HP 39g+ User Manual

hp 39g graphing calculator user’s guide H Edition 2 Part Number F2224-90001
Notice REGISTER YOUR PRODUCT AT: www.register.hp.com THIS MANUAL AND ANY EXAMPLES CONTAINED HEREIN ARE PROVIDED “AS IS” AND ARE SUBJECT TO CHANGE WITHO UT NOTICE. HEWLETT-PACKARD COMPANY MAKES NO WA RRANTY OF ANY KIND WITH REGA RD TO THIS MANUAL, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTI ES OF MERCHANTABILITY, N ON-INFRINGEMENT AN D FITNESS FOR A PARTICULAR PURPOSE. HEWLETT-PACKARD CO. SHALL NOT BE LIABLE FOR A NY ERRORS OR FOR INCIDEN TAL OR CONSEQUENTIAL DAMA GES IN CONNECTION WITH THE FURNISHING, PERFORMANCE, OR USE OF THIS MANUAL OR THE EXAMP LES CONTAINED HEREIN. © Copyright 1994-1995, 1999 -2000, 2003 Hewlett-Packard Development Company, L.P. Reproduction, adaptation, or translation of this manual is prohibited without prior written permission of Hewlett- Packard Company, except as allowed under the copyright laws. Hewlett-Packard Company 4995 Murphy Canyon Rd, Suite 301 San Diego,CA 92123 Printing History E diti on 2 December 200 3
Contents 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 ............. ............. ............. ............. ........... 1-12 Aplets (E-lessons) ........... ............. ............. ............. ............. .. 1 -12 Aplet library ............ ............. ............. ............. ............. .. 1 -16 Aplet views ........... .......... ............. ............. ............. ........ 1-16 Aplet view configuratio n............. ............. ............. ........... 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 sp litting the graph ............. ..... 2-14 About the numeric view .............. ............. ............. ........... 2-16 Setting up the table (Numeric view setup) ............... ........... 2-17 Exploring the table of numbers .... ................ ............. ........ 2-18 Building your o wn table of number s ................ ............. ..... 2-19 “Build Your Own” me nu keys ...... ............. ............. ........... 2-20 Example: plotting a circle .............. ............. ............. ........ 2-21
ii Conten ts 3 Function aplet About the Function ap let .............. ............. .......... ............. ...... 3-1 Getting started w ith the Function aple t ......... ............. .......... 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 Statistics aplet About the Statistics aplet ........... ............. ............. ............. ...... 8-1 Getting starte d with the Statistic s aplet ... ............. ............. ... 8-1 Entering and editing s tatistical data ........... ............. ............. ... 8-6 Defining a regression model .......... ............. ............. ........ 8 -12 Computed st atistics ........ ............. ............. ............. ............. . 8-13 Plotting .. ............. .......... ............. ............. ............. ............. . 8-15 Plot types ................. .......... ............. ............. ............. .... 8 -16 Fitting a curve to 2VAR data ...... ................ ............. ........ 8-17 Setting up the plot (Plot setup vie w) ....... ............. ............. . 8-18 Trouble -shooting a plot ........... ............. ............. ............. . 8-18 Exploring the g raph ..... ............. ............. ............. ........... 8-19 Calculating predicted values ... ............. ............. ............. . 8-20
Contents iii 9 Inference aplet About the Inference a plet ......... ............. ............. ............. ....... 9-1 Getting started with the Infere nce aplet .............. ............. .... 9-1 Importing samp le statistic s from the Statis tics aplet ............ .... 9-4 Hypothesis tes ts ...... ............. ............. ............. ............. .......... 9-8 One-Sample Z-Test .... ............. ............. ............. ............. .... 9-8 Two-Samp le Z-Tes t ........... ............. ............. .......... ............. 9-9 One-Propo rtion Z-Tes t .... ............. ............. ......... ............. .. 9 -10 Two-Proportion Z-Te st .... ............. ............. ............. ........... 9-11 One-Sample T-Test .... ............. ............. ............. ............. .. 9-1 2 Two-Samp le T-Test .............. ............. .......... ............. ........ 9-14 Confidence intervals ...... ............. ............. ............. ............. .. 9-15 One-Sample Z-Interval ...... ............. ............. ............. ........ 9-15 Two-Samp le Z-Interv al ......... .......... ............. ............. ........ 9-16 One-Propo rtion Z-Interva l ............ ............. ............. ........... 9-17 Two-Proportion Z-Interval .. ............. ............. ............. ........ 9-17 One-Sample T-Interval ... ............. ............. ............. ........... 9-18 Two-Samp le T-Interval ............. ............. ............. ............. .. 9-19 10 Using the Finance Solver Calculating Amo rtizations ....... ............. ............. ............. .. 10-7 11 Using mathematical functions Math functions ........ ............. ............. ............. ............. ........ 11-1 The MATH menu ... ............. ............. ............. ............. ..... 11-1 Math functions by category ...... ............. ............. ............. ..... 11-2 Keyboard function s ................ ............. ............. ............. .. 11-3 Calculus functions ............... .......... ............. ............. ........ 11-6 Complex number fu nctions...... ............. ............. ............. .. 1 1-7 Constants ............. ............. ............. ............. ............. ..... 11-8 Hyperbolic trigon ometry ... ............. ............. ............. ........ 11-8 List functions ......... ............. ............. ............. ............. ..... 1 1-9 Loop functions . ............. ............. ............. ............. ........... 11-9 Matrix functions .... ............. ............. ............. ............. ... 11 -10 Polynomial fu nctions ........... ............. ............. ............. ... 11 -10 Probability functions ................... ............. ............. ......... 11-12 Real-number functio ns ...... ............. ............. ............. ...... 11-13 Two-variable statistics ....... ............. ............. ............. ...... 11-16 Symbolic functions .... ............. ............. ............. .......... ... 11 -17 Test function s ........ .......... ............. ............. ............. ...... 11-18 Trigonometry functio ns ........... ............. ............. ............. 11-19 Symbolic calculations ........... ............. ............. ............. ...... 1 1-20 Finding derivatives ............. ............. ............. ............. ... 1 1-21
iv Conten ts 12 Variables and memory management Introduction ..... ............. ............. ............. ............. .......... .... 12-1 Storing and recalling variables ............... ............. ................ . 12-2 The VARS menu ...... ............. ............. ............. ............. ........ 12-4 Memory Manager ...... ............. ............. ............. ............. .... 12-9 13 Matrices Introduction ..... ............. ............. ............. ............. .......... .... 13-1 Creating an d storing matrices ...... ............. ............. ............. . 13-2 Working with matrices ................ ............. ............. ............. . 13-4 Matrix arithmetic .... ............. ............. ............. ................. .... 13-6 Solving systems of linear equa tions ............. ............. ........ 13-8 Matrix functions a nd commands ......... ............. ................. .... 13-9 Argume nt convention s ............ ............. .......... ............. .. 13-10 Matrix functio ns .............. ............. ............. ............. ...... 13 -10 Examples .. ............. .......... ............. ............. ............. ......... 13 -13 14 Lists Displaying and editing lis ts .......... ................ ............. ........... 14-4 Deleting lists ............. ............. ............. ............. ............. . 14-6 Transmitting lists. ............. ............. ............. ............. ........ 14-6 List functions. .............. ............. ............. ............. ............. .... 1 4-6 Finding stat istical values for lis t elements ............... ............. .... 14-9 15 Notes and sketches Introduction ..... ............. ............. ............. ............. .......... .... 15-1 Aplet note view ...... ............. ............. ............. ............. ........ 15-1 Aplet ske tch view. ............. ............. ............. ............. ........... 15-3 The notepad .... ............. ............. ............. ............. ............. . 1 5-6
Contents v 16 Programming Introduction ............... ............. ............. ............. ............. ..... 16-1 Program catalog ...... ............. ............. ............. ............. .. 16-2 Creating and editing p rograms ........ ............. ............. ........... 16-4 Using programs ............ ............. ............. ............. ............. .. 16-7 Customiz ing an aplet ..... ............. .......... ............. ............. ..... 1 6-9 Aplet naming convention .................. ............. ............. ... 16 -10 Example ......... ............. ............. ............. ......... ............. 16-10 Programming co mmands....... ............. ............. ............. ...... 16-13 Aplet commands ................... ............. ............. ............. 16-1 4 Branch commands .............. ............. ............. ............. ... 16 -17 Drawing commands ................... ............. ............. ......... 16-19 Graphic co mmands ......... ............. ............. ............. ...... 1 6-20 Loop commands .... ............. ............. ............. .......... ...... 1 6-22 Matrix commands ......... ............. ............. ............. ......... 16-23 Print commands ............... ............. ............. ............. ...... 16-25 Prompt commands .............. ............. ............. ............. ... 16 -25 Stat-One and Stat-Two c ommands ......................... ......... 16-28 Stat-Two commands ......... ............. ............. ............. ...... 1 6-29 Storing and re trieving variables in pro grams ........... ......... 16-30 Plot-view variables ........... ............. ............. ............. ...... 1 6-30 Symbolic-vie w variables ...... ............. ............. ............. ... 16-37 Numeric-view variables .............. ............. ............. ......... 16-39 Note variable s ...... ............. ............. ............. ............. ... 1 6-42 Sketch variables ....... ............. ............. ............. .......... ... 16 -42 17 Extending aplets Creating new aplets based on e xisting ap lets ................. ........ 17-1 Using a cus tomized aplet . ............. ............. ............. ........ 17-3 Resetting an a plet.... ............. ............. ............. ............. ........ 17-3 Annotating an aplet with notes ..................... ................ ........ 17-4 Annotating an aplet with sketches .......... ............. ............. ..... 17-4 Downloading e-lessons fro m the web ............. ............. ........... 17-4 Sending and re ceiving aplets ................ ............. ................ .. 17-4 Sorting items in the aplet library menu list ...... ............. ........... 17-5
vi Conten ts Reference information Glossary ............. ............. .......... ............. ............. ............. ... R-1 Resetting the hp 39g ....... .......... ............. ............. ............. ... R-3 To erase all me mory and reset defaults ........ ............. .......... R-3 If the calculator do es not turn on ........ ............. ............. ...... R-4 Operating details .......... ............. ............. ............. ............. ... R-4 Batteries ........... .......... ............. ............. ............. ............. R-4 Variables .. ............. .......... ............. ............. ............. ............. R-6 Home variables ........... ............. ............. ............. ............. R-6 Function aplet variables ................ ............. ............. .......... R-7 Parametric aplet variables ....... ............. ............. ............. ... R-8 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 Program commands ............ ............. ................ ............. . R-16 Status message s ......... ............. ............. ............. ............. .... R-17 Limiting Warranty Service ....... ............. ............. ............. ............. ............. .. W-3 Regulatory info rmation............ ............. ............. ............. .. W-5 Index
Preface P-1 Pr eface The hp 39g is a feature-rich graphing c alculator. It is also a powerful mathematics learning tool. The hp 39g is designed so that you can use it to explore mathematical functions and their prop erties. You can get more information on the hp 39g from Hewlett-Packard’s 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 Packard’s 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 esse s ar e repr es ented a s f ollo ws: , , , 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 epresented as fo llo w s: CLEAR , MODES , ACOS , etc. • Numbers and letters ar e r epre sented normally , as fo llo w s: 5, 7 , A, B, et c. • Menu opti ons, that is, the f u ncti ons that y ou select using the men u k ey 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 ies a s 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
P-2 Preface 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.  Copyright 2003 Hewle tte-Packard Development Company, L.P. The programs that control your hp 39g are copyrighted and all rights are reserved. Reproduction, a daptation, or translation of those programs without prior wri tten permission from Hewlett-Packard Company is also prohi bited.
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 ca lculator 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 is the calculator’s 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.
1-2 Getting started The display To adjust the contrast Simultaneously press and (or ) to increase (or decrease) the contrast. To clear the display • Pres s CANCEL to c lear the edit line . • Pres s CLEAR to c lear the edit line and the display history . Parts of the display Menu key or soft key labels. The la bels f or the menu k e ys ’ cur ren t meanings. is the label f or the fir st menu k ey in this pi ctur e. “Pr ess ” means to pr ess the fir st menu k e y , that is, the leftmo st top-r ow k ey on the calc ulator k e yboar d. Edit line. The line of current 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 D egrees ang le mode is set for HOME. The T and S symbols indicate whether there is more history in the HOME displa y. Press the and to scroll in the HOME display. NOTE This user’s guide contains images from the hp 39g and do not display the menu key label. Title Edit line History Menu k e y labels
Getting started 1-3 Annunciators . Annunciators are sy mbols that ap pear 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. Menu Key Labels Menu Keys Cursor Aplet Control Alpha Key Shift Key Enter Keys Key Keys
1-4 Getting started • On the calculato r k e yboar d, the top r ow of k ey s are called menu k ey s. The ir meanings depend on the conte xt—that’s w h y their to ps ar e blank. The menu k e y s ar e sometimes called “ s oft k e ys ” . • The bo ttom line of the dis pla y sho ws the la bels f or the menu k ey s ’ curr ent meanings. Aplet control keys The aplet control keys are: K e y Meaning Displays the Symbolic view for the current aplet. See “Symbolic view” on page 1-16. Displays the Plot view for the current aplet. See “Plot view” on pa ge 1-17. Displays the Numeric vi ew for the current aplet. See “Numeric vie w” on page 1-17. Displays the HOME view. See “HOME is the calculator’s 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 the current aplet is displayed in the title of the home view.” on page 1-1. Displays the Aplet Library menu. See “Aplet library” on pa ge 1-16. Displays the VIEWS menu. See “Aplet views” on page 1-16.
Getting started 1-5 Entry/Edit keys The entry and edit keys are: K ey 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 “=”. When or is present as a menu key, acts the same as pressing or . Enters a negative number. To enter –25, 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 i f 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.
1-6 Getting started Shifted keys trokes 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 M eaning (Continued) Key D e sc r i pt io n Press the key to access the operations printed in blue above the keys. F or insta nce, to access t he Modes screen, press , then press . ( MODES is labeled in blue above the key). You do not need to hold down when you press HOME. Th is action is depicted in this manual as “press MODES .” To cancel a shift, press again. The alphabetic keys are also shifted keystrokes. For instance, to type Z, press Z. (The le tters are printed in orange to the lower right of each key.) To cancel Alph a, press again. For a lower case letter, press . For a string of letters, hold down while typing.
Getting started 1-7 HELPWITH The hp 39g built-in help is available in 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 as sine , cosine , and tangent 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. P ress 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. • The ar ro w ke y s sc r oll thr ough the list ( , ) and mo ve fr om the category list in the left column to the item list in the r ight column ( , ) . • Pres s to insert the selected command onto the edit line . • Pre ss to dismis s the MA TH menu w ithout selec ting a command . • Pres sing displa ys the lis t of Pr ogram Co nstants. Y ou can u se these in pr ogr ams that yo u d eve l op.
1-8 Getting started • Pr essing tak es yo u to the beginning of the MA TH men u . See “Math functions by category” on page 11-2 for details of the math functions. HINT When using the MA TH menu , or an y menu on the hp 3 9g , pressing an alpha k e y tak es y ou str aight to the fir st menu opti on beginning w ith that alpha char acter . With this method , y ou do not need t o pr ess fir st. J ust pr ess the k ey that co rr esponds to the command’s beginning alpha char acter . Program commands Pressing CMDS displays the list of Program Commands. See “Programming commands” on page 16 -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 item s abov e. To search a menu • Pr ess or to sc r oll thr ough the list . If you pre ss or , y ou’ll go all the w a y to the end or the beginning o f the list . Highli ght the item y ou wa nt to selec t , then pres s (or ). !
Getting started 1-9 • If ther e are tw o c olumns , the left column sho ws gener al categor ies and the r ight column sho ws spec ifi c cont ents w ithin a categor y . Highli ght a gener al category in the left column, the n highligh t an item in the r ight column . The lis t in the ri ght column c hanges w hen a diffe r ent catego r y is hi ghlighte d. Pr ess or w hen y ou ha ve hi ghlight ed y our sele ction. • T o spee d-sear ch a list , type the f irs t letter o f the w or d . F or ex ample , to f ind the Matr i x category in , pr ess , the Alpha “M” k ey . • T o go up a page , you 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, pr ess CLEAR .
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 use the SETUP keys ( and ) . Press MODES to access the HOME MODES input form. Setting Options Angle Measure Angle values are: Degrees . 360 degrees in a circ le. Radians . 2 π radians in a ci rcle. Grads . 400 grads in a circle. 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.
Getting started 1-11 Numb er 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 be comes 123.46 in Fixed 2 format . Scientific . Displays results with an exponent, one digit to the left of the decimal point, and the speci fied number of decimal places. Example: 123.456789 becomes 1.2 3E2 in Scientific 2 format. Engineering . Displays result with 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 in 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 “Using fractions” 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)
1-12 Getting started Setting a mode This example demonstrates how to change the angle measure from the default mode, radians, to degrees for the current aplet. The procedur e is the same for changing number format and decimal mark modes. 1. Pr ess MODES to open the HOME MODES input form. T he cur sor (hi ghlight) is in the fir st f ield, A ngle Measur e . 2 . Pr ess to display a li st of choices. 3. P r e 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 9g (initial pur chas e) . • Aplets cr eated by sa ving e xisting aplets , w hic h hav e been modified , with spec ific confi gur ations . See “Cr eating new aplets bas ed on ex isting aplets ” on page 17-1. • Do w nloaded fr om HP’s Calc ulators w eb site.
Getting started 1-13 • Cop ied fr om another calculator . Aplets are sto red in th e Aplet library. See “Aplet lib rary” on page 1-16 for further information. You can modify configuration settings for the graphical, tabular, and symbolic views of the aplets in the following table. See “Aplet view configuration” 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 g is supplied with two teaching aplets: Quad Explorer and Trig Explorer. You cannot modify configurati on settings for these aplets. 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 : . 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 – U n 2 – U 1 0 = U 2 1 = U n U n 2 – U n 1 – = x 1 x 2 x –2 – =
1-14 Getting started A great many more teaching ap lets can be found at HP’s web site and other web sites created by educators, together with accompanying documentation, often with student work sheets. These can be downloaded free of charge and transferred to the hp 39g using the separately supplied 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 c hange in the equation. HINT More detailed documentation, and an accompanying student work sheet can be found at HP’s web site. Pr ess , selec t Quad Explorer , and then pr ess . The Qu ad Expl orer 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. ya x h () 2 v =
Getting started 1-15 A button is provided to evaluate the student’s knowledge. Pressing displays a ta rget quadratic graph. The student must manipulate the equation’s parameters to make the equation match the target graph. When a student feels that they have correctly chosen the parameters a button evaluates the answer and provide feedback. An button is provided for those who give up! Trig Explorer aplet The Trig Explorer aplet is used to inv estigate 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 ‘point of control’ is at the origin (0,0) and the a nd keys control vertical and horizontal transformations. When is chosen the ‘point of control’ is on the first 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. ya b x c () d sin = Origin π 21 , ⁄ () Extremum
1-16 Getting started 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 or key changes the parameter’s values. The default angle setting for this aplet is radians. The angle setting can be changed to degrees by pressing . Aplet library Aplets are stored in the Aplet library. To open an aplet Press to display the Aplet library menu . Select 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 il lu 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). Symbolic view Press to display the aplet’s S ymboli c vi e w . 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 “About the Symbolic view” on page 2-1 for further information.
Getting started 1-17 Plot view Pr ess to display the aplet’s P lot vi ew . In this v ie w , the f uncti ons that y ou ha v e def ined ar e displa y ed gr aphicall y . See “About the Plot view” on page 2-5 for furth er information. Numeric view Press to display the aplet’s Numeric vie w. In this view, the functions that you have defined are displayed in tabular format. See “About the numeric view” 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 “Other views for scaling and splitting the graph” on page 2-14 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 “Other views for scaling and splitting the graph” on page 2-14 for further information .
1-18 Getting started Overlay Plot view The VIEWS menu contains the Overlay Plot view. Select Overlay Plot Plots the current expression(s) without erasing any pre-ex isting pl ot(s). See “Other views for scaling and splitting the graph ” on page 2-14 for further information. Note view Press NOTE to display the aplet’s 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 “Notes and ske tches” on page 15-1 for further information. Sketch view Press SKETCH to disp lay the aplet’ s sketc h view. Display s pictur es to supplement an aplet. See “Notes and sketches” on page 15-1 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 aplet’s plot settings. Angle measure is controlled using the MODES view. Plot Setup Press SETUP - PLOT . Sets parameters to plot a graph.
Getting started 1-19 Numeric Setup Press SETUP - NUM . Sets parameters for bui lding a table of numeric values. Symbolic Setup This view is only available in the Statistics aplet in mode, where it plays an important role i n choosing data models. Press SETUP - SYMB . To change views Each view is a separate environment. To ch ange 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 one—like 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 39g calculators. See “Sending and r eceiving aplets” on page 17-4. 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 “Programming commands” on page 16-13 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 xpr es sion in to the hp 3 9g in the same left- to -right or der that y ou would w rite the e xpres sion . T his is called algebr a ic entry . • T o enter functions, select the k ey or MA T H menu item 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 ou t its name .
