeric view 2-17 X-zoom 2-9 Y-zoom 2-10 HP 3 9gs Engl ish. book Pa ge 13 We dnes day, Dec embe r 7, 2005 11 : 24 PM
HP 3 9gs Engl ish. book Pa ge 14 We dnes day, Dec embe r 7, 2005 11 : 24 PM