1-20 Getting started • Pres s to ev aluate the expr essio n y ou hav e in the edit line (w here the blinking c urso r is) . An e xpressi on can contain n umbers , functi ons, and va riab l es. 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, (–5) 2 = 25, whereas –5 2 = –25. 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 23 2 14 8 – 3 – --------------------------- - 45 () ln 23 14 8 3 45 51 0 4 × 3.21 10 7 – × 41 0 13 – × () 61 0 23 × () 31 0 5 – × ----------------------------------------------------
Getting started 1-21 Explicit and implicit multiplication Implied multiplication takes place when two operands appear with no operator in between. If you enter AB , for example, the result is A*B . However, for clarit y, 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: “Invalid Use r Function”. This is because the calculator interprets A(B 4) as meaning ‘evaluate function A at the value B 4 ’, 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 39g calculates according to the order of algebraic precedence (the next topic). Following are some examples using parentheses. Entering ... Calculates... 45 π sin (45 π) 45 π sin (45) π 85 9 85 9 85 9 × 85 9 ×
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 xpression s with in p arenthe ses. Nes ted p arenthe ses ar e ev aluated fr om inner to outer . 2 . Pr efi x functi ons, suc h as SIN and L OG . 3 . P ostfi x func tions , such a s ! 4. P o w er functi on, ^, NTHR OO T . 5 . Negati on , multiplicati on , and di v ision . 6 . Addition and subtr action . 7. A N D a n d N O T . 8. OR and X OR. 9 . Le ft ar gument of | ( w her e) . 10. E quals, =. Largest and smallest numbers The smallest number the hp 39g can represent is 1×1 0 –499 (1E–499). A sma ller result is displayed as zero. The largest number is 9.99999999999 × 10 499 (1E499). A greater result is displayed as this num ber. Clearing numbers • clears 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 ( ) c lears the edit line . • CLEAR c lears all inpu t and outpu t in the display , in c luding t he display histor y . 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
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 ANS (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 the n 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 value in t he HOME display by highlighting the expression (using the arrow keys), then pressing . See “Using previous results” on page 1-22 for more details. The variable ANS is different from the numbers in HOME’s 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.
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 HOME’s 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 12, “Variables and memory management” for more information on variables. For example: 1. P erf orm a calc ula tion . 45 8 3 2 . Stor e the result in the A varia b l e. A 3 . P er f orm an other calc ulation u sing the A v ari able. 95 2 A
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 It’s a good habit to cl ear the display his tory ( CLEAR ) whenever you have finish ed 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 Fracti ons, as follows: Setting Fraction mode 1. In HOME , o pen the HOME M ODE S input for m. 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.
1-26 Getting started 2 . Select Number Format , press to display the optio ns, and hi ghlight Fract ion . 3 . Pr ess to select the Number F ormat option , then mo ve to the prec ision value fi eld. 4. Enter the prec ision v alue that yo u want to us e , and pr ess to set the pr ec ision . Pres s to retu rn to HOME . See “Setting fr action pr ec i si on ” belo w f or mor e infor mation. Setting fraction precision The fraction precision setting determines th e precision in which the hp 39g 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 dec imal 0.6666 becomes 3333/5 000 (6666/10000 ) whereas 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:
Getting started 1-27 • Pr ec ision set to 1: • Pr ec ision set t o 2: • Pr ec ision set to 3: • Pr ec ision set t o 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 acti on. • T o en ter a mi xed f rac tion , for e xam ple , 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. Se t the Number for mat mode to Fraction and spec if y a pr ec ision value o f 4. Select Fraction MODES Sele ct Fraction 4
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 i n the HOME v ie w . 3 . E valuat e the calc ulation . Converting decimals to fractions To convert a decimal value to a fraction: 1. Set the number for m at mode to Fraction . 2 . E ither r etr ie ve the v alue fr om the His tory , or e nter the v alue on the command line. 3 . Pr ess to con vert the number t o a fr acti on . When converting a decimal to a fraction, keep the following points in mind: • When con v erti ng a r ec urr ing decimal to a fr action , set the f r actio n pr ec ision to abo ut 6 , and ensur e that y ou include mor e than six dec imal places in the r ec urr ing dec imal that y ou en ter . In this e x ample , the fr action pr ecisi on is set to 6. T he top calc ulation r eturn s the corr ect r esult . The bottom one does no t . • T o conv er t an ex act decimal to a fr action, set the fr action pr ec ision t o at least tw o mor e than the number of dec imal plac es in the dec imal . In this e x ample , the fr action pr ecisi on is set to 6.
Getting started 1-29 Complex numbers Complex results The hp 39g can return a comp lex number as a result for some math functions. A comp lex number appears as 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 th e imaginary part, and i is the im aginary constant, : • ( x, y ) or • x iy . To enter i : • pr ess or • pr ess , or keys t o se l e c t Constant , to mo ve to the ri ght column of 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 compl ex number , press , enter the v ari able to st or e the number in, and pr ess . 45 Z 0 1 – 1 –
1-30 Getting started Catalogs and editors The hp 39g has several cata logs and editors. You use them to create and manipulate object s. They access features and stored values (numbe rs or text or other items) that are independent of aplets. • A catalog lists items, w hic h y ou can delete or tr ansmit , for e xam ple an aple t . • An editor lets y ou c reate or modify items and number s, for e xample a no te or a matr ix . Catalog/Editor Contents Aplet library () Aplets. Sketch editor ( SKETCH ) Sketches and diagrams, See Chapter 15, “N otes and sketches”. List ( LIST ) Lists. In HOME, lists are enclosed in {}. See Chapter 14, “Lists”. Matrix ( MATRIX ) One- and two-dimensional arrays. In HOME, arrays are enclosed in []. See Chapter 13, “Matrices”. Notepad ( NOTEPAD ) Notes (short text entries). See Chapter 15, “N otes and sketches”. Program ( PROGR M ) Programs that you create, or associated with user-defined aplets. See Chapter 16, “Programming”.
Aplets and their views 2-1 2 Aplets and t heir vie 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 Function, Parametric, Polar, and Seque nce aplets. The other views are derived from the symbolic expression. You can create up to 10 different defini tions 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 Seq uence aplets start in the S ymboli c v ie w . If the highli ght is on an e xis ting expr essi on , sc r oll to an empty line—unless y ou don ’t mind wr iting ov er the e xpr essi on— or , c lear one line ( ) or all lines ( CLEAR ). Expr es sions ar e selected (c h ec k mark ed) on entry . T o deselect an e xpressi on , pr ess . All selected e xpres sions ar e plotted.
2-2 Aplets and their views – For a Function definiti on , en ter an e xpr essi on to def ine F(X) . T he only independent variab l e i n t h e ex p res s io n i s X. – Fo r a P arametric definiti on , en ter 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 . – Fo r a P o l a r definiti on , en ter an e xpr essi on to def ine R ( θ ). T he only independent variab l e i n t h e ex p res s io n i s θ . – Fo r a S eq u en c e definiti on , ei ther : Enter the f irst and second terms for U (U1 , or ... U9 , or U0 ). De f in e t he n th term of the sequ ence in ter ms of N or of th e p rior t erms, U(N–1) and U(N–2) . The e xpr essi ons should pr oduce r eal-v alued s equence s w ith intege r domains . Or def ine the n th term as a non - recursive exp ression in term s o f n only . In this case , the calc ulato r inserts the f irs t two te rms based on t he expr ession that y ou define .
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. Ch oose the F unctio n apl et. Sele ct Function 2 . En ter the e xpre ssi ons in the F uncti on aplet ’s S ymboli c vi ew . A B F1 F2 3 . H ighli ght 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) .
2-4 Aplets and their 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 expres sion, 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 arithmetric expressions. Displays a menu for entering variable names or contents of variables.
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 settings shown in the next two table s. 1. H ighligh t the fi eld to edit . – If there is a number to ent er , t ype it in and pr ess or . – If there is an option to c hoose , pre ss , highli ght y our choi ce, and pr ess o r . As a shortcut to , just highlight the f ield to c hange and pres s to cy c le thr ough the optio ns. – If there is an option to select or deselect , pr ess t o ch e ck o r u n ch eck i t. 2 . Pr ess to vi e w mor e settings . 3 . W hen done , pr ess to vi e w the ne w plot . Displays the menu for en tering math operations. CHARS Displays 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. CLEA R Deletes all expressions in the list or clears the edit line. K ey Meaning (Continued)
2-6 Aplets and their 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; “Faster” plots in alternate pixel columns; “Detail” 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 Sequence aplet: Stairstep or Cobweb ty pes. 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.
Aplets and their views 2-7 Reset plot settings To reset the default values for all plot settings, press CLEA R 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 i v e s y o u a s e l e c ti o n o f ke y s a n d m e n u ke y s t o 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 ey Meaning CLEA R Erases the plot and axes. Offers additional pre-defined views for splitting the screen and for scaling (“zooming”) the axes. Moves cursor to far left or far right. Moves cursor between relations. or Interrupts plotting. Continues plotting if interr upted.
2-8 Aplets and their 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 cu rsor. 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 al so 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. • Pres sing once display s the full r ow o f labels . • Pres sing a second time r emo ves the r ow of labels to displa y only the gr aph. • Pres sing a third 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 “Analyse graph with FCN functions” on page 3-4). Displays the current, defi ning expression. Press to restore the menu. K e y Meaning (Continued)
Aplets and their views 2-9 To jump direc tly 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 o n trace mode by pr essing . • T o turn the co or dinate display off , press . 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 “Other views for scaling and splitting the graph” on page 2-14. 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 ver tical 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.
2-10 Aplets and the ir views Y-Zoom In Divides ver tical scale only, using Y-factor. Y-Zoom Out Multipli es vertical 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 defa ult value s for XRNG (–6.5 to 6.5) and YRNG (–3.1 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 = π /24 radians, 7.58, or 8 1 / 3 grads; rescales vertic al axis so 1 pixel = 0.1 unit. (Not in Sequence or Statistics aplets.) Option M eaning (Continued)
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 -zoo m. X-Zoom In : X-Zoom In Now un -zoo m. Un-zoom Ret urns 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
2-12 Aplets and the ir views X-Zoom Out : X-Zoom Out Now un-zoom. 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 turn o n the menu -k e y 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 rec tangle . Pr ess . 4. Use the cursor k ey s ( , etc.) to drag to the op posite corner .
Aplets and their views 2-13 5 . Pr ess to z oom in on the bo xe d ar ea . To set zoom factors 1. In the P lot vi e w , pre ss . 2. P r e s s . 3. S e l e c t Set Factors... and pr es s . 4. Enter the z oom f actor s. T her e is one z oom facto r for the hori z ontal sc ale ( XZOOM ) and one f or the ve rtical sca le ( YZOOM ). Z ooming out m ultiplies the s cale b y the fac tor , so that a gr eater scale distance appears on the sc r een. Z ooming in div ide s the sc ale by the fac tor , so that a shorter s cale distance appear s on the sc r een.
2-14 Aplets and the ir views 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 chan ging Plot view settings. For instance, if you have defined a trigonometric function, then you could select Tr ig to plot your function on a trigonometric scale. It also contains split-screen options. In certain aplets, for example those that you download from the world wide web, the preset viewing options menu can also contain option s 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). 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 (–6.5 to 6.5) and YRNG (–3.1 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.)
Aplets and their views 2-15 Split the screen The Plot-Detail view can give you two simultaneou s views of the plot. 1. Pr ess . Selec t Plot-Detail and pr ess . The graph is plot ted twice . Y ou can now z o om in on the r ight si de. 2. P r e s s , selec t the z oom method and pres s or . T his z ooms the r ight si de. Her e is an e x ample of split sc reen w ith Zoom In . – The P lot menu k e y s ar e av ailable a s for the f ull plot (fo r trac ing, coor dinate di spla y , equati on display , and so on ) . – mo ves the leftmost c ursor to the scr een’s left edge and mo ves the r ightmo st c ursor to the s cr een ’s r ight edge . – The menu k e y copie s the r igh t plot to the le ft plot . 3 . T o un -split the sc r een , pr ess . The le ft side 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 . Selec t Plot-Table and pr ess . The scr e en display s th e plot on the left side and a table of numbers on the right side. Trig Rescales horizontal axis so 1 pixel = π /24 radian, 7.58 , or 8 1 / 3 grads; rescales vertical axis so 1 pixel = 0 .1 unit. (Not in Sequence or Statistics aplets.) Option M eaning (Continued)
2-16 Aplets and the ir views 2 . T o mo ve up and do wn the table , use the and c urso r k e y s. T hese k ey s mov e the tra .ce poin t left or r ight alo ng the plot , and in th e table , the corr esponding v alues ar e highlighted . 3 . T o mo ve between functi ons, u se the and c urso r k e ys t o mo ve the c ursor fr om one gr aph to another . 4. T o r eturn to a full Numer ic (or P lot) v ie w , pr ess (or ) . Overlay plots If you want to plot over an existing plot withou t erasing that plot, then use Overlay Plot instead of . Note that tracing follows only the current functions from the current aplet. Decimal scaling Decimal scaling is the default scalin g. 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 each pixel is and the ori gin is near the screen ce nter. Trigon ometric scaling Use trigonometric scaling when ever you are plotting an expression that includes trigonometric functions. Trigonometric plots are more likely to intersect the axis at points factor ed b y π . 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. 11 ×
Aplets and their views 2-17 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. H ighligh t the fi eld to edit . Use the arr ow k ey s to mov e from fie l d to fie l d. – If there is a number to ent er , t ype it in and pr ess or . T o modify an ex isting number , pr ess . – If there is an option to c hoose , pre ss , highli ght y our choi ce, and pr ess o r . – Sh ortc ut : Pr ess the k ey to cop y values fr om th e Plot Setup i nto NUMSTART and NUMSTEP . Effecti vel y , the menu k ey allo ws y ou to mak e the table matc h the pi xel co lumns in the gr aph v iew . 2 . W hen done , pr ess to vi ew the table o f num b ers. Numeric view settings The following table details the fields on the Numeric Setup input form. F ield Meaning NUMSTART The inde pendent variable’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.
2-18 Aplets and the ir views 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. ZOOM options The following table lists the zoom options: K e y Meaning Displays ZOOM menu list. Toggles between two character sizes. Displays the defining function expression for the highlighted column. To cancel this display, press . 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 .)
Aplets and their views 2-19 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 indepe ndent variable value in the tab le, use the arrow keys to place the cursor in the independent variable column, then ente r the value to jum p 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. Building your own table of numbers The default NUMTYPE is “Automatic”, which fills the table with data for regular intervals of the independent ( X , T , θ , or N ) variable. With the NUMTYPE option set to “Build Your Own”, 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 x pr essi on defined (in S ymboli c v ie w) in th e ap l et of your choic e. Note: F unctio n, P olar , P ar ametric , and Sequence aplets only . 2 . In the Nume ri c Setup ( NUM ), choo se NUMTYPE: Build Your Own . 3 . Open the Numer ic v iew ( ) . 4. Cle ar ex isting data in the table ( CLEAR ). Trig Changes intervals for independent variable to π /24 radian or 7.5 degrees or 8 1 / 3 grads. Starts at zero. Un-zoom Ret urns the display to the previous zoom. Option M eaning (Continued)
2-20 Aplets and the ir views 5 . Ente r the independent values in the le ft -hand column. T y pe i n a number and press . Y ou do not hav e to enter them in order , b ecause the function can r earr ange them. T o inser t a number between tw o oth ers, use . Clear data Press CLEAR , to erase the data from a table. “Build Your Own” menu keys F1 and F2 entries are generated automatically You enter numbers into the X column 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 row of zero values 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.
Aplets and their views 2-21 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 1. In the F unction aple t , spec if y the func tio ns. Select Function 9 9 2 . R eset the gr aph setup t o the def ault s ettings . SETUP - PLOT CLEAR 3 . P lot the two f uncti ons and hide the men u so that y ou can see all the ci rc l e . 4. R ese t the numer ic s etup to the de fault s ettings. SETUP - NUM CLEAR y 9 x 2 – ± = y 9 x 2 – = y 9 x 2 – – =
2-22 Aplets and the ir views 5 . Displa y the functi ons in numer ic f orm .
Function aplet 3-1 3 F unc tion apl et 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: • c r eate gr aphs to f ind r oots, in ter cepts, slope , signed ar ea, and e xtrema • cr eate tables to ev aluate functi ons at par tic ular va l ue s. This chapter demonstrates the basic tools of the Function aplet by stepping you through an example. See “Aplet views” 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 qu adratic equation . Open the Function aplet 1. Open the Func tion aplet . Select Function 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 – = yx 3 () 2 2 – =
3-2 Function aplet Define the expressions 2 . T her e are 10 f uncti on def inition f ields o n the F u ncti on aplet’s S y mbolic v ie w sc r een . The y 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 e nter a n e xpr essi on . (Y ou 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 scale s of the x and y axes, graph resolution, and the spacing of the axis ticks. 3 . Displa y plot settings. SETUP - PLOT Note: F or our e x ample , you can lea ve the plot settings at t heir defa ult values si nce w e will be using the Auto Scale f e atur e to choo se an appr opri ate 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 res tor e the defa ult val u es. 4. Spec ify a gri d f or the gr aph . Plot the functions 5 . P lot the functi ons.
Function aplet 3-3 Change the scale 6 . Y ou can chan ge t he sca le to see mo r e or l ess of your gr aphs . In this e xam ple , choos e Auto Scale . (S ee “VIEW S menu options ” on page 2 -14 for a de script ion of Aut o Sc a le ) . Select Auto Scale Trace a graph 7 . T r ace the lin ear fu nctio n . 6 times Note: B y defa ult , the tr acer is acti ve . 8. Jum p fr om the linear func tion to the quadr ati c func tio n.
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 Functi on aplet (and any Function-based ap lets). The FCN fun ctions act on the currently selected graph. S ee “FCN func tions ” on page 3-10 f or further infor mation . To find a root of the quadratic function 10. Mov e the c urs or to the gr aph of the quadr atic equati on b y pr es sing the or ke y . T hen mov e the c urs or so that it is near b y pressing 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 r oot ( as in our exa mp l e ) , t h e coor dinates of the r oot clos est t o the cur rent c urs or position ar e display ed. To find the intersection of the two functions 11. Find the in ters ecti on of the tw o func tions . x 1 – =
Function aplet 3-5 12 . Ch oose the linear f unctio n wh ose in ter sec tion w ith the quadr atic functi on y ou w ish to f ind . T he coor dinates of the inters ecti on po int 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 o f the inter sec tion po int c lose st to the c urr ent c urso r positi on 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 po int . Sele ct Slope T he slope v alue is display ed at the bottom of th e scr een. To find the signed area of the two functio ns 14. To find the area between the two functions in the range –2 ≤ x ≤ –1, firs t mo ve the c ursor to and select the si gned area opti on . Sele ct Signed area F 1 x () 1 x – =
3-6 Function aplet 15 . Mo v e the c urso r to b y pr essing the or key . 16 . Pr ess to acce pt using F2(x) = (x 3) 2 – 2 as the other boundar y for the integr al. 17 . Choos e the end value for x . 2 Th e cu r so r ju mp s to x = –2 on the linear func tion . 18. Display the numerical value of the integral. Note: See “Shading ar ea” 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 cur sor t o the quadr atic equati on and f i nd the e xtr emum o f the quadrati c. Select Extremum The coordina tes of the ext rem u m are display ed a t the bottom of the sc r e en . x 1 – =
Function aplet 3-7 HINT The Root and Extremum functions return one value only even if the function has more than one root or extremum. The function finds the value closest to the position of the cursor. You need to re-l ocate the cursor to find other roots or extrema that may exist. Display the numeric view 20. Di spla y the numer ic v iew . Set up the table 21. Display the n u mer ic se tup . SETUP - NUM See “Sett ing up the table (N umeri c v ie w setup)” on page 2 -17 fo r mor e infor mation . 2 2 . Match the table s ettings to the pi xel co lumns in the gr aph v ie w . Explore the table 2 3 . Displa y the ta ble of va lues .
3-8 Function aplet To navigate around a table 2 4. Mov e to X = –5 .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 fac tor of 4. Note: NUMZOOM has a setting of 4 . In To change font size 2 7 . Displa y table numbe rs in lar ge font . To display the symbolic definition of a column 2 8. Displa y the s ymboli c def inition f or the F1 column. The symbolic definition of F1 is display ed at the bottom of the screen.
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 “FCN functions” on pag e 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 ria bl e To access FCN variable in th e Function aplet’s Symbolic view: Sele ct Plot FCN or to choo se a var iable
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 “Interpreting results” 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 Sele ct 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.
Function aplet 3-11 Shading area You can shade a selected area between functions. This process also gi ves you an appro ximate measurement of the area shaded. 1. Open the Functi on aplet. T h e F unction aplet opens in the S ymboli c v ie w . 2 . Selec t the e xpr essi ons w hos e curv es y ou wan t to stu dy . 3 . Pre ss to plot the functi ons. 4. Pr ess or to positi on the c urs or at the starting point o f the area y ou want t o shade . 5. P re s s . 6 . Pr ess , then select Signed area and pr ess . 7 . Pr ess , c hoose the f unction 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 calc ulate the ar ea. T he 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)
3-12 Function aplet Plotting a piecewise-defined function Suppose you wanted to plot the following piecewise- defined function. 1. Open the F unctio n apl et. Sele ct Function 2 . Highlight the line y ou wa nt to us e , and ente r the e xpre ssion . (Y ou can press to delete an e xis ting line , or CLEAR to clear all lines .) 2 CHARS ≤ 1 CHARS > 1 AND CHARS ≤ 1 4 CHARS > 1 Note: Y ou can us e the menu k e y to assist in the entry of equations . It has the same effect as pr essing . f x () x 2 x 1 – ≤ ; x 2 1 – x 1 ≤ < ; 4 xx 1 ≥ ; –      =
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 arametr ic aplet . Select Parametric Define the expressions 2 . Def ine the e xpr essi ons . 3 3 xf t () = yg t () = xt () 3 t yt () 3 t cos = sin =
4-2 Parametric aple t Set angle measure 3 . Set the ang le meas ure to degr ees. MODES Select Degrees Set up the plot 4. Display the graphing options. PLOT T he P lot Setu p input fo rm has tw o fie lds not inc luded in the Func tion aplet , TRNG and TSTEP . TRNG spec if ie s the r ange of t val u es. TSTEP specif ies th e 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 expr ession. 7 . T o see all the c irc le , pr ess tw ice .
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 (w ithout c hanging the equation) becaus e the c hanged value o f TSTEP ensur es that points be ing plot ted ar e 120 ° apart instead o f nearl y continuou s. Y ou ar e able to e xplor e the graph u sing trace , z oom, split sc reen , and scaling f unctio nality av ailable in the F unction aple t . See “Explor i ng the gr aph ” on page 2 - 7 fo r fu r t h er i n for ma t io n. 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 value , 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 -val ue in the t able . You are able to explore the table using , , build your own table, and split screen functionality availablfe in the Function aplet. See “Exploring the table of numbers” on page 2-18 for further information.

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 o lar aplet. Sele ct Polar L ik e the Func tion a plet , the P o lar aplet opens in the S ymboli c v ie w . Define the expression 2 . Def ine the polar equati on . 2 π 2 Specify plot settings 3 . Spec if y the plot settings . In this ex ample , w e w ill use the def ault se ttings, e x cept fo r the θ RNG fi el d s . SETUP - PLOT CLEAR 4 π Plot the expression 4. P lot the ex pr essi on. r 2 πθ 2 ⁄ () θ () 2 cos cos =
5-2 Polar aplet Explore the graph 5 . Display the P lot v ie w menu k ey labe ls. Th e Pl o t vi ew o p t i o n s av ailable ar e the same as those f ound in the F unction aplet . See “Explor ing the gra ph ” on page 2 - 7 fo r further infor mation . Display the numbers 6 . Dis play the t able of value s fo r θ and R1. Th e Nu m e ric vi ew optio ns av ailable ar e the same as th ose fo und in the F unction aplet . See “Explor ing the table of n umber s ” on pa g e 2 - 1 8 fo r f ur th er i n for ma t io n.
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 o f U1 ( n–1) •i n ter ms of U1 ( n–2) • in ter ms of another sequence , for e xample , U2 ( n) • in an y combination of the a bo ve . The Sequence aplet allows you to create two types of graphs: – A Stairstep s gr ap h plot s n on the ho ri z ontal ax is and U n on the v ertical ax i s . – A Cob w eb graph plots U n– 1 on the hor i z ontal ax is and U n on the ve rtical ax is. Getting started with the Sequence aplet The following example defines and then plots an expression in the Sequence aplet. Open the Sequence aplet 1. Open the Sequ ence aplet. Sele ct Sequence T he Sequ ence aple t starts in the S ymboli c vi ew .
6-2 Sequence aplet 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 t w o terms: , , fo r . In the S ymboli c v iew o f the Sequence aplet , highligh t the U 1 (1) fi eld and begin defining y our sequence . 1 1 Note: Y ou can us e the , , , , and menu k e ys to assist in the ent ry of equations . Specify plot settings 3. In P lot Setu p , firs t set the SEQPLOT opti on to Stairstep . R ese t the defa ult plot s ettings by clear i ng the P lot Setup v iew . SETUP - PLOT CLEAR 8 8 Plot the sequence 4. P lot the F ibonacc i sequ enc e. 5. In Plot Setup, set the SEQPLOT optio n to Cobweb. SETUP - PLOT U 1 1 = U 2 1 = U n U n 1 – U n 2 – = n 3 >
Sequence aplet 6-3 Select Cobweb Display the table 6. Display the table of values f or this ex ample.

Solve aple t 7-1 7 Solv e aplet About the Solve aplet The Solve aplet solves an equation or an expression for its unknown variable . You defi ne an equation or expression in the symbolic view, then supply valu es for all the variables except one in the nu meric view. Solve works only with real numbers. Note the differences between an equation and an expression: • An equation contains an equals sign . Its soluti on is a v alue for the unkno w n var iable that mak es both sides hav e the same value . • An expression d oes n ot contain an eq uals sign . Its solu tion is a r oot , that is, a v alue for the unkno w n v ari able that mak es the expr essi on ha ve a v alue of ze r 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 ymboli c vi e w , yo u spec ify the expr essi on or equation to solve . Y ou can define up to ten equations (or e xpre ssions), named E0 to E9 . E ach eq uation can contain up to 2 7 r eal var ia bles, named A to Z and θ. • In Numeri c vi ew , y ou spec ify the values of the know n v ari ables , highlight the v ari able that y ou w ant to sol v e fo r , and pr ess . You can s olve t he equat ion 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,
7-2 Solve ap let should be solved using matrices or graphs in the Function aplet. 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 distan ce of 100 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 ymbolic v ie w . Define the equation 2. Define the equa tion. V U 2 A D Note: Y ou can u se the menu k ey to as sist in the entry of eq uations . Enter known variables 3 . Display the Solv e numeri c vie w scr een. V 2 U 2 2 AD =
Solve aple t 7-3 4. Enter the v alues f or the know n var iable s. 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 for the unkno w n var iable ( A ). T her ef ore , the acceler ation needed to inc r ease the speed of a car fr om 16.6 7 m/sec (60 kph) to 2 7 .7 8 m/sec (100 kph) in a di stance of 100 m is appr ox imately 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 solu tions . Plot the equation T he P lot v ie w sho ws one gr aph for eac h side of the selected equation. Y ou can choose an y of the v ar iable s to be the independen t var iable . T he c urr ent equati on is . One of these is , w ith , that is, . This gr aph w i ll be a hor iz on tal line . T he other gr aph w ill be , wi th and , that is, . T his graph is also a line . The desir ed soluti on 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 =
7-4 Solve ap let 6. P lot the equati on for v ar iable A . Sel ect 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 bot tom left corner of the scr een. T he Plo t vi e w pr o v ides a con venie nt wa y to find an appr ox imation to a so lutio n instead o f using the Numer ic v ie w Sol ve opti on. See “P lotting to find gu esses” on p ag e 7 - 7 for m ore in forma tion. Solve aplet’s NUM view keys The Solve aplet’s 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 “Interpreting results” 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.
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 ore plo tting, mak e sure the unkno w n var iable is highli ghted in the n umeri c vie w . Plo t the equati on to help y ou s elect an initi al gues s w hen y ou don ’t kno w the ra nge in whi ch to look f or the soluti on . See “P lot ting to f ind guesses ” on page 7 - 7 for fu r ther information . 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 You 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 “Mode settings ” 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 appropria te in this case. Clears highlighted variable to zero or deletes current character in edit line, if edit line is active . CLEA R Resets all variable values to zero or clears the edit line, if cursor is in edit line. K e y Meaning (Continued)
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 Con dition Zero The Solve aplet found a point where the value of the equation (or the root of the expression) is zero within the calculator’s 12-digit accuracy. Sign Reversal Solve found two points where the value of the equation has opposite signs, but it cannot find a point in between where the value is zero. This might be becau se either the two points are neig hbours (t hey dif fer by one in the twelfth digit), or the equation is not real-valued between the two points. Solve returns the point where the value is closer to zero. If the value of the equation is a continuous real function, this point is Solve’s best approximatio n of an actual root. Extremum Solve found a point where the value of the equation approximates a local minimum (for posi tive values) or maximum (for negative values). This point may or may not be a root. Or: Solv e stopped searching at 9.99999999999E4 99, the largest number the calculator can represent.
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 – 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 =
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 equation . 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 . Fi rst set appropri ate 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 on e 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 – 5 to 35. Keep the XRNG default of – 6.5 to 6.5. SETUP- PLOT 5 35 4. P lot the gr aph. YX = X 30 = Y 30 =
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 po i nt s o f inter sec tion sho w that ther e ar e t w o soluti ons f or this equati on . Ho w ev er , on ly p os i t ive va l u es fo r X m ak e sense , so w e wan t to fi nd the soluti on f or the int ers ecti on on the r ight side of the y -ax is. 6 . Retur n to the Numer ic vi ew . Note: the T -value is f illed in w ith the positi on of the c ursor from the Plot vie w . 7. Ensur e that the T v alue 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 body’s 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
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 ty pes, such as M 1 (a matrix variable). Home variables All home variables (othe r than those 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 rede fine 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 aplet’s Numeric view if you wish.) Aplet variables Func tions defined in other aplets can also be referenced 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 .
Statistics aplet 8-1 8 Statis tic s apl et 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 aplet’s 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 tis ing minu tes (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
8-2 Statistics aplet Open the Statistics aplet 1. Open the S tatisti cs aplet and c lear ex isting data b y pr essing . Select Statistics Th e S t at i s t ic s ap l e t 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 statist ical explorations: on e - var iable ( ) or t w o-v ari able ( ) . T h e 5th menu k ey labe l in the Numeri c v ie w toggles between these tw o options and sho ws the c urr ent option . 2 . Select . Y ou need to selec t because in this e x ample w e ar e analyzing a dataset compr ising two v ar iable s: ad ve rtising minut es and r esulting sales . Enter data 3 . Enter the data into the columns . 2 1 3 5 5 4 to mo ve to the next column 1400 9 20 1100 2 2 6 5 2 8 90 2 200 1VAR/2VAR men u k ey label
Statistics aplet 8-3 Choose fit and data columns 4. Se lect a f it in the S y mbolic setup v ie w . SETUP - SYMB Sele ct Linear Y ou c a n c re a te up t o five ex pl o ra t i o n s of t wo - va ri a b l e data , named S1 to S5 . I n t h i s exa m p l e, we wi l l cre a t e jus t on e : S1 . 5 . Spec if y the columns that hold the dat a y ou 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 . Find the mean ad vertising time ( MEANX ) and the mean sales ( MEANY ). MEANX is 3 .3 minu tes and MEANY is abou t $17 9 6 . 7 . Sc r oll dow n to displa y the value f or the corr elation coeff ic ient ( CORR ). T he CORR value indicates how w ell the linear model f its the data . 9 times T he value is .8 99 5 .
8-4 Statistics aplet Setup plot 8. Change the plotting range t o ensur 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 r e gr essio n c urve (a c ur ve t o fit the data points). T his dra ws the r egr essio n line f or the best linear f it. Display the equation for best linear fit 11. Return t o the S ymboli c vie w . 12 . Displa y the equati on f or the bes t linear fit . 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 4 25. 8 7 5. T h e y -inter cept ( b ) is 3 7 6. 25.
Statistics aplet 8-5 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 highli ght Stat-Two ) (to highlight PREDY ) 6 14. Retur n 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 edicted y -value in the left bottom corner of the screen.
8-6 Statistics aplet Entering and editing statistical data The Numeric view ( ) is used to enter data 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 sta tistics. You can also store statistical da ta values by copying lis ts from HOME into Statistics data columns. F or example, in HOME, L1 C1 stores a copy of the list L1 into the data-column var iable C1 . Statistics aplet’ s NUM view keys The Statistics aplet’s 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.
Statistics aplet 8-7 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 Statistics apl et . Sele ct Statistics 2 . Enter t he measurement data. 160 16 5 17 0 17 5 180 Deletes the currently highlighted value. CLEA R Clears the current column or all columns of data. Pregss CLEA R 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 (Con tinued)
8-8 Statistics aplet 3 . Fi nd the mean of the sample. Ensur e the / menu k e y label r eads . Pr ess to see the statistic s calc ulated fr om the sample data in C1 . Note that the title o f the colu mn o f st atis ti cs i s H1 . T here ar e 5 data set de f initions a vailable for one -var iable sta ti st ics: H1–H5 . If data is entered in C1 , H1 is automa ticall y set to use C1 f or data , and the fr equenc y of each dat a poin t is set to 1. Y ou can selec t other columns of dat a fr om the St atisti cs S y mbolic setu p v ie w . 4. Pr ess to c lose the statisti cs w indow and pr ess k ey to s ee 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 requenc y , or the column that holds the frequ en cies. T he ke ys y ou can use f r om this windo w are: 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 ( ).
Statistics aplet 8-9 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 . Displays the cu rrent variable expression in standard mathematical form. Press when done. Evaluates the variables in the highlighted column (C1, etc.) express ion. 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. CLEA R 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 (Con tinued) Heig ht (cm) Freq ue n cy 160 5 165 3 170 8 175 2 180 1
8-10 Statistics aplet 5 . Mov e the highli ght bar into the r igh t column of the H1 def i nitio n and r epla ce the frequency v alue of 1 w ith the name C2 . 2 6 . R etur n to the numer ic v ie w . 7 . Enter the f r equenc y data sho wn in the abo ve ta ble . 5 3 8 2 1 8. Displa y the computed sta ti stics. The mean height is approxi mately 167.63cm. 9 . Setup a histogr am plot for the data . SETUP - PLOT Enter s et up inf ormatio n appropriate to your data. 10. Plot a his togr 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.
Statistics aplet 8-11 Edit a data set In the Numeric view of the Statis tics aplet, highlight the data value to change. T ype a new value and press , or press t o copy the value to the edit line for modification. Pr ess after modifying the value on the edit line. Delete data • T o delete a single data item, hi ghlight 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 , highlight an entry in that column and press CLEA R . Select the column name . • T o delete all columns of data , pr ess 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 , highlight the column y ou want to sort, and pr ess . 2 . Spec if y 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 . F or 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 or ting and C1 the dependent column. – T o sort just one co lumn, c hoose None f or the dependent column . – Fo r one -var iable st atisti cs w i th two dat a columns, spec ify the fr equenc y column as the depe ndent column. 4. Pr ess .
8-12 Statistics aplet Defining a regression model The Symbolic view includes an expression (Fit1 through Fit5) that defines the regression model, or “fit”, to use for the regression analysis of each two-variable data set. There are three ways to select a regression model: • Accept th e default option to fit the data to a straight line . • Select one of the a vaila ble f it options in S y mbolic Setup v ie w . • Enter y our o wn mathematical e xpres sio n in S ymboli c v ie w . This e xpr ession w ill be plot ted, but 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 trigo nometric 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 displ ay the S ymbolic Setup v ie w . H ighli ght the F it number ( S1FIT to S5FIT ) y ou w ant to def ine. 3 . Pres s and select fr om the list . Pres s when done . Th e r egr essi on form ula fo r the fit is displa yed in S ymboli c vi e w . Fit models Eight fit models are available: F it model Meaning Lineair (Default.) Fits the data to a straight line, y = mx b . Uses a least-squares fit. Logaritmisc h Fits to a logarithmic curve, y = m ln x b . Macht Fits to an exponential curve, y = be mx . Power Fits to a power curve, y = bx m .
Statistics aplet 8-13 To define your own fit 1. In Numer ic v ie w , make sur e is set. 2 . Di spla y the S ymboli c v ie w . 3 . Highli ght the F it expr essi on ( Fit1 , etc.) f or the desir ed data set. 4. T yp e in an e xpr es sion a nd pr es s . The independent variable must be X , and the e xpr ession 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. Computed statistics One-variable Quadratic Fits to a q uadratic 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 , or—if L = 0—let L be computed automatically. User Defined Define your own expression (in Symbolic view.) F it model M eaning (Continued) y L 1 ae bx – () ------------------------- - = 1.5 x cos × 0.3 x sin × Statistic Definition N Σ Number of data points. TOT Σ Sum of data values (wi th their frequencies).
8-14 Statistics aplet When the data set contains an odd number of values, the data set’s median value is no t us ed when calculating Q1 and Q3 in the ta ble above. For exa mple, 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. Two-variable MEAN Σ Mean value of data set. PVAR Σ Population variance of data set. SVAR Σ Sample variance of data set. PSDEV Population standard deviation of data set. SSDEV Sample standard deviati on of data set. MIN Σ Minimum data value in data set. Q1 First quartile: median of values to left of median. MEDIAN Median value of data set. Q3 Third quartile: median of values to right of median. MAX Σ Maximum data value in data set. Statistic Definition (Continued) 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 - (depende nt) values. Σ Y Sum of y -values.
Statistics aplet 8-15 Plotting You can plot: • histogr ams ( ) • bo x -and-whisk er plots ( ) • sca tte r pl ots ( ) . Once you have ente red your data ( ), defined your data set ( ), and defined your F it model for two- variable statistics ( SETUP - SYMB ), you can plot your data. You can plot up to five scatter or box -and-whisker plots at a time. You can plot only one histogram at a time. To pl ot stat ist ical data 1. In S ymboli c vie w ( ) , select ( ) the data sets y ou want to plot . 2 . F or one -var iab le data ( ) , select the plot type in P lot Setup ( SETUP - PLOT ) . Highli ght ST A TPLOT , pr ess , select either Histogram or BoxWhisker , and pres s . 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 relative error for the selected fit. Provides a measure of accuracy for the fit. Statistic Definition (Continued)
8-16 Statistics aplet 3 . Fo r any plot , but espec iall y f or a histogr am, adj ust the plotti ng scale a nd r ange i n the Plot Setup v iew . If yo u find histogr am bars too fat or too thin, y ou can adju st them b y adj usting the HWIDTH setti n g. 4. Pr ess . If y ou hav e not adj ust ed the Plot S etup y ours elf , yo u can try sel e 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 key. 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. Scatter Plot Two-variab le 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.
Statistics aplet 8-17 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 “To choose the fit” on page 8-12. The e xpre ssion 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 v ariable. It is a measure of fit to a linear curve only. Regardless of the Fit model you have chosen, CORR relates to the linear model. Relative 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 relati ve error is stored in a variable named RELERR . The relative error provides a measure of fit accuracy for all fits, and it does depend on the Fit model you have chosen.
8-18 Statistics aplet 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 “Setting up the plot (Plot view setu p)” on page 2-5. Settings unique to the Statistics aplet are as follows: Plot type (1VAR) STATPLOT enables you to specify either 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 specify 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 range HRNG 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 re sulting line is not the regression curve. The order of plotting is according to the ascending order of independent values. 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, chec k that you have the following:
Statistics aplet 8-19 • T he cor r ect or menu labe l on (Numer ic vi ew ) . • T he corr ect fit (r egre ssion model), if the data set is tw o -v ar ia ble . • Only the data sets to compute or plot are chec kmark ed (S ymbolic v ie w) . • T he corr ect plotting r ange. T r y using A uto Scale (instead o f ) , or adju st the plotting par ameters (in Plo t Setup) f or the range s of the ax es and the w idth of histogr am bars ( HWIDTH ). In mode, ensur e that both paired columns contain data, and that they are the same length. In mod e, ensure t hat a paired col umn of frequenc y 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 described in“Exploring the graph” on page 2-7. Statistics aplet’s PLOT view keys K ey Meaning CLEA R 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. Displays ZOOM menu. Turns trace mode on/off. The white box appears n ext to the option when Trace mode is active.
8-20 Statistics aplet Calculating predicted values The functions PREDX and PREDY estimate (predict ) values for X or Y given a h ypothetical 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 , dr aw the r egr ess ion c ur ve f or the data set. 2 . Pres s to mo ve to the r egr essi on c urve . 3 . Pres s and enter the v alue of X . The c urso r jumps to the specif ied point on the curve and the coor dinate displa y sho ws X and the pr edicted v alue of Y . In HOME, • Enter PREDX ( y-value ) to f ind the pr edict ed v alue for the indepe ndent v a r iable giv en a h y potheti cal dependent v alue. • Enter P RED Y( x-value ) to f ind the pr edicted v a lue of the dependent var iable gi v en a h ypothetical independent va ria b le. 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)
Statistics aplet 8-21 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.

Inference aplet 9-1 9 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 Student’s 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 • difference between 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. T his 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 calculator’s on-line help provides a descripti on of what the example data represents. Getting started with the Inference aplet This example describes the Inference aplet’s options and functionality by stepping you through an example using the examp le data for the Z-T est on 1 mean. Open the Inference aplet 1. Open the Inference aplet. Select Inference . The Inference aplet opens in the Symbolic view.
9-2 Infere nce aplet Inference aplet’s SYMB view keys The table below summarizes the options available in Symbolic view. If you choose one of the hypoth esis test s, 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 ≠ . 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 -Test on 1 mean Z-Int: 1 µ , the confidence interval for 1 mean, based on the Normal distribution Z: µ 1 – µ 2 , the Z-Test on the difference of two means Z-Int: µ 1 – µ 2 , the confidence interval for the difference of two means, based on the Normal distribution Z: 1 π , the Z-Test on 1 proportion Z-Int: 1 π , the confidence interval for 1 proportion, based on the Normal distribution Z: π 1 – π 2, the Z-Test on the difference in two proportions Z-Int: π 1 – π 2, the co nfidence 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 Student’s t-distribution T: µ 1 – µ 2 , the T- Test on the difference of two means T-Int: µ 1 – µ 2 , the confidence interval for the difference of two means, based on the Student’s t-distribution
Inference aplet 9-3 Select the inferential method 2. Select the Hypothesis Test inferential method. Select HYPOTH TEST 3. Define the type of test. Z–Test: 1 µ 4. Select an alternative hypothesis. µ< µ0 Enter data 5. Enter the sample stat istics 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 σ Population standard deviatio n Sample mean n Sample size α Alpha level for the test x
9-4 Infere nce aplet By default, each field already contains a value. These values constitu te the example database and are expla ined in the feature of this ap let. 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 va lue 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 varia ble 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
Inference aplet 9-5 A calculator produces the following 6 ran dom numbers: 0.529, 0.295, 0.95 2, 0.259, 0.925, a nd 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 number s 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-vari able statistics. Do this by pressing the fifth menu key until is displayed as its menu label. Calculate statistics 4. Calculate statistic s. 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.
9-6 Infere nce aplet Open Inference aplet 6. Open the Inference aple t and clear cu rrent settings . Select Inference Select inference method and type 7. Select an inference method. Select CONF INTER VAL 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
Inference aplet 9-7 Import the data 10. Import the data from the Statistics aplet. 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. Di splay the confidence interval in the Numeric v iew. 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.
9-8 Infere nce aplet 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 39g hypothesis tests use the Normal Z-distribution or Student’ s t-distribution to calc ulate 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 Η 0 : µ = µ 0 . You select one of the following alternative hypotheses 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 ≠ Field name Definition Sample mean. n Sample si ze. µ 0 Hypothetical population mean. σ Population standard devi ation. α Significance level. x
Inference aplet 9-9 Results The results are: Two-Sample Z-Test Menu name Z-Test : µ 1– 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 ≠ Field name Defini tion Sample 1 mean. Sample 2 mean. n1 Sample 1 size . n2 Sample 2 size . σ 1 Population 1 standard deviation. x1 x2
9-10 Inference a plet Results The results are: One-Proportion Z-Test Menu name Z-Test: 1π 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 : π = π 0 You select one of the following alternative hypotheses against which to test the null hypothesis: σ 2 Population 2 stan dard deviation. α Significance level. Field name Definition Result Descri ption 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 : ππ 0 < H 1 : ππ 0 > H 1 : ππ 0 ≠
Inference aplet 9-11 Inputs The inputs are: Results The results are: Two-Proportion Z-Test Menu name Z-Test : π 1 – π 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 hypothesis against the null hypothesis. The null hypothesis is that the proportion of successes in th e two populations is equal H0: π 1 = π 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. π 0 Population proportion of successes. α Significance level. Result Description Test P Proportion of successes in the sample. Test Z Z- Test statis tic. Prob Probability associated with the Z-Test statist ic. Critical Z Bounda ry value of Z associated with the level you supplied. H 1 : π 1 π 2 < H 1 : π 1 π 2 > H 1 : π 1 π 2 ≠
9-12 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, Η 0 :µ = µ 0 You select one of the following alternative hypotheses 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 Descri ption Test π 1– π 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 ≠
Inference aplet 9-13 Inputs The inputs are: Results The results are: Field name Defini tion Sample mean. Sx Sample standard deviation. n Sample size. µ0 Hypothetical population mean. α Significance level. x Result Description Test T T-Test statistic. Prob Probability associated wi th 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
9-14 Inference a plet Two-Sample T-Test Menu name T-Test: µ 1 – 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 hypotheses 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 ≠ Field name Definition Sample 1 mean. Sample 2 mean. S1 Sample 1 standard deviation. S2 Sample 2 standard deviation. n1 Sa mple 1 si ze. n2 Sa mple 2 si ze. α Si gnificance level. _Pooled? Check this option to pool samples based on their standard d eviations. x1 x2
Inference aplet 9-15 Results The results are: Confidence intervals The confi dence interv al calcul ations that the hp 39g can perform are based on the Normal Z-distribution or Student’s 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 TheT i nputs are: Result De scription Test T T-Test statistic. Prob Probability associated with the T-Test statist ic. Critical T B oundary values o f T associated with the α level that you supplied. Field name Definition Sample mean. σ Population standard deviation. n Sample size . C Confide nce level. x
9-16 Inference a plet Results The results are: Two-Sample Z-Interval Menu name Z-INT: µ1 – µ2 This option uses the Normal Z- distribution to calculate a confidence interval for the difference between the means of two populations, µ 1 – µ 2 , when the population st andard deviations, σ 1 and σ 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 Sa mple 1 si ze. n2 Sa mple 2 si ze. σ 1 Population 1 standard deviation. σ 2 Population 2 standard deviation. C Confidence level. x1 x2 Result Description Critical Z Critical value for Z. µ Min Lower bound for µ 1 – µ 2 . µ Max Upper bound for µ 1 – µ 2 . ∆ ∆
Inference aplet 9-17 One-Proportion Z-Interval Menu name Z-INT: 1 π 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 si ze, n , has a number of successes, x . Inputs The inputs are: Results The results are: Two-Proportion Z-Interval Menu name Z-INT : π 1 – π 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 su ccess count. n Sample size . C Confide nce level. Result Description Critical Z Critical value for Z. π Min Lower bound for π . π Max U pper bound for π . Field name Definition Sample 1 success count. Sample 2 success count. x1 x2
9-18 Inference a plet Results The results are: One-Sample T-Interval Menu name T-INT: 1 µ This option uses the Student’s 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 Sa mple 1 si ze. n2 Sa mple 2 si ze. C Confidence level. Field name Definition (Continued) Result Description Critical Z Critical value for Z. π Min Lower bound for the difference between the proportions of succes ses. π Max Upper bound for the difference between the proportions of succes ses. ∆ ∆ Field name Definition Sample mean. Sx Sa mple standard deviatio n. n S ample size. C Confidence level. x1
Inference aplet 9-19 Results The results are: Two-Sample T-Interval Menu name T-INT: µ 1 – µ 2 This option uses the Student’s t-distribution to calculate a confidence interval for the difference between the means of two populations, µ 1 – µ 2, when the population standard deviations, s1 and s2, are unknown. Inputs The inputs are: Result Description Critical T Critical value for T. µ Min Lower bound for µ . µ Max Upp er 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 Confide nce level. _Pooled Whether or not to pool the samples based on their stand ard deviations. x1 x2
9-20 Inference a plet Results The results are: Result Description Critical T Critical value for T. µ Min Lower bound for µ 1 – µ 2 . µ Max Upper bound for µ 1 – µ 2 . ∆ ∆
Using th e Finance So lver 10-1 10 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 resulting screen shows the different elements involved in the solution of financial problems with your hp 3 9g calculator. Background information on and applications of financial calculations are provided next. Background The Finance Solver application 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 combined amount earns interest at a certain rate.
10-2 Using the Finance Sol ver 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 someti me in the future. A dollar today can be inv ested at a certain interest ra te and generate a return that the s ame dollar in the future cannot. This TVM pri nciple und erlies th e notion of int erest rate s, 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 representing the compounding periods. Arrows represent the cash flow s, which could be positive (upward arrows) or negati ve (downward arrows), depending on the point 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 of 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 Pres ent value (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 }
Using th e Finance So lver 10-3 modes: Begin mode and End mode. The following cash 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 iz e d 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 co mpounding 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.
10-4 Using the Finance Sol ver Performing TVM calculations 1. Launch the F inanc ial Sol v er as indicated at the beginning of this secti on. 2 . Use the ar r o w ke ys to highligh t the diffe r ent f ields and enter the kno wn v ari ables in the TVM calc ulations , pr essing the soft -menu k ey after enter ing each kno wn value . Be sur e that value s ar e enter ed for at least f our of the fi ve TVM var ia bles (namel y , N , I%YR, PV , P MT , and FV). 3 . If necessar y , enter a differ ent value for P/YR (default v alue is 12 , i.e ., monthly pa yments). 4. Pres s the k e y to change the P ay ment mode (Beg or End) as re quired . 5 . Use the arr ow k e ys to highligh t the T VM va ri able you w i sh to sol v e fo r and pres s the soft-monu ke y . PMT The periodic payment amount. The payments are the same amount each period and the TV M calculation assumes that no payments are skipped. 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.
Using th e Finance So lver 10-5 Example 1 - Loan calculations Suppose you finance the purcha se of a car with a 5-year loan at 5.5% annual interest, compounded monthly. The purchase price of the car is $19,500, and the down payment is $3,000. What are the required monthly p a y m e n t s ? W h a t i s t h e l a r g e s t l o a n y o u c a n a f f o r d i f y o u r maximum monthly payment is $300? Assume that the payments start at the end of the first period. Solution. The following cash flow diagram illustrates the loan calculations: Start the Finance Solver, selec ting P/YR = 12 and End payment option. • Enter the kn o w n TVM var iables as sh o w n in the diagr a m abo ve . Y our input f orm should look as fo llo w s: • Hi ghlighting the P MT fi eld , pre ss the soft menu k ey to obtain a pa yment of -315 .17 (i.e ., P MT = -$315 .17) . • T o deter mine the max imum loan possible if the monthl y pay ments ar e only $3 00, t y pe the value - 300 in the P MT f ield , highlight the PV f ield , and pr ess the soft men u k e y . The r esulting value is PV = $15, 7 05 .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 = ?
10-6 Using the Finance Sol ver Example 2 - Mortgage with balloon payment Suppose you have taken o ut 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 b alloon payment. Find the size of the balloon payment -- the value of the mortgage after 10 years of payment. Solution. The following cash flow diagram ill ustrates t he case of the mortgage with balloon payment: • Start the F inance Solv er , s electing P/YR = 12 and End pa yment opti on . • Enter the kno w n T VM var iables as sho wn in the diagr am abov e. Y our inpu t fo rm , f or calc ulating monthl y pa ymen ts fo r the 30 -yr mortgage , should look as fo llo w s: • Highlighting t he P M T fi eld, pr ess th e soft menu k ey to obt ain a pay ment of -9 48.10 (i .e ., P MT = -$9 48.10) • T o deter mine 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 ess the soft menu k e y . The r esulting v alue is FV = -$12 7 ,164.19 . The negativ e value indicates a p a yment fr om th e homeo wner . Check that the r equired balloo n pay ments at the end of 20 y ears (N=2 4 0) 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 = ?
Using th e Finance So lver 10-7 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. Start the F inance Sol v er as indicated at the beginning of t h is sect ion. 2 . Set the f ollo w ing T VM v ar iables: a Numbe r of pa y ments pe r yea r (P/YR) b P ay ment at beginning or end of per iods 3 . Stor e value s for the TVM var iables I%YR , PV , P MT , and FV , whi ch def ine the pay ment schedule . 4. Press the soft menu k ey and en ter the number o f pay ments to amorti z e in this batch . 5 . Pres s the soft menu ke y to amortiz e a batch o f pa yme nts . The calc ulator w ill pro vi de for y ou the amount applied to inter est, to pr inc i pal, 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 PA YMENTS field, and press the soft menu key to produce the results shown to the right. To continue amortizing the loan: 1. Press the sof t menu k ey to stor e th e new balance after the pr ev ious amorti z ation as PV . 2 . Enter the numbe r of pa yments t o amorti z e in the new batch .
10-8 Using the Finance Sol ver 3 . Pres s 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 pa y ment p-1 . 2 . Stor e the new balance in PV using the soft menu k ey . 3 . Amortiz e the se ri es of pay ments starting 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 by using after each amortization.
Using mathemati cal functions 11-1 11 Using math ematical func tions Math functions The hp 39g contains many math functions. 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 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 press , yo u see the menu lis t of Math categor ies in the left column and the cor r espo nding func tions o f the highli ghted cate gory in the r ight column . The menu k e y indicate s that the MA TH FUNCTIONS menu lis t is acti v e . To select a function 1. Pres s to displa y the MA TH menu . The categori es appear in alp habetical order . Pres s or to sc ro ll thr ough the categor ie s. T o skip dir ectl y to a category , pres s the fir st letter of the category’s name . Note: Y ou do not need to pr ess first .
11-2 Using math ematical functions 2 . The list o f func tions (on the r ight) appli es to the c urr entl y highligh ted category (on the left). Use and to sw itch between the categor y list and the func tion lis t . 3 . Highlight the name of the func tio n yo u wa nt and pr ess . This copi es the f uncti on name (and an initial par enthesis, if appr op r iate) to the edit line . Function categories Math functions by category Syntax Each function’s definition incl udes i ts syntax, that is, the exact order and spelling of a function’s 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. π F or a desc ripti on, s ee “ π ” on page 11-8. ARG F or a desc ripti on, see “ ARG ” on page 11- 7. F or a desc ripti on, s ee “ ” on page 11- 7 . AND F or a desc r iption , see “ AND” on page 11-19. ∂ • Cal cul us • Comp l ex num b ers • Const ant • Hyperb ol ic trigonometr y (Hy perb .) • Li s t s • Lo o p • Matri ces (Matrices) • Po l y n o m i a l (P ol ynom .) • Probabil it y (Prob . ) • R eal numbers (Real) • Tw o - v a r i a b l e statistics (Stat- T wo) • Sym b o l ic • Te s t s • T rigonometr y (T r ig)
Using mathemati cal functions 11-3 Keyboard functions The most frequently used functions are availa ble directly from the keyboard. Many of the keyboard functions also accept complex numbers as arguments. ,, , Add, Subtract, Multiply, Di vide. Also acc epts complex numbers, lists and matrices. va l ue 1 va l u e 2 , etc. e x Natural exponential. Also accepts complex numbers. e^ val u e Example e^5 re t u rn s 148.41315910 3 Natural logarithm. Also accepts complex numbers. LN ( val u e ) Example LN(1) re t u rn s 0 ! F or a d esc ription , see “CO MB(5,2) r eturns 10. That is , ther e are ten diff ere nt w ay s that fi ve things can be combined tw o at a time.!” on page 11-12. ∑ F or a d esc ription , see “ Σ ” on page 11-10. EEX F or a d esc ription , see “Sc ientifi c notati on (po w ers of 10)” on page 1- 20. F or a d esc ription , see “ ” 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. ∫ ∫ x 1 –
11-4 Using math ematical functions 10 x Exponential (antilogarithm). Also acc epts complex numbers. 10^ val u e Example 10^3 r eturns 1000 Common logarithm. Also accepts co mplex numbers. LOG ( val ue ) 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 ue ) COS ( val ue ) TAN ( val ue ) Example TAN(45) r eturns 1 (Degr ees mode) . ASIN Arc sine: sin –1 x. Output range is from –90° to 90°, – π /2 to π /2, or –100 to 100 grads. Inputs and outputs depend on the current angle format. Also accepts complex numbers. ASIN ( val ue ) Example ASIN(1) r eturns 90 (Degr ees mode) . ACOS Arc cosine: cos –1 x . Output range is from 0° to 180°, 0 to π , or 0 to 200 gr ads. Inputs 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 ue ) Example ACOS(1) ret u rn s 0 (Degr ees mode) . 1 – x 1 ≤≤
Using mathemati cal functions 11-5 ATAN Arc tangent: tan –1 x . Output range is from –90° to 90°, 2 π /2 to π /2, or –100 to 100 grad s. Inputs and outputs depend on the current an gle format . Also acce pts complex numbers. ATAN ( valu e) Example ATAN(1) re t u rn s 45 (D egr ees mode) . Square. Also accept s complex numbers. va l u e 2 Example 18 2 r etur ns 324 Square root. Also accepts complex numbers. val ue Example r etur ns 18 Negation. Also accepts complex numbers. – val u e Example -(1,2) r etur ns (-1,-2) Power ( x raised to y ). Also accepts comple x numbers. va l ue ^ po w er Example 2^8 r etur ns 256 ABS Absolute value. For a complex number, this is . ABS ( val u e ) ABS (( x ,y )) Example ABS(–1 ) r etur ns 1 ABS((1,2)) ret u r n s 2.2360679775 324 x 2 y 2
11-6 Using math ematical functions Takes the n th root of x . ro ot NTHROOT va lu e Example 3 NTHROOT 8 r eturns 2 Calculus functions The symbols for differentiation and integration are available directly form the k eyboard— and S respectively—as well as from the MATH menu. Differentiates expr ession with respect to the variable of differentiation. From the command line, use a formal name (S1, etc.) for a non-numeric result. See “Finding derivatives” on page 11- 21. va ria b le ( ex p re ss i on ) 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 varia ble 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 “Using f or mal var iables ” on page 11- 20 f or fur t he r de ta il s. Example (0,s1,2*X 3,X) finds the indefinite result 3*s1 2*(s1^2/2) See “T o find the indef inite integr al using f ormal v ari ables ” on page 11- 2 3 for mor e infor mation on finding inde finite integr als. n ∂ ∂ ∂ ∫ ∫ ∫
Using mathemati cal functions 11-7 TAYLOR Calculates the n th order Taylor polynomial of expression at the point where the given variable = 0. TAYLOR ( e xpre ssion , v ari able , n ) Example TAYLOR(1 sin(s1) 2 ,s1,5) w ith Radians angle measur e and F rac tion n u mber f ormat (s et i n 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 (Degree s 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 complex 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
11-8 Using math ematical functions Constants The hp 39g has an internal numeric repr esentation for these constants. e Natural logarithm base. Internally represented as 2.71828182846. e i Imaginary value for , the co mplex number (0,1). i MAXREAL Maximum real number. Internally represented as 9.99999999999 x 10 499 . MAXREAL MINREAL Minimum real number. In ternally represe nted as 1 x 10 -499 . MINREAL π Internally represented as 3.14159265359. π Hyperbolic trigonometry The hyperbolic trigonometry functions can also take complex numbers as arguments. ACOSH Inverse hyperbolic cosine : cosh –1 x . ACOSH ( val ue ) ASINH Inverse hyperbolic sine : sinh –1 x . ASINH ( val ue ) ATANH Inverse hyperbolic tangent : tanh –1 x . ATANH ( val ue ) COSH Hyperbolic cosine COSH ( val ue ) SINH Hyperbolic sine. SINH ( val ue ) 1 –
Using mathemati cal functions 11-9 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) EXP Natural exponential. This is more 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 ( valu e) LNP1 Natural log plus 1 : ln( x 1 ). This is more accurate than the natural logarithm function when x is close to zero. LNP1 ( valu e) List functions These functions work on list data. See “List functions” on page 14-6. 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( expression , var iable , initial value , #times ) Example ITERATE(X 2 ,X,2,3) r eturns 256 e x e x 1 –
11-10 Using mathe matical functions RECURSE Provides a method of defini ng a sequence without using the Symbolic view of the Seque nce aplet. I f used with | (“where”), 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 ial-calculating f uncti on named U1. When y ou enter U1(5) , for e xam ple , the functi on calc ulates 5! (120 ). Σ Summation. Finds the sum of expr ession with respect to variable from i nitialvalue to finalvalue. Σ ( varia b le = initial value , fi n a lv a l u e, expr essi on ) Example Σ (C=1,5,C 2 ) r eturns 5 5 . Matrix functions These functions are for matrix data stored in matrix variables. See “ Matrix fu nctions and commands” on page 13-9. Polynomial functions Polynomials are products of constants ( coefficients ) and variables raised to powers ( terms ). POLYCOEF Polynomial coefficients. Retu rns the coefficients of the polynomial with the specified roots . POLYCOEF ([ r oots ]) Example T o f ind the poly nomial w ith r oots 2 , –3, 4 , –5: POLYCOEF([2,-3,4,-5]) r eturns [1,2,-25, -26,120] , r e pr esenting x 4 2x 3 –25x 2 –26x 120 .
Using mathemati cal functions 11-11 POLYEVAL Polynomial evaluation. Evaluates a polynomial with the specified coefficients for the value of x . POLYEVAL([ coeff ici ents ] , va l u e ) Example Fo r x 4 2x 3 –25x 2 –26x 120 : POLYEVAL([1,2,-25,-26,120], 8) re t u r n s 3432 . POLYFORM Polynomial form. Creates a polynomial in vari able1 from expression. POLYFORM ( expression , var iable1 ) Example POLYFORM((X 1)^2 1,X) ret u r n s X^2 2*X 2 . POLYROOT Polynomial roots. Returns the roots for the n th-order polynomial with the specified n 1 coefficients . POLYROOT ([ coeffi ci ents ]) Example Fo r x 4 2x 3 –25x 2 –26x 120 : POLYROOT([1,2,-25,-26,120]) r etur ns [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. It is better to store the results of POLYROOT to a matrix. For examp le, POLYROOT([1,0,0,-8] M1 will store th e three c omplex cube roots of 8 t o matrix M1 as a complex vec tor. Then you can see th em easil y by going to the Matrix Catalog. and access them individually in calculations by referring to M1(1 ), M1(2) etc.
11-12 Using mathe matical functions Probability functions COMB Number of combinations (wi thout 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 h at is, ther e are te n differ ent wa ys that fi ve things can be comb ined two at a time .! Factorial of a positive integer. For non-integers, ! = Γ (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 h at is, ther e are 20 differ ent permutati ons of fi ve things tak en t w o at a time . RANDOM Random number (between zero and 1 ). Produced by a pseudo-random number sequen ce. 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 calculator, 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-Square d Probability given degrees of freedom, evaluated at value . Returns the probability that a χ 2 random variable is greater than value. UTPC ( degr ees , valu e )
Using mathemati cal functions 11-13 UTPF Upper-Tail Snedecor’s F Probability given numerator degrees of freedom and denominator degre es 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 , de nomina tor , val u 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 th e standard deviation . UTPN ( mean, varia n c e, valu e) UTPT Upper-Tail Student’s 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 greate r than or equal to value . CEILING ( val u e ) Examples CEILING(3.2) r eturns 4 CEILING(-3.2) r eturns -3 DEG → RAD Degrees to radians. Converts value from Degrees angle format to Radians a ngle format. DEG →RAD ( val u e ) Example DEG →RAD( 180) r eturns 3.141592 65359 , the va l ue o f π . FLOOR Greatest inte ger less than or equal to value . FLOOR ( valu e) Example FLOOR(-3.2) r eturns -4
11-14 Using mathe matical functions FNROOT Function root-finder (lik e the Solve aplet). Finds the value for the given variable at which expression most nearly evaluates to zero. Uses guess as initial estimate. FNROOT ( e x pr essi on , var iable , guess ) Example FNROOT(M*9.8/600-1,M,1) r eturns 61.2244897959 . FRAC Fractional part. FRAC ( val ue ) Example FRAC (23.2) r eturns .2 HMS → Hours-minutes-seconds to deci mal. Converts a n umber 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 → ( H.M MSSs ) Example HMS → (8.30) r eturns 8.5 → HMS Decimal to hours-minutes-seco nds. Converts a number or expression in x.x format (number of hours or degrees with a decimal fraction) to H.MMSSs format (time or angle up to fractions of a second). → HMS ( x.x) Example → 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 ( val ue ) Example MANT(21.2E34) r eturns 2.12
Using mathemati cal functions 11-15 MAX Maximum. The greater of two values. MAX ( val u e 1 , val u e2 ) Example MAX(210,25) r eturns 210 MIN Minimum. The lesser of two values. MIN ( val u e 1 , val u e2 ) Example MIN(210,25) re t u r n s 25 MOD Modulo. The remainder of value1 / value2. va l ue 1 MOD va l u e 2 Example 9 MOD 4 r etur ns 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( y–x )/ x . % CHANGE( x , y) 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 25 0 RAD → DEG Radians to degrees. Converts value from radians to degrees. RAD →DEG ( valu e ) Example RAD →DEG( π) r eturns 180
11-16 Using mathe matical functions 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 7.68 ROUND (0.0036757,-3) r eturns 0.00368 SIGN Sign of value . If positive, the result is 1. If negative, –1. If zero, result is zero. For a complex number, this is the unit vector in the direction of the number. SIGN ( val ue ) SIGN (( x, y)) Examples SIGN (–2) re t u rn s –1 SIGN((3,4)) r eturns (. 6,.8) TRUNCATE Truncates value to decimal plac es . Accepts complex numbers. TRUNCATE ( valu e , places ) Example TRUNCATE(2.3678,2) r etur ns 2.36 XPON Exponent of value . XPON ( val ue ) Example XPON(123.4) r eturns 2 Two-variable statistics These are functions for use with two-variable statistics. See “Two-variable” on page 8-14.
Using mathemati cal functions 11-17 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 “Test functions” on page 11-18.) exp ress i o n 1 = expr ession2 ISOLATE Isolates the first occurrence o f variable 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 r n s -4 ISOLATE(A B*X/C,X) r eturns - (A*C/B) LINEAR? Tests whether express ion is linear for the specified variable . Returns 0 (false) or 1 (true). LINEAR?( expression , var iable ) Example LINEAR?((X^2-1)/(X 1),X) r etur ns 0 QUAD Solves quadr atic expres sion= 0 for variable and returns a new expression, where variable = newexpression. The result is a general solution that represents both positive and negative solutions by in cluding the formal variable S1 to represent any sign: or – . QUAD( e xpressi on , va ria b l e ) Example QUAD((X -1) 2 -7,X) r etur ns (2 s1*5.29150262213)/2
11-18 Using mathe matical functions QUOTE Encloses an expression that should not be evaluated numerically. QUOTE( exp re s s io n ) Examples QUOTE(SIN(45)) F1(X) stor es the e xpre ssion S IN(4 5) r a ther than t he value of SIN( 45 ) . Another meth od is to enclo se the e xpr ession in single quotes. Fo r e xa 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=value1, v ar 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 l u e1 < val u e2 ≤ Less than or equal to. Returns 1 if true, 0 if false. va l u e1 ≤ val u e2 = = Equals (logical test). Returns 1 if true , 0 if false. va l u e1 == va l ue 2 ≠ Not equal to. Returns 1 if true, 0 if false. va l u e1 ≠ val u e2 > Greater than. Returns 1 if true, 0 if false. va l u e1 > val u e2
Using mathemati cal functions 11-19 ≥ Greater than or equal to. Returns 1 if true, 0 if false. va l ue 1 ≥ va l u e 2 AND Compares value1 and value2 . Return s 1 if they are both non-zero, otherwise returns 0. va l ue 1 AND va l u e 2 IFTE If expression is true, do the trueclause ; if not, do the falseclause. IFTE( e xpressi on , truec lause , fals ecla use ) Example IFTE(X>0,X 2 ,X 3 ) NOT Returns 1 if value is zero, otherwise return s 0. NOT val ue OR Returns 1 if either value1 or value2 is n on-zero, otherwise returns 0. va l ue 1 OR va l u e 2 XOR Exclusiv e OR. Returns 1 if either value1 or value2 —but not both of them—is non-zero, otherwise r eturns 0. va l ue 1 XOR va l u e 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 ) ACSC Arc cosecant. ACSC ( valu e) ASEC Arc secan t. ASEC ( valu e) COT Cotangent: cos x /sinx . COT ( val u e ) CSC Cosecant: 1/sin x CSC ( val u e )
11-20 Using mathe matical functions SEC Secant: 1/cos x . SEC ( val ue ) Symbolic calculations The hp 39g has the ability to perform symbolic calculations, for example, symbolic integration and differentiation. You can perform symbolic calculations in HOME and in the Function aplet. In HOME When you perform calculations tha t contain normal variables, the calc ulator substitutes values for any variables. For example, i f you enter A B on the command line and press , the calculator retrieves the value s 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 39g 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 39g does not carry out any substitutions. You can mix formal names an d real variables. Evaluating (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 follow s: (The | symbol is in the CHARS menu: press CHARS . The = sign is listed in th e MATH menu un der Symbolic functions.)
Using mathemati cal functions 11-21 Symbolic calculations in the Function aplet You can perform symbolic operations i n the Function aplet’s Symbolic view. For example, to find the derivative of a function in the Function aplet’s 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 “To find derivatives in the Function aplet’s Symbolic view ” on page 11-22 for an example. Finding derivatives The hp 39g can perform symbolic differentiatio n on some functions. There are two ways of using the hp 39g to find derivatives. • Y ou can perfor m differ entiati ons in HOME b y using the f ormal 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 , th e differentiation function su bstitutes the value that X holds, and returns a numeric result. For example, consider the function: 1. Enter the diffe r enti ation f uncti on ont o the command line , subs tituting S1 in place of X . S1 S1 2 S1 2 . Ev aluate the func tio n. dx x ( 2 ) sin ( 2 x () ) cos
11-22 Using mathe matical functions 3 . Sho w the r esult . To find derivatives in the Function aplet’s Symbolic view To find the derivative of the fu nction in the Function aplet’s 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 plet’s S y mbolic v iew and def ine F1. 2 2. D e f i n e F 2 ( X ) as the der i vati ve o f F(1) . F1 3 . Select F 2( X ) and eva l u a t e i t. 4. Pr ess to display the r esult . Note: Use the arro w ke ys to v iew the entir e functi on . | Y ou could als o ju st def ine . hp 39g x 2 () sin 2 x cos hp 39g F 1 x () xx 2 () 2 x () cos sin () d =
Using mathemati cal functions 11-23 To find the indefinite integral using formal variables F or ex ample, to f ind t he ind ef inite i ntegral of use: 1. Enter the func tion . 0 S1 3 X 5 X 2 . Sho w the r esult for mat. 3 . Press to close the sho w w indow . 4. Copy the r esult and eva l u a te. Th us , substit uting X for S1, it can be seen th at: This result is derived from substituting X = S1 and X = 0 into the original expression found in ste p 1. However, substituting X = 0 will not always evaluate to zero and may result in an unwanted constant. To see this, consider: 3 x 2 5 – x d ∫ () ∫ − X X S , 5 3 , 1 , 0 2 hp 39g 3 x 2 5 – x 5 x –3 x 3 3 ---- - X ∂ ∂ X () -------------- -      = d ∫ x 2 – () 4 x x ( 2 ) 5 – 5 ------------------- = d ∫
11-24 Using mathe matical functions The ‘extra’ constant of 6.4 results from the substitution of into ( x –2 ) 5 /5 , and should be disregarded if an indefinite integral is required. x 0 =
Variables an d memory manage ment 12-1 12 V ar iables and memor y manag ement Introduction The hp 39g has approximately 232K 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 39g 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 calculator’s 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 editor, 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.
12-2 Variables and memory managemen t 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 o re. 2. P r e s s 3 . Enter a name f or the va ria b le. 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 command line, then store it. 1. P erfo rm the calc ulation f or the r esult y ou w a nt to s tor e . 3 86 3 2 . Mov e the highlight to the r esult y ou wish t o stor e . 3 . Press to cop y the result t o the command line . 4. Pr ess .
Variables an d memory manage ment 12-3 5 . Enter a name f or the v ar iable . A 6. P re s s to stor e the resu lt . 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 variable’s 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 variable’s value in the calculation: 65 A
12-4 Variables and memory managemen t 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 A RS men u . 2 . Use the arr o w k ey s or pres s the alpha k e y of the f i rs t letter in the category to select a v ari able category . Fo r e xa 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 . Mov e the highlight to the v a r iab les column . 4. Use the arr o w k e y s to se lect the v ar iable that y ou w ant . F or ex ample , to select the M2 v a r iable , pres s .
Variables an d memory manage ment 12-5 5 . Choos e whether t o place the var iable name or the v ari able v alue on the command line . – Pres s to indicate that y ou w ant the v ari able ’s c ontents t o appear on the command line . – Pres s to indicate that y ou wan t the v ari able ’s name to appear on the command line . 6 . Pres s to place the v alue or name on the command line . The s elect ed objec t appears on the command line . Note: T he V AR S menu can also be us ed to enter the names or va lues of var iables into pr ograms. 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. Di spla y the L ist Ca talog. LIST to select L1 2 . Enter the data for L1. 88 90 89 65 70 3 . Retur n to the List C atalog to c reate L2 . LIST to select L2
12-6 Variables and memory managemen t 4. Enter data for L2 . 55 48 86 90 77 5. P re s s to access HOME . 6 . Open the v ar iable men u and selec t L1. 7 . Cop y it to the command line . Note: Because th e option is hi ghlighted , the var iable ’s name , r ather than its contents , is copied to the command line . 8. Insert the operato r and select the L2 v aria ble fr om t h e Li s t va ria b l e s. 9 . S tor e the ans w er in the L ist catalog L3 v aria ble . L3 Note: Y ou can also type list name s dir ectl y fr om the k e yboar d.
Variables an d memory manage ment 12-7 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 mat rices in va riab les other than M0 to M 9. Ca te- 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 typ ing (r ,i) , wher e r r epres ents the r e al par t , and i r epr esen ts the imaginar y par t . Graphic G0 to G9 See “Graphic commands” on page 16 - 20 for more information on storing graphic objects via programming commands. See “To store into a graphics variable” on page 15 -5 for more information on storing graphic object via the sketch view. Library Aplet library variables 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 matrices 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 Program variables store programs. Real A to Z and θ. Fo r ex a m p l e , 7 . 4 5 A .
12-8 Variables and memory managemen t Aplet variables Aplet variables store values that are unique to a particular aplet. These include s ymbolic 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 aplet that contains the v aria ble y ou w ant to re c a l l. 2 . Pr ess to displa y the V ARS men u . 3 . Use the ar r o w k ey s to select a v ari able category in the left column, then press to access th e var iables in the ri ght column. 4. Use the arr o w k ey s to selec t a var iable in the r igh t column. 5 . T o copy the name of the v ar iable o nto the edit line , pr ess . ( is the def ault se tting. ) Categor y A v ailabl e names Function F0 to F 9 (Symbolic view). See “Function aplet variab les” on page R-7. Parametric X0, Y0 to X9, Y9 (Symbolic view). See “Parametric aplet va riables” on page R-8. Polar R0 to R9 (Symbolic view). See “Polar aplet variab les” on page R-9. Sequence U0 to U9 (Symbolic view). See “Sequence aplet variables” on page R-10. Solve E0 to E9 (Symbolic view). See “Solve aplet variab les” on page R-11. Statistics C0 to C9 (Numeric view). See “Statistics aplet v ariables” on page R-12.
Variables an d memory manage ment 12-9 6 . T o copy the v alue of the v ar iable in to the edit line , pres 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. Start the Memor y Manager . A list of var iable 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 eac h categor y , the memor y it uses , and the per centage of the total memory it uses . 2 . Select the cat egory with w hic h you w ant to wo rk and pr ess . Memory Manager display s memory details of v aria bles w ithin the category . 3 . T o delete v ar iables in a catego r y : – Pres s to de lete the s elected v ari able . – Press CLEAR to delete all v aria bles in the selec ted category .

Matrices 13-1 13 M atrices Introduction You can perform matrix calc ulation s in HOME and in programs. The matrix and each row of a matr ix 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-dimensional ar rays. 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
13-2 Mat rice s 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 matrices—named or unnamed—-in HOME. For example, the command: POLYROOT([1,0,–1,0]) XM1 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 –0 = 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 39g or a disk drive. See “Sending and receiving aplets” on page 17-4. Receiv es a matrix f rom anothe r hp 39g or a disk d rive. See “Sending and receiving ap lets” on page 17-4. Clears the highlighted matrix. CLEAR Clears all matrices. or Moves to the end or the be ginning of the catalog.
Matrices 13-3 To create a ma trix in the Matrix Catalog 1. Press MATRIX to open the Matr i x Catalog . The Matri x catalog lists the 10 av ailable matri x var iables, M0 to M9 . 2 . Highli ght the matr i x var iable name y ou want to use and pres s . 3 . Select the ty pe of matr ix to cr eate . – For a v ector (o ne -dim ensional array) , sele ct Real vector or Complex vector . Certain oper atio ns ( , – , CRO SS ) do not r ecogni z e a one-dime nsi onal matr i x as a v ec tor , so t hi s sel ect ion i s i mpor t ant. – For a ma trix (two -dimension al array) , sele ct Real matrix or Complex matrix . 4. F or each elemen t in the matri x, type a n umber or an e xpr ession , and pres s . (The e xpr ession ma y not cont ain sy mbolic v ar iable name s.) For c o m p l e x n u m b e rs , ente r eac h nu mber in comple x fo rm; that is , (a, b) , wher e a is the r eal par t and b is the imaginar y part. Y ou mu st include the par entheses and the comma . 5 . Use the c ursor k ey s to mov e to a differ ent r ow or column . Y ou can change the dir ection o f the highligh t bar by pre ssing . The menu ke y toggles betw een the f ollo w ing thr ee options: – spec ifi es that the c u rs or mo v es to the cell belo w the cur r ent cell w hen y ou pre ss . – specif ies that the c ursor mo v es to the cell t o the r ight o f the c urr ent cell w hen y ou pres s . – spec if ie s that the c urso r sta ys in the c urr ent cell when y ou pr ess . 6 . When done , pr ess MATRIX to see the Matr i x catalog , or pr ess to r eturn to HO ME . The matr i x entr ies ar e aut omaticall y st or ed .
13-4 Mat rice s A matrix is listed with two dimensions, even if it is 3×1. 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 9 g calc ulators ’ infr ared po rts. 2 . Open the Matri x catalogs on both calc ulators. 3 . Highlight the matri x to send . 4. Pr ess . 5 . Pres s on the r e cei ving calculat or . 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 following 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. Deletes the highlighted cells, row, or column (you are prompted to make a choice). CLEAR Clears all elements from the matrix.
Matrices 13-5 To display a matrix • In the Matri x catalog ( MATRIX ) , highlight the matri x name and pr ess . • In HOME , ent er the name of the matr ix v ar iable 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. Enter the matr ix in the edit line . Start and end the matri x and each r o w with square br ack ets (the shifte d and k e y s) . 2 . Sepa r ate each element an d each r o w w ith a comma. Ex ample: [[1,2],[3,4]] . 3 . Pre ss to en ter and dis play the matr ix . The left screen below shows the matrix [[2.5,729],[16,2]] being stored into M5. The screen on the right shows the vector [66,33,11] 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. Moves to the first row, last row, first column, or last column respectively. K ey Meaning (Con tinued)
13-6 Mat rice s 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 ( , –, ×, / ) with matrix arguments. Division left-multiplies by the inverse of the divisor. You can enter the matrices themselves or enter the names of stored matrix variables. The matrices can be real or complex. For the next four example s, store [[1,2],[3,4]] i n t o M 1 a n d [[5,6],[7,8]] into M2. Example 1. Cr eate the fir st matr ix . MATRIX 1 2 3 4 2 . Create the s econd matr i x. MATRIX 5 6 7 8
Matrices 13-7 3 . Add the matr ices that yo u cr e 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 divide by a square matrix For division of a matrix or a vecto r by a square matrix, the number of rows of the dividend (or the number of elements, if it is a vector) must equal the number of rows in the divisor. This operation is not a mathematical division: it is a left- multiplication by the inverse of the divisor. M1/ M2 is equivalent to M2 –1 * M1.
13-8 Mat rice s 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 –1 . 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 Matri x catalog a nd cr e ate a ve ct or . MATRIX 2 . Create the vec tor o f the constan ts in the linear s ystem . 5 7 1 3 . Retur n to the Matr ix Catal og. MATRIX In this e x ample , the v ector y ou cr eated is listed as M1. 2 x 3 y 4 z 5 xy z – 7 4 xy –2 z 1 = = =
Matrices 13-9 4. Create a ne w matri 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 you c reat ed is listed as M2 . 6 . Retur n to HOME and e nter the calc ulation to left-multipl y the constants v ector b y the in ve rse o f the coeff ic ien ts matr i x . M2 x –1 M1 The result is a vector of the solutio ns: • • • An alternative method, is to use the RREF function. See “RREF” on page 13-12. Matrix functions and commands About functions • F unction s can be used in an y aplet or in HOME . The y ar e listed in the MA TH menu unde r the Matri x category . The y can be used in mathematical e xpr essions —primar ily in HO ME—as w ell as in pr ogr ams. x 2 = y 3 = z 2 – =
13-10 Matri ces • F u ncti ons al wa ys pr oduce and displa y a re sult . The y do not c hange any st or ed var iables , such as a matri x va ria b le. • F uncti ons hav e argumen ts that are enc losed in pare ntheses and separ ated by commas; f or e xample , CROSS ( vect or 1 , ve c to r 2 ) . The matr ix in put can be either a matr ix v ar iable name (suc h as M1 ) or the actual matr i x data inside br ack ets. F or e xample , CROSS(M1,[1,2]) . About commands Matrix commands are listed in the CMDS menu ( CMDS ), in the matrix category. See “Matrix commands” on page 16-23 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 u mber of the r ow (counting fr om the top , starting wi th 1) or the number of the column (counting fr om the left , starting with 1). • The ar gument matr ix can r efe r to e ither a ve ctor o r a matr i x. Matrix functions COLNORM Column Norm. Finds the maximum value (over all columns) of the sums of the absolute values of all elements in a column. COLNORM ( matr ix ) COND Condition Number. Finds the 1-norm (column nor m) of a square matrix . COND ( matr ix ) CROSS Cross Product of vector1 with vector2 . CROSS ( ve ct o r 1 , ve c to r 2 )
Matrices 13-11 DET Determinant of a square matrix . DET ( matr ix ) DOT Dot Product of two arrays, matrix1 matrix2 . DOT ( matr ix1, matr i x2 ) EIGENVAL Displays the eigenvalue s in vector form for matri x . EIGENVAL ( matr ix ) 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 ( matr ix ) IDENMAT Identity m atrix. Creates a square matrix of dimension size × size whose diagonal elements are 1 an d off- diagonal elements are zero. IDENMAT ( si z e ) INVERSE Inverts a square matrix (real or complex). INVERSE ( matr ix ) LQ LQ Factorization . Factors an m × n matrix into three matrices: {[[ m × n lowertrapezoidal ]],[[ n × n orthogona l ]], [[ m × m permutation ]]}. LQ ( matr i x ) LSQ Least Squares. Displays the minimum no rm least squares matrix (or vector ). LSQ ( matr ix1, matr i x2 ) LU LU Decomposition. Factors a square matrix into three matrices: {[[ lowertriangular ]],[[ uppertriangular ]],[[ permutation]] } The uppertriangular has ones on its diagonal. LU ( matr i x ) MAKEMAT Make Matrix. Creates a matrix of dimension ro ws × columns , using expr ession to calculate each element. If expression contains the variables I and J, then the
13-12 Matri ces calculation for each element substitutes the current row number for I and the current column number for J. MAKEMAT ( ex p re ss io n , rows, columns) Example MAKEMAT(0,3,3) r eturns a 3×3 z er o matri x, [[0,0,0],[0,0,0],[0,0,0]] . QR QR Factorization. Factors an m × n matrix into three matrices: {[[ m ×m orthogonal ]],[[m ×n uppertrapezoidal ]], [[ n × n permutation ]]}. QR ( matr ix ) RANK Rank of a rectangular matrix . RANK ( matr ix ) ROWNORM Row Norm. Finds the maximum value (over all rows) for the sums of the absolute values of all elements in a row. ROWNORM ( matri x ) RREF Reduced-Row Echelon Form. Changes a rectangular matrix to its reduced row-echelon for m. RREF ( matr ix ) SCHUR Schur Decomposition. Factors a square matrix into two matrices. If matrix is real, then the result is {[[ orthogonal ]],[[ upper-quas i triangular ]]}. If matrix is complex, then the result is {[[ unitary ]],[[ upper-triangular ]]}. SCHUR ( matri x ) SIZE Dimensions of matrix . Returned as a list: {rows,columns}. SIZE ( matr ix ) SPECNORM Spectral Norm of matrix . SPECNORM ( matr i x ) SPECRAD Spectral Radius of a square matr ix . SPECRAD ( matri x )
Matrices 13-13 SVD Singular Value Decomp osition. Factors an m × n matrix into two matrices and a vector: {[[ m × m square orthogonal ]],[[ n × n square orthogonal ]], [ real ]}. SVD ( matr ix ) SVL Singular Values. Returns a vector containing the singular values of matrix. SVL ( matr ix ) 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 ix ) TRN Transposes matr ix . For a complex matrix, TRN finds the conjugate transpose. TRN ( matr ix ) Examples Identity Matrix You can create an identity matrix with the IDENMAT function. For example, IDENMAT(2) creates the 2×2 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 × 4 matrix showing the numeral 1 for all elements except zeros on the diagonal. The logical operator ¼ return s 0 w hen I (the row number) and J (the column number) are equal, and returns 1 when they ar e not equ al. Transposing a Matrix The TRN function swaps the row-column and column-row elements of a matrix. For instance, element 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 example, TRN([[1,2],[3,4]]) creates the matrix [[1,3],[2,4]] .
13-14 Matri ces 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 ec helon 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: The final row of zeros in the reduced-row echelon form of the augmented matrix indicates an inconsistency. x 2 y –3 z 1 4 2 xy z – 3 4 x – 2 y –2 z 1 4 = = = 12 –3 1 4 21 1 –3 – 42 –2 1 4 34 × xy z – 5 2 xy –7 x 2 y – z 2 = = =
Lists 14-1 14 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 o f 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 list 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 lists—named or unnnamed—in HOMEg 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 . Highli ght the lis t name y ou w ant to assing to the ne w list (L1, etc .) and pres s to display the List editor .
14-2 Lists 3 . E nter th e val ues you want in t he li st, 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 th e Lis t catal og, or pr ess t o re turn to HO ME . List catalog keys 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 39g or a PC. See “Sending and receiving ap lets” on page 17-4 for further information. Receives a list from another hp 39g or a PC. See “Sending and receiving aplets” on page 17-4 for further information. Clears the highlighted list. CLEAR Clears all lists. or Moves to the end or the beginning of the catalog.
Lists 14-3 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 th e list on t he edit l ine . Start and end the list w ith br aces (the shifted and k e y s) and separ ate each element with a comma. 2. P r e s s to e valuate and displa y the list . Immediatel y after typ ing in the list , y ou can stor 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 L 1. Note: Y ou can omit the final br ace when enter i ng 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. CLEA R Clears all elements from the list. or Moves to the end or the beginning of the list.
14-4 Lists Displaying and editing lists To display a list • In the L ist catalog , highli ght the list name and pr ess . • In HOME , enter the name o f 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 the List catalog. LIST . 2. P r e s s or to hig hlight the name of the lis t y ou w ant to edit (L1, etc.) and pr ess to display the list contents. 3. P r e s s or t o highli ght the element y ou w ant 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 .
Lists 14-5 To insert an element in a list 1. Open the List catalog. LIST . 2. P r e s s or to 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 ar e inser ted 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 li st. 3 . Pre ss to the insertion position, then pr ess , and p r ess 9. 4. Press . 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) .
14-6 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 CLEA R . 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 9 g calc ulators ’ infr ared po rts. 2 . Open the List catalogs o n both calc ulators. 3 . Highlight the list to send . 4. Pr ess . 5 . Pres s on the r e cei ving calculat or . 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 Li st functions, select a function, and press . List functions have the following syntax: • F uncti ons hav e argumen ts that are enc losed in pare ntheses and separ ated by commas . Ex ample: CONCAT(L1,L2) . An argument can be e ither a list v ari able name (such as L1) or the ac tual list . F or exa mp l e, REVERSE({1,2,3}) .
Lists 14-7 • If Dec i mal Mark in Mode s is set to Comma , use peri ods to separa te ar guments. F or e xample , CONCAT(L1.L2) . Common operators like , –, ×, and / c an take lists as arguments. I f there ar e two ar guments and both ar e 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 r n 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 r n s {1,2,3,4} . ∆ 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 –x 1 ... x n –x n–1 } . ∆ LIST( list1) Example In HOME, store {3,5,8,12,17,23} in L5 and find the first differences for the list. { 3,5, 8 ,12 ,17 ,2 3 } L 5 L Sele ct ∆ LIST L5
14-8 Lists MAKELIST Calculates a sequence of elements for a new list. 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 Select MAKELIST A A 2 3 27 1 Π LIST Calculates the product of all elements in list. Π LIST( lis t ) Example Π LIST({2,3,4}) ret u r n 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 position of the first occur rence is returned. A value of 0 is returned if there is no occurrence of the spe cified 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)
Lists 14-9 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 r n s 9 . SORT Sorts elements in ascending o rder. 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, and 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. Create L1 w ith values 8 8 , 90, 8 9 , 6 5, 7 0, and 8 9 . { 8 8 90 89 65 7 0 89 } L1
14-10 Lists 2 . In HOME , stor e L1 into C1. Y o u w ill then be able to see the list dat a in the Numer ic v ie w of the S tatisti cs apl et. L1 C1 3 . Start the Statis tic s aplet , and selec t 1-var ia ble mode (pr ess , if necessary , to display ). Sele ct Statistics Note: Y ou r list values ar e no w in column 1 (C1) . 4. In t h e Sy mb ol ic view , defin e H1 ( for ex amp l e) as C 1 (sample ) and 1 (fr equenc y) . 5 . Go to the Numer ic v iew t o displa y calc ulated statisti cs . See “One - var iable ” on p age 8-13 for the meaning of each com puted statisti c.
Notes and sketches 15-1 15 Notes and sk etc h es Introduction The hp 39g has text and picture editors for entering notes and sketc hes. • E ach aplet has its o wn independent Note v ie w and Sk etc h vi e w . Not es and sk etc hes that y ou c r 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 w ell. • Th e Notepad is a collec tion of no tes 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 fo r the Note v ie w . 2 . Use the n ote editing k ey s sho w n in the table in the fo llo w i ng sec tion . 3 . Set Alpha loc k ( ) for q uic k entry of letters . For lo wer case Alpha lock , pr ess . 4. While Alpha lock is on: – T o t y pe a single letter of the opposite cas e , pres s letter . – T o type a single n on-alpha char acte r (suc h as 5 or [ ) , press firs t . (Thi s tu rns of f Al ph a lo ck for on e cha ract er . ) Y our w or k is automati cally s av ed. Pr ess an y vi e w ke y (, , , ) or to e x it the Notes v ie w .
15-2 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- page 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 .
Notes and sketches 15-3 Aplet sketch view You can attach pictures to an aplet in its Sketch view ( SKE TCH ). Y our w ork is au tomaticall y sav ed w ith th e aplet . Press an y other vi ew k e y or to e xit the Sk etch v ie w Sketch keys To dr aw a li ne 1. In an aplet, pr ess SKETCH for the Sk etch v ie w . 2 . In Sk etch v ie w , pres s and mo ve the c ursor to w her e y ou w ant to start the line 3 . Pres s . T his turns on line -dra wing . 4. Mov e the cur sor in an y dir ection to the end po int of the line b y pr essing the , , , ke ys . 5 . Press to finish the li ne . 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. CLEA R 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.
15-4 Notes and sketches To draw a box 1. In Sk etc h v ie w , pr ess and mo ve the c urs or to wher e you w ant any corner of the bo x to be. 2. P r e s s . 3 . Mov e the cu rsor to mar k the opposite corner fo r the bo x . Y ou can adj ust the si z e of the bo x b y mo ving the cu rs o r . 4. Pres s to f inish the bo x . To draw a circle 1. In Sketc h vie w , pr ess and mov e the c ursor t o wher e you w ant th e 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. Pres s to dra w the cir cle . 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 cursor’s starting position to the cursor’s current position. Press when you have finished. You can draw a line at any angle. Draws a box from the cursor’s starting position to the cursor’s current position. Press when you have fini shed. Draws a circle with the cursor’s starting position as the center. The radius is the distance between the cursor’s starting and ending position. Press to draw the circle.
Notes and sketches 15-5 To label parts of a sketch 1. Pres s and type the t ext o n the edit line . T o loc k the Alpha shift on , pre ss (f or uppercas e) or (for lo w er case). T o mak e the label a smaller c har act er si z e , turn o f f befo r e pres sing . ( i s a toggle betw een small and lar ge font si z e) . The smaller c har acter si z e cannot displa y low er case lette rs . 2. P r e s s . 3 . P ositi on the label w here y ou want it b y pr essing the , , , k ey s . 4. Press again to affi x the label. 5. P re s s t o 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 new , blank page. Y ou can no w mak e a new sk etch , whic h becomes part of the c urr ent s et of sk etc hes. • T o v iew the ne xt sk etch in an e xisting set , pres s . Hold dow n for animation . • T o r em o ve the c urr ent pag e in the cur r ent sketc h ser ies , pre ss . To stor e into a graphics variable You can define a portion of a s ketch inside a box, and then store th at graphic into a graphics variable. 1. In the Sk etc h v ie w , dis play the sk etc h y ou want t o copy (stor e into a var iable ) . 2. P r e s s . 3 . Highli ght the v ar iable name y ou wan t to use and pr ess . 4. Dra w a bo x ar oun d the portion y ou want to copy : mo ve the c ursor to one cor ner , press , then mo ve the curs or to the opp osite corner , and press .
15-6 Notes and sketches To import a graphics variable You can copy the contents of a grap hics variable into the Sketch view of an aplet. 1. Open the Sketch v iew o f th e aplet ( SKETCH ). T he graphi c w ill be copied her e. 2 . Press , . 3 . Highlight Graphic , then pr ess and highligh t the name of the v ari able ( G1 , etc.) . 4. Pres s to r ecall the conte nts of the gr aphics va ria b le. 5 . Mov e t he box to wher e y ou 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 aplets’ Note view s , but these can be imported. See “To import a note” on page 15-8 . To create a note in the Notepad 1. Display the No tepad catalog. NOTEPAD 2 . Create a ne w note . 3 . Enter a name f or y our note. MYNO TE
Notes and sketches 15-7 4. W rite y our note . See “Note e dit k ey s ” on page 15- 2 fo r mor e infor mation on the entry and editing of notes. 5 . When you ar e finished, press or an aplet ke y to e xit Notepad . Y our wor k is automati cally s av 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 39g or PC. Receives a note being transmitted from another hp 39g or PC. Deletes the selected note. CLEA R Deletes all notes in the catalog.
15-8 Notes and sketches To import a note You can import a note from the Notepa d into an aplet’s Note view, and vice versa. Supp ose you want to copy a note named “Assignments” fr om the Notepad into the Function Note view: 1. In the Func tion aplet , displa y the Note v iew ( NOTE ). 2 . Pres s , hi ghlight Notepad in the left column, then hi ghlight the name “ Assignments ” in the r ight co lumn . 3 . Pres s to cop y the contents o f “ Assignments ” to the F unction Note vi e w . Note: T o r ecall the name instead 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 , “ A ssi gnments ” . 2. P r e s s , highligh t Note in the left column , then pr ess and highligh t NoteText in the r ight column . 3 . Pres s to r ecall the contents o f the Note v ie w into the note “ Assignments ” .
Programming 16-1 16 Pr ogramming Introduction This chapter describes how to pro gram using the hp 39g . In this chapter you’ll 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 v ari ables in pr ograms • pr ogr amming var iables. HINT More information on programming, including examples and special tools, can be fo und at HP’s calculators web site: http://www.hp.com /calculators The Contents of a Program An hp 39g program c ontains 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 stru ctures to control the execution flow. You can take advantage of structured programming by creating building-bloc k programs. Each building -block program stands alone—and 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 .
16-2 Programmin g 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 simple—or 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 Progr am catalog • cr eate a ne w pr ogr am • enter commands f r om the pr ogr am commands menu • enter f unctio ns fr om the MA TH men u • edit a pr ogram • run and de bug a pr ogram • stop a pr ogr am • copy a pr ogr am • send and recei ve a pr ogr am • delete a progr am or its contents • cu stomi z e an aplet . Open Program Catalog 1. Pr ess PROGRM . T he Pr ogram C atalog displa y s a list of pr ogram names . The Pr ogr am Catalog cont ains a built -in entr y called Editline . Editline cont ains the last e xpre ssi on that y ou enter ed fr om the edit line in HOME , or the last data y ou enter ed in an input f orm . (If you pr ess fr om HOME w ithout ente ring an y data , the hp 3 9g 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 amiliar with the Pr ogr am catalog menu k e y s. Y ou can use an y of the follo wing k e ys (both menu and k ey boar d) , to per for m tasks in the Pr ogram catalog .
Programming 16-3 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 39g or to a disk drive. Receives the highlighted program from another hp 39g or from a disk drive. Runs the highlighted program. or Moves to the beginning or end of the Program catalog. Deletes the highlighted program. CLEA R Deletes all programs in the program catalog.
16-4 Programmin g Creating and editing programs Create a new program 1. Pr ess PROGRM to open the Pr ogr am catalog . 2. P r e s s . The hp 3 9 g prompts yo u f or a n a m e. A pr ogr am name can contain spec ial char acters , such as a space . Ho we ver , if yo u use spec ial char acter s and then run the pr ogram b y typ ing it in HOME , y ou mus t enclo se the pr ogram name in double quotes ( " " ) . Don't use the " s ymbol within y our pr ogr am name. 3 . T ype y our pr ogr am name , then pres s . When y ou pr ess , the Pr ogr am E ditor opens. 4. Enter yo ur pr ogram . When done , start any other acti vity . Y our w ork is sa v ed auto maticall y . Enter commands Until you become familiar with the hp 3 9g 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 ogr am edit or , pr ess CMDS to open the Pr ogr am Commands men u . CMDS
Programming 16-5 2 . On the left , us e or to highlight a co mmand category , then pres s to access the commands in the category . Select the command that y ou w ant . 3 . Pres s to paste the command into the pr ogram editor . Edit a program 1. Pr ess PROGRM to open the Pr ogram catalog. 2 . Use the ar r ow k ey s to highligh t the pr ogr am y ou want to edit, and pr ess . T he hp 3 9g op ens 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 o gr am .
16-6 Programmin g 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 th e 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 Di splays menus for se lecting progr am conmmands. CHARS Displays all characters. To type one, highlight it and press . To enter several characters in a row, use the menu key while in the CHARS menu.
Programming 16-7 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 39g 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 hp39g 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. Pres s to edit the progr am. T he insert c urs or appear s in the pr ogr am at the poin t w her e the err or occur red . 2 . E dit the pr ogr am to f ix the er r or . 3 . Run the pr ogram . 4. Repeat the pr ocess until y ou corr ect all err ors . Stop a program You can 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.
16-8 Programmin g Copy a program You can use the following procedure if you want to make a copy of y our work before editing—or if you want to use one program as a template for another. 1. Pr ess PROGRM to open the Progr am catalog . 2. P r e s s . 3 . T ype a ne w file name , then ch oose . T he Progr am E ditor opens with a ne w progr am. 4. Pr ess to open the var iables menu . 5 . Pr ess to quickl y scr oll to Pr ogram . 6 . Pr ess , then highlight the pr ogr am y ou w ant to copy . 7 . Press , then press . T he conte nts of the hi ghlight ed pr ogr am ar e copi ed into the c urr ent pr ogram at the c u rs 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 calculators’ infrared port s, open the Program catalogs on both calculators. Highlight the program to send, then press on the sending calculator and on the receivi ng calculator. You can also send programs to, and receive progra ms from, a remote storage devi ce (aplet di sk drive or computer). This takes place via a cable connectio n and requires an aplet disk driv e or specialized software running on a PC (such as a connectivi ty kit).
Programming 16-9 Delete a program To delete a program: 1. Press PROGRM to open the Pr ogram catalog . 2 . Highli ght a pr ogram to de lete , then pr ess . Delete all programs You can delete all programs at once. 1. In the Progr am catalog , pr ess CLEAR . 2. P r e s s . Delete the contents of a program You can clear t he contents of a program without deleting the program name. 1. Press PROGRM to open the Pr ogr am catalog. 2 . Highli ght a pr ogram , then pr ess . 3. P re s s CLEAR , then pr ess . 4. The cont ents of the pr ogram ar e deleted , but the pr ogr am name r emain s . Customizing an aplet You can customize an 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. Decide on the built-in aplet that y ou wa nt to c ustomi ze . F or e xample y ou could c ustomi ze the F unction aplet or the S tatistic s aplet . The c ustomi z ed aplet inher its all the pr operties o f the built -in aplet . Sa v e the cu stomi z ed aplet with a uni que name . 2 . Cus tomi z e the new aplet if y ou need to , for e xample b y pr esetting ax es or angle mea sure s. 3 . Dev elop the progr ams to wo rk w ith your c usto mi z ed aplet . When yo u dev elop the apl et’s pr ograms , use the standar d aplet naming conv ention . T his allow s y ou to k eep trac k of the progr ams in the Progr am catalog t hat belong to each aplet . See “ Aplet naming con ven tion ” on page 16 -10.
16-10 Programming 4. D ev elop a progr am that uses the SE T VIEW S command to modify the aplet’s VIEW S menu . The menu opti ons pr o v ide links to ass oc iated pr ogr ams. Y ou can spec i fy an y other pr ograms that y ou want transfer r ed with the aplet. See “SETVI EW S” on page 16 - 14 f or infor mation on the command . 5 . Ensure that the c ustomi z ed aplet is selected , then run the menu conf igur atio n pr ogram to conf igur e the aplet’s VIEW S menu . 6 . T es t the c us tomi z ed aplet and debug the as soc iated pr ogr ams. (R efer to “Debug a pr ogram ” on page 16 - 7) . Aplet naming convention To assist users in kee ping tr ack of a plets and associated programs, use the f ollowing naming convention when setting up an aplet’s programs: • Start all pr o gr am names 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 ogra ms called by men u entr ies in the VIEW S menu number , after the entry , fo r e xam ple: – APL .ME1 f or the pr ogr am called b y menu optio n 1 – APL .ME2 f or the pr ogr am called b y menu optio n 2 • Name the pr ogr am that confi gur es the new VIEW S menu option APL .S V wher e S V stands for SE T VIEW S. For example, a customized aplet called “Differentiation” might call programs called DIFF.ME1, DIFF.ME2, and DIFF. SV. Example This example aplet is designed to demo nstrate the process of customizi ng an aplet. The new ap let is based on the Function aplet. Note: This aplet is not intended to serve a serious use, merely to illu strate the process.
Programming 16-11 Save the aplet 1. Open the F uncti on aplet and sa ve it as “EXP ERIMENT ” . The ne w aple t appears in the A plet library . Select Function EXP ERIMENT 2 . Create a pr ogram called EXP .ME1 w ith 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 . Create a pr ogram called EXP .ME2 w ith contents as show n. T his pr ogr am sets the numer ic v ie w options fo r the aplet , and runs the pr ogr am that y ou can us e to conf igur e the angle mode . 4. Create a pr ogram called EXP .ANG w hic h the pr e v io us tw o pr ogr ams call . 5 . Create a pr ogram called EXP .S w hic h runs 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 aple t plots. Configuring the Setviews menu option programs In this secti on w e will begin b y confi guring the VIEW S menu by using the SETVI EW S command. W e w ill then c r eate the “helper ” pr ogr ams called b y the VIEW S menu whi ch w ill do the actual w or k.
16-12 Programming 6 . Open the Pr ogram cat alog and cr eate a pr ogr am named “EXP .S V” . Inc lude the follo wing code in the pr ogr am. E a c h entry line after the command SETVIEW S is a tri o th at consists of a VIEW S menu te xt line (a space indicate s none), a progr am name , and a number that def ines the vi ew to go to after the pr ogr am has run its cour se. A ll pr ograms listed here w il l transfer w ith an aplet when the ap let is transfer red . SETVIEWS ’ ’ ’ ’ ; ’ ’ ’ ’ ; 18; Sets the f i rs t menu opti on to be “ Aut o scale ” . T his is the fo urth standar d F uncti on aplet v ie w menu opti on and the 18 “ A uto scale ” , specif ies that it is to be included in the ne w menu . The empty quotes w ill ensur e that the old name of “ Auto s cale ” appears on the ne w menu . See “SETVIEWS” on page 16 - 14. ’ ’ My Entry1’ ’ ;’ ’ EXP.ME1’ ’ ;1; Sets the seco nd menu option . This opti on runs pr ogram E XP .ME1, then r eturns t o view 1 , Pl ot vi ew . ’ ’ My Entry2’ ’ ;’ ’ EXP.ME2’ ’ ;3; Sets the third men u option . This option runs the pr ogra m EXP .ME2 , then r etur ns to v ie w 3, the NUM vie w . ’ ’ ’ ’ ;’ ’ EXP.SV’ ’ ;0; This line spec ifi es that the pr ogram to s et the V ie w menu (this pr ogr am) is tr ansf err ed with the a plet . T he space char acter between the fir st set of quotes in the tr io sp ec ifie s that no men u option appears f or the entry . Y ou do not need to tr ansfe r this progr am w ith the aplet , but it allo ws user s to modify the aplet’s menu if the y wan t to .
Programming 16-13 ’ ’ ’ ’ ;’ ’ EXP.ANG’ ’ ;0; The pr o gr am EXP .ANG is a sma ll ro utine that is called by other pr ogr ams that the aplet u ses . This e ntry spec ifi es that the pr ogr am EXP.ANG is tr ansferr ed when the aplet is tr ansfer r ed , but the space in the fi rst q uotes en sur es that no entry appears on the menu . ’ ’ START’ ’ ;’ ’ EXP.S’ ’ ;7: T his spec ifi es the S tar t menu optio n. T he pr ogr am that is ass oc iated w ith this entry , EXP.S, runs a utomati cally when y ou start the aple t . B ecau se this menu opti on spec if ies v ie w 7 , the VIEW S menu opens when y ou star t the aplet. Y ou onl y need to run this pr ogr am once to conf igur e y our aplet’s V IEW S menu . Onc e the aplet’s VI EW S menu is conf igur ed, it r emains that wa y until you ru n SETVIEW S again. Y ou do not need to inc lude this pr ogram f or y our aplet to w ork , but it is use ful t o spec ify that the pr ogr am is attached to the aplet, and tr ansmi tted w hen the aplet is transmitted . 7 . R eturn to the pr ogra m catalog. T he progr ams that y ou cr eated sh ould appear as f ollow s: 8. Y ou mu st now t he pr ogr am EXP .S V to e xec ute the SETVIEW S command and cr eate th e modified VIEWS menu . Check tha t the name of the ne w aplet is highlighted in the A plet vi ew . 9 . Y ou can n o 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 39g . You can enter these commands in your program by typing th em or by accessi ng them from the Commands menu.
16-14 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 checkmar k 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 “Customizing an a plet” on page 16-9 for an e xample of using the SETVIEWS command. When you use the SETVIEWS command, the aplet’s 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 th e 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 aplet’s standard V ie ws men u options . If you w ant to us e an y of the standar d options on y our r econf igur ed VI EW S menu , y ou must inc lude t hem in the configur a tion . • When y ou in v ok e the SETVIEW S command, the changes to an aplet’s VIEW S menu re main with the aplet . Y ou need t o inv ok e the command on the aplet 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 aplet is tr ansfer r ed, f or ex amp le to an other calculator or to a PC. • As part of the VIEW S menu confi gurati on, y ou can spec i fy progr 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
Programming 16-15 options u se , or the pr ogram that def ines the aplet’s VIEW S menu . • Y ou can inclu de a “Start ” optio n in the VIEW S menu to spec if y a pr ogr am that y ou w ant to r un auto maticall y when the aplet s tarts. This pr ogram typically sets up the aplet’ s initial configur ation . The S T AR T optio n on the menu is also use ful f or re setting the aplet . Command syntax The syntax for the command is as follows: SETVIEWS " Pr ompt1 " ; " Progr amName1 " ; ViewN um b er 1 ; " Pr ompt2 " ; " Progr amName2 " ; ViewN um b er 2 : (Y ou can r epeat as many Prompt/ProgramName/ ViewNumber tri os o f 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 you r 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 “Start”, 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 “Reset” which is auto-run if the user choo ses the button in the APLET view.
16-16 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 aplet’s 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 aplet’s standard VIEWS menu options in your customized menu, set up the arguments trio as follows: • The f irs t ar gument spec ifi es the menu item name: – Leav e the a r gument empt y to use th e standard V ie w s menu name f or the item, or – Enter a menu item name to r eplace the standar d name . • The second argument specif ies th e pr ogram to run: – Lea v e the ar gument empty to r un the standar d menu option . – Inser t a pr ogram name to run the pr ogram be for e the standar d menu opti on is selec ted. • The thir d ar gument s pec if ies the v ie w and the men u number f or the item . Deter mine the menu number fr om the Vi e w numbers ta ble belo w . Note: SE TVIEW S w i th no ar guments r esets the vi ew s to def ault of the base aple t .
Programming 16-17 View numbers The Function aplet views are numbered as follows: 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 progr am make a decision 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 t he true-clause only if the test-clause evaluate s to true. I ts syntax is: IF test-clause THEN true-clause END Example 1 X A : IF A==1 THEN MSGBOX " A EQUALS 1" : 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
16-18 Programming IF... THEN... ELSE... END Executes the true-clause seque nce 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 false-clause END Example 1 X A : IF A==1 THEN MSGBOX "A EQUALS 1" : ELSE MSGBOX "A IS NOT EQUAL T O 1" : END CASE...END Executes a series of test-clause commands that execute the appropriate true- clau se sequence of commands. Its syntax is: CASE IF test-clause 1 THEN true-clau se 1 END IF test-clause 2 THEN true-clau se 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... END... Many conditions are automatica lly recognized by the hp 39g as error conditions and are automatically treated as errors in programs. IFERR...THEN...END allows a pr ogram to intercept error conditions that otherwise would cause the program to abort. Its syntax is: IFERR tr ap-clause THEN er ro r- cl a u se END
Programming 16-19 RUN Runs the named program. If your program name contains special characters, such as a space, then you must enclose the fi le name in double quotes (" "). RUN " pr ogram name " : or RUN pr ogramname : 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 39g default settings with the Function aplet as the current aplet. ARC Draws a circular arc, of given radians, whose centre is at (x,y) The arc is draw n from start_angle_measurement , and end_ang le_measu rement . ARC x;y; radius ; start_angle_measurement ; end_angle_measurement : Example ARC 0;0;2;0;360: FREEZE: Dr aw s a ci r cle cen ter ed at (0, 0) of r a dius 2 . T he FREEZE command causes th e circle to r emain display ed on the scr een until you 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 aw s a box , lo w er corner at (–1,–1), upp er cor ner at (1,1)
16-20 Programming ERASE Clears the display ERASE: FREEZE Halts the program, freezing the current 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: Example TLINE 0;0;3;3: Er ases pr e v iou sly dr aw n 4 5 degree line f r om (0, 0) to (3, 3) , or dra ws that line if it doesn ’t alread y e x ist . Graphic commands The graphic commands use the graphics variables G0 through G9—or the Page va riable from Sketch—as graphicname arguments. The positio n argument takes the form ( x,y ). Position coordinates depen d on the current aplet’s scale, whic h is specified by Xmin, Xmax, Ymin, and Ymax. The upper left corner of the tar get graphic ( graphic2 ) is at (Xmin,Ymax). You can capture the c urrent disp lay and store it in G0 by simultaneously pressing . DISPLAY → Stores the current display in graphicname . DISPLAY → gr aphicname :
Programming 16-21 → DISPLAY Disp lays graphic from graphicname in the display. → DISPLAY gr aphi cname : → GROB Creates a graphic from expres sion , 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 39g creates a graphic display li ke that created by the SHOW operation. → GROB gr aphicname ; exp ress i on ; fo nt s 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 aphicname1 ; position ; gra phicname2 : GROBXOR Using the logical XOR, superimposes graphicname2 onto graphicname1 . The upper left corner of graphicname2 is placed at position . GROBXOR gra phicname1 ; positi on ; graphi cname2 : MAKEGROB Creates graphic with given width, height, and hexadecimal data, and stores it in graphicn ame . MAKEGROB gr aphicname ; wid t h ; hei ght ; hexdata : PLOT → St ores the Plot vie w di splay as a graphic in graphicname . PLOT → gr aphicname : PLOT → and DISPLAY → 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 X PageNum: PLOT →Page: FREEZE: This program stores the current PLOT vie w to the first page in the sketch view of the cu rrent aplet and then displays the sketch as a graphic object until any key is pressed.
16-22 Programming → PLOT Puts graph from graphicname into the Plot view display. → PLOT gr aphicname : REPLACE Replaces portion of graphic in graphicname1 with graphicname2 , s tarting at position . REPLACE also works for lists and matrices. REPLACE gr aphi cname1 ; ( position ) ; gr aphicname2 : SUB Extracts a port ion of the named graphic (or list or matrix), and stores it in a new variable, name . The portion i s specified by position and positions. SUB name ; gra phicname ; ( positi on ) ; ( positi ons ) : ZEROGROB Creates a blank graphic with given width and height , and stores it in graphicname . ZEROGROB gr aphicname ; wi d t h ; height : Loop commands Loop hp allow a program to exec ute a routine repeatedly. The hp 39g has three loop structures. The example programs below illustrate each of these structures incrementing the variable A from 1 to 12. DO…UNTIL …END Do ... Until ... End is a loop command that ex ecutes th e 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 exe cuted at least once. Its syntax is: DO loop-cla use UNTIL test-clause END 1 X A: DO A 1 X A UNTIL A = = 12 END
Programming 16-23 WHILE… REPEAT… END While ... Repeat ... End is a loop command that repeatedly evaluates test-clause and executes 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- claus e REPEAT loop-clau se END 1 X A: WHILE A < 12 REPEAT A 1 X A END FOR…TO…STEP ...END FOR name= start -expr ession TO end-expr ession [STEP incr ement ]; loop-c lause END FOR A=1 T O 12 S TEP 1; DISP 3;A: END 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 M 0–M9 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 separ ated by commas and the number of valu es must be the same as the number of rows i n the matrix name . ADDCOL name ;[ val ue 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 must be separated by commas and the number of values must be the same as th e number of columns in the matrix name . ADDROW name ;[ valu e 1 ,..., val u e n ]; r ow_n umber :
16-24 Programming DELCOL Delete Column. Deletes the specified column from the specified matrix . DELCOL name ; column_number : DELROW Delete Row. Delete s the specified row from the specified matrix. DELROW nam e ; 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 : 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 –9 to 9. RANDMAT name ; rows ; columns : REDIM Redimensions the specified matrix or vector to size . F or a matrix, size is a list of two integers {n1,n2} . For a vector, size is a list containing one integer {n} . REDIM name ; siz e : REPLACE Replaces portion of a matrix or vector stored i n name with an object starting at position start . start for a matrix is a list containing two numbers; for a vector, it is a single number. Replace also works with lists and graphics. REPLACE name ; start ; objec t : SCALE Multiplies the specified row_number of the specified matrix by value . SCALE name ; va l u e ; rown u m b e r : SCALEADD Multiplies the row of the matrix name by value , then adds this result to the second specified row. SCALEADD name ; va l u e ; row 1 ; row 2 :
Programming 16-25 SUB Extracts a sub-object— a portion of a list, matrix, or graphic fro m object —and 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 ), fo r graphics. SUB name ; object ; sta r t ; end : SWAPCOL Swaps Columns. Exch anges column1 and column2 of th e specified matrix . SWAPCOL name ; column1 ; column2 : SWAPROW Swap Rows. Exchanges row1 and ro w2 in the specified matrix . SWAPROW name ; row 1 ; row 2 : Print commands These commands print to an HP infrared pri nter, 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 contents of variablename . PRVAR var iablename : You can also use the PRVAR command to print the contents of a program or a note. PRVAR pr ogramname ;PROG: PRVAR notename ; NOTE: Prompt commands BEEP Beeps at the frequency and for the time you specify. BEEP fr equency ; seconds :
16-26 Programming CHOOSE Creates a choose box, which is a box containing a list of options from which the user chooses one. Each option i s 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 def ault_option_number ; title ; opti on 1 ; optio n 2 ; ... option n : where default _option_number is the number of the option that will be highlighted by default whenever the choose box is displa yed, title is the text dis played in the title bar of the choose box, an d option 1 ...option n are the options listed in the choose box . Example 3 X A:CHOOSE A; "COMIC STRIPS"; "DILBERT"; "CALVIN&HOBBES"; "BLONDIE": DISP Di splays textitem in a row of the di splay at the line_number . A text item consists of any n umber of expressions and quoted strings of text. The expressions are evaluated and turned into strings. Line s are numbered from the top of the screen, 1 being the top and 7 being the bottom. DISP line_numbe r ; te xtitem : Example DISP 3;"A is" 2 2 Res u l t : A is 4 (displa y ed on line 3) 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.
Programming 16-27 Examples 5.152000 X DATE( sets the date to May 15, 2000) . 10.1500 X TIME (sets the time to 10:15 am) . EDITMAT Matri x Editor. Opens the Matrix editor for the specifi ed matrix. Returns to the program when user presses EDITMAT matr i xname : The EDITMAT command can also be used to create matrices. 1. Press CMDS 2. P r e s s M 1, and then pr ess . T he Matri x catalog o pens w i th M1 av ailable for editing. EDITMAT matrixname is a shortcut to opening the matrix editor with matrixname . FREEZE This co mmand prevents the display from being updated after the program runs. This allows you to view the graphics cr eated by the program. Cancel FREEZE by pressing any key. FREEZE: GETKEY Waits for a key, then stores t he keyco de 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 ; defa ult :
16-28 Programming Example INPUT R; "Circular Area"; "Radius"; "Enter Number";1: MSGBOX Displays a message box containing textitem. A text item consists of any number of e xpressions and quoted strings of text. The expressions are evaluated and turned into strings of text. For example, "AREA IS:" 2 2 becomes AREA IS: 4 . Use CHARS to t ype the q uote marks " ". MSGBOX te xtitem : Example 1 X A: MSGBOX "AREA IS: " π*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 type AREA IS . The position line MSGBOX NoteText " " π *A^2: will display the same mess age box as the previous example. PROMPT Displays an input box with name as the title, and prompts for a value for name . name can only be one characte r in length. PROMPT nam e : WAIT Halts program execution for the specified number of seconds. WAIT seco nds : Stat-One and Stat-Two commands The following commands are used for analyzing one- variable and two-varia ble statistical data.
Programming 16-29 Stat-One commands DO1VSTATS Calculate s STAT S using datasetname and stores the results in the corresp onding variables: N Σ , Tot Σ, Mean Σ , PVar Σ , SVar Σ , PSDev, SSDev, Min Σ , Q1, Me dian , Q3, and Max Σ . Datasetname can be H1 , H2, ..., or H5. Datasetname must include at least two data points. DO1VSTATS datasetname : SETFREQ Sets datasetname frequency according to column or value. Datasetname can be H1, H2,. .., or H5, column can be C0–C9 and value can be any positive integer. SETFREQ datasetname ; column : or SETFREQ def inition ; val u e : SETSAMPLE Sets datasetname sample according to column. Datasetname can be H1–H5, and column can be CO–C9. SETSAMPLE datasetname ; column : Stat-Two commands DO2VSTATS Calculate s STAT S using datasetname and stores the results in corresponding variables: MeanX, Σ X, Σ X2, MeanY, Σ Y, Σ Y2, Σ XY, Corr, PCov, SCov, and RELER R. 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, …, or S5 and column can be C0–C9. SETDEPEND datasetname ; column : SETINDEP Sets datasetname independent column . Datasetname can be S1, S2,…, or S5 and column can be C0–C9. SETINDEP datasetname ; column :
16-30 Programming Storing and retrieving variables in programs The hp 39g has both Home variables and Aplet variables. Home va riables are used for real numbers, complex numbers, graphics, lists, and matrices. Home variables keep the s ame valu es in HOME and in aplets. Aplet variables are those whose values depend on the current aplet. The aplet variables are used in programming to emulate the defin itions and settings you make when working with aplets interactive ly. You use the Variable menu ( ) to retrieve either Home variables or aplet vari ables. See “The VARS menu” on page 12-4. Not all varia b les are available in every aplet. S1fit–S5fit, for example, are only available in the St at is t ic s a pl e t. Un de r e a ch va ri a bl e n am e is a l i st o f th e aplets where the variable can be used. 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 X Axes —to turn axes on (def ault) . 0 X Axes —to turn axes 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 X Connect — to connect plo tted points (de fault , e x cept in St atistic s w her e the default is o ff) . 0 X Connect — no t to connect plotted po ints .
Programming 16-31 Coord Function Parametric Polar Sequence Solve Statistics Turns the coordinate-display mode in Plot view on or off. From Plot view, use the Menu mean key to toggle coordinate display on a n off. In a program, type 1 X Coord —to tur n coor dinate displa y on (de fault). 0 X Coord —to turn coor dinate display o ff . Extremum Function Contains the l ast value fo und by the Ex tremum operat ion 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 Fa ster or More Detail. or In a program, type 1 X FastRes —for f aster (def ault) . 0 X FastRes —f or mor e detail . Grid All Ap lets Turns the background grid in Plot v iew on or off. Fro m Plot setup, check (or uncheck) GRID . or In a program, type 1 X Grid to tur n the gr id on . 0 X Grid to turn the gr id 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 X Hmin X Hmax wh e re n 1 n 2 n 2 n 1 >
16-32 Programming Hwidth Statistics Sets the width of histogram bars. From Plot Setup in 1VAR sta ts set a value for Hwidth or In a program, type n X Hwidth Indep All Aplets Defines the value of the inde pendent variable us ed in tracing mode. In a program, type n X Indep InvCross All Aplets Toggles between solid crosshairs or inverted crosshairs. (Inverted is useful if the background is solid). From Plot Setup, check (o r uncheck) InvCross or In a program, type: 1 X InvCross —to in vert the c r oss hairs. 0 X InvCross —f or soli d c r os shairs (de fa ult) . 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 X Labels —to turn labels on . 0 X Labels —to turn labels o ff (def ault) .
Programming 16-33 Nmin / Nmax Sequence Defines the minimum and maxi mum independent variable values. Appears as the NRNG fields in the Plot Setup input form. From Plot Setup, enter values for NR NG . or In a program, type X Nmin X Nmax wh e re Recenter All Ap lets Recenters at the crosshairs locations when zooming. From Plot-Zoom-Set Factors, check (or unc heck) Recenter or In a program, type 1 X Recenter — to tur n r ecenter on (de fault). 0 X Recenter —to tur n r ecenter o ff . Root Function Contains the last value found by the Root function in the Plot-FCN menu. S1mark–S5mark 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 X S1mark wh e re 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 Cobweb . or In a program, type 1 X SeqPlot —for Stairstep. 2 X SeqPlot —for Cob web. n 1 n 2 n 2 n 1 >
16-34 Programming 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 X Simult —for sim ultaneou s gr aphing. 0 X Simult —for s equenti 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-Whi sker. From Plot Setup, select StatPlot , then choose Histogram or BoxWhisker . or In a program, type 1 X StatPlot —for Hist ogram. 2 X StatPlot —for Box-and-W hisker. Umin/Umax Polar Sets the minimum and maxi mum independent values. Appears as the URNG field in the Plot Setup input f orm. From the Plot Setup input form, enter values for URNG . or In a program, type X Umin X 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 X Ustep wher e n 1 n 2 n 2 n 1 > n 0 >
Programming 16-35 Tmin / Tmax Parametric Sets the minimum and maxi mum independent variable values. Appears as the TRNG field in the Plot Setup input form. From Plot Setup, enter values for TR NG . or In a pr ogr am , type X Tmin X Tmax wh e re Tracing All Ap lets Turns the tracing mode on or off in P lot view. In a program, type 1 X Tracing —to turn T r ac ing mode on (def ault) . 0 X Tracing —to turn T rac ing mode off . 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 X Tstep wh e re Xcross All Ap lets Sets the horizontal coordinate of the c rosshairs. Only works with TRACE off. In a program, type n X Xcross Ycross All Ap lets Sets the vertical coordinate of the crosshairs. Only works with TRACE off. In a program, type n X Ycross n 1 n 2 n 2 n 1 > n 0 >
16-36 Programming Xtick All Aplets Sets the distance between ti ck marks for the horizontal axis. From the Plot Setup input form, enter a value for Xtick . or In a program, type n X Xtick whe re 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 X Ytick whe re Xmin / Xmax All Aplets Sets the minimum and maximum horizontal values of the plot sc reen. Appe ars as th e XRNG fields (horizontal range) in the Plot Setup input form. From Plot Setup, enter values for XRNG . or In a program, type X Xmin X 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 X Ymin X Ymax whe re n 0 > n 0 > n 1 n 2 n 2 n 1 > n 1 n 2 n 2 n 1 >
Programming 16-37 Xzoom All Ap lets Sets the horizontal zoom factor. From Plot-ZOOM-Set Factors, enter the value for XZ OOM . or In a program, type n X XZOOM wh e re Yzoom All Ap lets Sets the vertical zoom factor. From Plot-ZOOM-Set Factors, enter the value for YZ OOM . or In a program, type n X YZOOM Symbolic-view variables Angle All Ap lets Sets the angle mode. From Symbolic Setup, choose Degrees , Radians , or Grads for angle measure. or In a program, type 1 X Angle —for Degrees. 2 X Angle —for Radians. 3 X Angle —for Grads. F1...F9, F0 Function Can contain any expression. Independent variable is X . Example 'SIN( X)' X F1( X) You must put single quotes around an expression to kee p 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)' X Y1(T):'2*SIN(6*T)' X X1(T) n 0 >
16-38 Programming R1...R9, R0 Polar Can contain any expression. In dependent variable is θ . Example '2*SIN(2* θ)' X R1( θ) U1...U9, U0 Sequence Can contain any expression. In dependent variable is N. Example RECURSE (U,U(N-1)*N,1,2) X U1(N) E1...E9, E0 Solve Can contain any equation or expression. Independent variable is selected by high lighting it in Numeric Vi ew. Example 'X Y*X-2=Y' X E1 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 User defined Example Cubic X S2fit or 6 X S2fit
Programming 16-39 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 th e Numeric view or In a program, type LIST XC n wh e re n = 0, 1, 2, 3 ... 9 Digits All Ap lets Number of decimal places to use for Number format. From Solve’s Numeric Setup view, enter a value in the second field of Number Format . or In a program, type n X Digits wh e re Except in the Solve aplet, the value of Digits takes effect only after the current aplet is saved with a new name. Until then, HDigit is in effect. Format All Ap lets Defines the number display format. From Solve's Numeric Setup view, choose Standard , Fixed , Scientific , or Engineer ing 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 Scientific 4 Engineering 0 n 11 <<
16-40 Programming Except in the Solve aplet, the value of Format takes effect only after the current aplet is saved with a new name. Until then, HFormat is in effect. Example Scientific X Format or 3 X Format NumCol All Aplets exce pt Statistics aplet Sets the column to be highlighted in Numeric view. In a program, type n X 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 X NumFont fo r small (def ault) . 1 X 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 X NumIndep NumRow All Aplets exce pt Statistics aplet Sets the row to be highlighted in Numeric view. In a program, type n X 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 X NumStart n 0 >
Programming 16-41 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 X NumStep wh e re 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 X NumType f or Build Y our Ow n. 1 X NumType for A utomatic (default) . 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 X NumZoom wh e re 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 X StatMode or 1 X StatMode n 0 > n 0 >
16-42 Programming 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 availa ble in Sketch view. Page All Aplets Sets a page i n a sketch set. A sketch set can c ontain up to 10 graphics. 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 X 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 X PageNum
Extending aplets 17-1 17 Extending aplets Aplets are the application environments where you explore different clas ses of mathematical operations. You can extend the capability of the hp 39g 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 measure , gr aphical or tabular settings, and annotations. • T r ansmit aplets between hp 3 9g 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 d’s Calc ulator w eb site. • Pr ogr am ne w aplets. See c hapter 16, Pr ogramming , for fu r t he r de t ai l s. 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 example demonstrates how to cre ate a new aplet by saving a copy of the bu ilt-in Solve aplet. The new aplet is saved under the name “TRIANGLES” contains the formulas commonly used in calculation s involving right-angled triangles.
17-2 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 fo ur fo rmu l as : θ O H θ A H θ OA AB C 3 . Deci de whether y ou wan t the aplet to oper ate in Degr ees , R adians , or Gr ads. MODES Degrees 4. Vie w the Aplet L ibrary . The “TR IANGLE S” aplet is listed in t he Aplet Libr a ry . T he Solv e aplet can no w be r eset and used f or other pr oblems.
Extending aplets 17-3 Using a customized aplet To use the “T riangles” 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. Select the a plet. TRIANGLES 2 . Choos e the sine fo rmula in E1. 3 . Change to the Numer ic vi ew a n d e n te r t he kno wn values . 35 5 4. Solv e for the missing va l ue. 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-in aplet if the programmer who created it has provided a Reset option.
17-4 Exten ding aplet s Annotating an aplet with notes The Note view ( NOTE ) attaches a note to the curre nt aplet. See Chapter 15, “Notes and ske tches”. Annotating an aplet with sketches The Sketch view ( SKET CH ) attaches a picture to the current aplet. See chapter 15, “Notes and sketches”. HINT Notes and s k etches that you attach to an apl et becom e par t of the aplet. When y ou transfer the aplet to another calculator , the assoc iated note a nd sketc h are tr ansferr ed 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-Packard’s 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-Packard’s Calculators web site can be found at : http://www.hp.com/calcul ators Sending and receiving aplets A convenient way to distribute or share problems in class and to turn in homework is to transmit (copy) aplets directly from one hp 39g to another. Th is takes place via the infrared port. You can also send aplets to, and receive aplets from, a remote storage device (aplet d i sk drive or computer). This takes place via a cab le connection and requires an aplet disk drive or special software running on a PC (such as the PC Connectivity Kit).
Extending aplets 17-5 To transmit an aplet 1. Connect the P C or aplet disk dr iv e to the calc ulator b y cable or align the tw o calc ulators ’ infr ar ed ports by mat ching up the tr iangle marks o n the rims o f the calc ulator s. P lace the calculato rs no mor e than 2 inches (5 cm) apar t. 2 . Sending calc ulator: Ope n the L ibr ary , hig hlight the aplet to se nd, and pr ess . – Y ou hav e t wo options : anot her h p 3 9g or a d isk dri ve o n a PC. H ighli ght y our selecti on and pr ess . – If transmitting to a disk dr i v e , y ou hav e the optio ns of se nding to the c ur r ent (de fault) directory or to an other d irectory . 3 . Rece iv ing calculator : Open the aplet library a nd pr ess . – Y ou hav e t wo options : anot her h p 3 9g or a d isk dr i ve (o r compute r ) . Highli ght y our select ion and pr ess . The T ransmit annunciator— —is display ed until tr ansmission is comp lete . If you are using the PC Connectivity Kit to download aplets from a PC, you will see a list of aplets in the PC’s current directory. Check as many i tems as you would like to receive . Sorting items in the aplet library menu list Once you have entered information into an aplet, you have defined a new ver sion of an aplet. The information is automatically saved under the current aplet name, such as “Function.” To create addi tional 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 environ ment for later use. The aplet library is where you go to manage your aplets. Press . Highlight (using the arrow keys) the name of the aplet you want to act on.
17-6 Exten ding aplet s To sort the aplet list In the aplet library, press . Select the sorting scheme and press . • Chronologically pr oduces a chr onolo gical or d er based on the dat e an aplet w as last used . (The last- used aplet ap pears first , a nd so on .) • Alphabetically pr o duces an alphabetical order 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 .
Reference in formation 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, and Statistics. 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 The 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.
R-2 Reference information 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 array 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 o r as a set of menu-key labels across the bottom of the display. menu keys T he top row of keys. Their operatio ns 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 array 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.
Reference in formation R-3 Resetting the hp 39g If the calculator “locks up” and seems to be stuck, 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 proc edure, “To erase al l memory a nd reset defaults”. To reset using the keyboard Press and hold the key and the thir d menu key simultaneously, then release them. If the c alculator d oes not resp ond to the above key sequence, then: 1. T urn the calc ulator ov er and locate the small hole in the bac k of the calc ulator . 2 . Insert the end of a str aightened metal paper clip into the hole as f a r as it w i ll go . Hold it ther e fo r 1 second , then r emo ve it . 3 . Pr ess If neces sary , pre ss and the fir st and last menu k ey s si multaneou sly . 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. Pres s and hold the ke y , the f irst men u k ey , and the last menu ke y si multaneously . 2 . Rele ase all k ey s. Note: T o cancel this pr oc ess , relea se only the top-r ow k e ys , then pr ess the thir d menu k ey . views The possible contexts for an aplet: Plot, Plot Setup, Numeric, Numeric Setup, Symbolic, Symbolic Setup, Sketch, Note, and special views like split screens.
R-4 Reference information If the calculator does not turn on If the hp 39g does not tu rn 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. Press and h old the ke y for 10 seconds . 2 . Pr ess and hold the k e y and the third menu k ey simultaneou sly . R elease the thir d menu k ey , then r elease t he ke y . 3 . Press and h old the k e y , the first men u k e y , an d the si xth men u k e y simultaneo usl y . Rele ase the si xth menu k ey , then r elease the f irst men u ke y , and then r elease t he ke y . 4. Locate 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 emo ve it . Pre ss the ke y . 5 . Remo ve the batter ies (see “Batte ri es ” on page R-4) , pr ess and hold the ke y for 10 seconds, and then put the bat ter ies back in . Pre ss the ke y . Operating details Operating temperature: 0 ° to 45 ° C (32 ° to 113 ° F). Storage temperature: –20 ° to 65 ° C (– 4 ° to 149 ° F). Operating and storage humidity: 90% relative humidity at 40 ° C (104 °F) maxi mum. Avoid getting the calculator wet. Battery operates at 4.5V dc, 60mA maximum. Batteries The calculator uses 3 AAA(LR03) batteries as main power and a CR2032 li thium battery for memory backup. Before using the calculator , please install the batteries according to the following procedure.
Reference in formation R-5 To install the main batteries a. Slide up the battery compartment cove r as illustrated. b. Insert 3 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: When the low battery icon is displayed, you need to replace the batteries as soon as possible. However, avoid removing th e backup battery and ma in batteries at the same time to avoid data lost. Plate Holder
R-6 Reference information Variables Home variables The home variables are: Categor y Av ailabl e 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
Reference in formation 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 A ngle F1 F2 F3 F4 F5 F6 F7 F8 F9 F0 Nume ric Digits Format NumCol NumFont NumIndep NumRow NumStart NumStep NumType NumZoom Note NoteText Sketc h Page PageNum
R-8 Reference information Parametric aplet variables The parametric aplet variables are: Categor y Av ailabl e 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
Reference in formation 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 A ngle R1 R2 R3 R4 R5 R6 R7 R8 R9 R0 Nume ric Digits Format NumCol NumFont NumIndep NumRow NumStart NumStep NumType NumZoom Note NoteText Sketc h Page PageNum
R-10 Reference information Sequence aplet variables The sequence aplet variables are: Categor y Av ailabl e 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
Reference in formation 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 A ngle E1 E2 E3 E4 E5 E6 E7 E8 E9 E0 Nume ric Digits Format NumCol NumRow Note NoteText Sketc h Page PageNum
R-12 Reference information Statistics aplet variables The statistics aplet variables are: Categor y Av ailabl e 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
Reference in formation 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 π Hype rb. ACOSH ASINH ATANH COSH SINH TANH ALOG EXP EXPM1 LNP1 List CONCAT ∆ LIST MAKELIST π LIST POS REVERSE SIZE Σ LIST SORT Loop ITERATE RECURSE Σ ∂ ∫
R-14 Reference information 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 →RAD FLOOR FNROOT FRAC HMS → → HMS INT MANT MAX MIN MOD % %CHANGE %TOTAL RAD →DEG ROUND SIGN TRUNCATE XPON Stat-Two PREDX PREDY Symbolic = ISOLATE LINEAR? QUAD QUOTE | Categor y Av ailabl e name (Continued)
Reference in formation R-15 Program constants The program constants are: Tests < ≤ = = ≠ > ≥ AND IFTE NOT OR XOR Trig ACOT ACSC ASEC COT CSC SEC Category Av ailable nam e (Continued) Category Av ailable name Angle Degrees Grads Radians Format Standard Fixed Sci Eng Fraction SeqPlo t Cobweb Stairstep S1...5fit Linear LogFit ExpFit Power QuadFit Cubic Logist User StatMode Stat1Var Stat2Var StatPlot Hist BoxW
R-16 Reference information Program commands The program commands are: Categor y 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 → → DISPLAY → GROB GROBNOT GROBOR GROBXOR MAKEGROB PLOT → → 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 BEE P CHOOSE DISP DISPTIME EDITMAT FREEZE GETKEY INPUT MSGBOX PROMPT WAIT Stat-One DO1VSTATS RANDSEED SETFREQ SETSAMPLE Stat-Two DO2VSTATS SETDEPEND SETINDEP
Reference in formation R-17 Status messages Message 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 MEMOR Y ). Insufficient Statistics Data Not enough data points for the calculation. For two-variable statistics there must be two columns of data, and eac h column must have at least four numbers. Invalid Dimension Array argument had wrong dimensions. Invalid Statistics Data Need two columns with equal numbers of data values. 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.
R-18 Reference information No Equations Checked You must enter and check 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 P roblem with data reception from a nother calculato r. Re- send the data. Too Few Arguments The command requires more arguments than you supplied. Undefined Name The glo bal variable named does not exist. Undefined Result The calcula tion 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 ). Messag e M eaning (Continued)
Limiting Warranty W-1 Li m i t i n g W a rran t y hp 39g Graphing Calculator; Warranty period: 12 months 1. HP warr ants to y ou , th e end-user c ustomer , that HP har dw are , accessor 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 per iod spec ified abo ve . If HP r ecei ves notice of such defects during t he warr ant y peri od, HP w ill, at its option , either r epair or r eplace pr oducts w hic h pr o ve to be def e cti ve . R eplacement pr oducts ma y be either ne w or like -ne w . 2 . HP war r ants to y ou th at HP softwar e w ill not fail to e x ecu te its pr ogr amming instru ctio ns after the date o f pur chase , for the per iod s pec ifi ed abo ve , due to def ects in mater ial and w orkmanship w h en pr operl y installed and used . If HP recei ves noti ce of such def ects dur ing the warr anty period , 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 not w arr ant that the oper ation of HP pr oducts w ill be uninter rupted or er r or fr ee. If HP is unable , within a r easonable time , to repair o r r eplace an y produc t to a condition as w arranted , you w ill be entitled to a r efund of the pur chase pr ice upon pr ompt r etur n of the pr oduct w ith pr oof of pu r c hase . 4. HP produc ts may contain r emanuf actur ed parts 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 defects r esulting from (a) impr oper or inadequate maintenance or calibr ation, (b) soft war e, interfac in g, parts or supplies not suppli ed b y HP , (c) unauthor iz ed modifi cation or mi suse, (d) o pe ratio n ou ts id e of t he pub l is he d en vir onmental s pecif ications f or the product , or (e) impr oper site prepar ation or maintenance .
W-2 Limiting Warranty 6 . HP MAKE S NO O THER EXPRE S S W ARRANTY OR CONDI T ION WHETHER WR ITTEN OR ORAL. T O THE EXTENT ALL O WED B Y L O CAL LA W , ANY IMP LIED W ARRANTY OR CONDI TION OF MERCHANT ABILITY , S A T ISF A CT OR Y Q U ALITY , OR FI TNE SS F OR A P A R T ICUL AR PURP OSE IS LIMI TED T O THE DUR A TION OF THE EXP RE S S W ARRANTY 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 abov e limitation or e x clu sio n might n ot appl y to y ou . This w arr anty gi v es 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 , state to state , or pro vince to pr ov inc e . 7 . T O THE EXTENT ALL O WED B Y L OCAL LA W , THE REMEDIE S IN THIS W ARRANTY S T A TEMENT ARE Y OUR S OLE AND EX CL US IVE REMEDI E S. E X CEPT A S INDICA TED ABO VE , IN NO EVENT WILL HP OR I T S S UPP LI ER S BE LIABLE FOR L O SS OF D A T A OR FOR DIRE CT , SPE CIAL, INCIDENT AL, C ONSE Q UENT IAL (INCL UDING L OS T PR OFIT OR D A T A), OR O THER D AMA GE , WHETHER B ASED IN C ONTRA CT , T OR T , OR O THERWI SE . Some countr ies, S tates or pr o v inces do not allo w the ex clusi on or limitation of inc iden tal or conseq uenti al damages, so the abo ve limit ation o r e x clu sion ma y not appl y to y ou . 8. The onl y war r anties for HP pr oducts and servi ces ar e set forth in the e x pr ess w arr anty statement s accompany ing such pr oducts and ser v ices . HP shall not be lia ble f or tec hnical or editor ial err ors o r omissions contai ned he r ein. 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.
Limiting Warranty W-3 Service Europe Country : T elephon e 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 33284 4 Ea s t e r n Eu ro p e countr ies 4 20-5- 414 2 2 5 2 3 Fi n l a n d 35 - 8964 0 0 0 9 F r ance 3 3-1- 4 9 9 3 9006 German y 4 9-6 9-9 5 30 7103 Gr eece 4 20 -5-414 2 2 5 2 3 Holland 31- 2 -06 54 5 301 Italy 3 9-0 2 - 7 5 419 7 8 2 No r way 4 7 -63 84 9309 P o rtugal 3 51- 2 2 9 5 7 0 200 Spain 34 -915-64 209 5 S weden 4 6 - 8 519 9 20 6 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 xe mbourg 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 : Telephone numbers A ust r alia 61-3-9 841-5 211 Singapor e 61- 3-9 841-5 211
W-4 Limiting Warranty P lease logon to http://www .hp .com for t he la test ser vice a n d s upp o r t in fo r m atio n . L.Ame ric a Country : T elephone nu mbers Ar gentina 0 -810 -5 5 5-5 5 20 Bra zil Sao P aulo 3 7 4 7 - 77 9 9; RO T C 0 -800 -15 77 51 M exi 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 8 0 0 - 4 7 46 - 8368 Chi le 800 -36 099 9 C o l u m b i a 9 - 8 0 0 - 1 1 4726 P er u 0- 800 -10111 Central Ame rica & Caribb ean 1-800 - 711- 2 88 4 Guatemala 1-8 00 -9 99-510 5 Pu e r t o R i c o 1 - 87 7- 232- 0 5 89 Cos ta R ica 0 - 800 -011-05 2 4 N.Americ a Country : T elephon e numbers U .S . 1800-HP INVENT Ca n a d a ( 905) 2 0 6 - 4663 o r 800 - HP INVENT RO T C = Rest of th e c ou nt r y
Limiting Warranty W-5 Regulatory infor mation This section contains information that shows how the hp 39g graphing calculator comp lies with regulations in certain regions. Any modificati ons to the calculator not expressly approved by Hewlett-Packard could void the authority to operate the 39g in these regions. USA This calculator generates , uses, and can radiate radio frequency energy and may interfere with radio and television reception. The calculator complies with the limits for a Class B digital devi ce, pursuant to Part 15 of the FCC Rules. The se limits are desi gned to p rovide reasonable protection agains t harmful interference in a residential installation. However, there is no guarantee that int erference will not occur in a particular installation. In the unlikely event that there is interference to radio or television re ception(wh ich can be determined by turning the calculator off and on), the user is encouraged to try to correct the interfe rence by one or more of the following measures:  Reor ient or relocate the r eceiv ing antenna.  Relocat e the calc ulator , with r espect t o the r ecei ver . Connections to Peripheral Devices To maintain compliance with FCC rules and regulations, use only the cable accessories provided. Canada This Class B digital apparatus c omplies with Canadian ICES-003. Cet ap pareil numerique de la classe B est conforme a la norme NMB-003 du Canada. Japan 󳆷 󳇒󱳾󱝯󳇓󳆏 󰕒󰀯󱂣󱳾󱝯󱔍󲒻󰳥󲑻 󰈣󱣥󱵺󱺰 󳌬󳍚󳍇󳍇 󳍍󳌭 󳇒󰀏󰷑 󳇏 󰀏 󳇉 󳆳 󱓺󰕒󰀯󰙼󱲻󱳾󱝯 󳇋 󳆽󳆐 󳆷 󳇒󱳾 󱝯󳇓󳆏 󰈦󰏙󱄄󰁛 󳇋 󱅋󳆽 󳇯 󳆷 󳇌 󳇶 󱊂󱈼 󳇌 󳆻 󳇊 󳆨 󳇢 󳆽 󳆰󳆏 󳆷 󳇒󱳾󱝯󳆰 󳉅 󳈔 󳈆 󳇨 󳈢 󳉈 󳈯 󳈔 󳉃 󳉏 󰭰 󳇏 󲃎󰜳 󳆻 󳇊  󱅋 󳆹 󳇰 󳇯 󳇌 󳆏 󲑻󰈣 󳇶 󰐢 󳆱 󱾁 󳆷 󳆽 󳆷 󳇌 󳆰 󳆦 󳇮 󳇢 󳆽󳆐 󰙳󱸲󰢠󰥁 󳫛 󰒆 󳫓 󳫖 󰯽 󳫇 󳪴  󳫺 󰙳 󳪴 󳬂 󳫇 󳫖 󳪿 󳫐 󳫅 󳪴 󳪜
W-6 Limiting Warranty Disposal of Waste Equipment by Users in Private Household in the European Union This s ymbol o n the pr oduct or on its pack aging indicates that this produc t m u s t n o t b e d i s p o s e d o f w i t h y o u r o t h e r household wa ste . Instead, it is yo ur responsibi li ty to di spose of your waste equipmen t b y handing it ov er to a designat ed collecti on po int f or the r ecy c ling of w aste elec tri cal and electr onic equipment. T he separate collection and r ecy cling o f y our w aste equipme nt at the time of disp osal w ill help to conserve natur al r esour ces and ensur e that it is r ecy cled in a manner that pr otects human health and the en v ir onment . F or more inf ormatio n about w here y ou can drop o ff y our wa ste equipment fo r rec yc ling, please contact y our local c ity offi c e , y our household w aste disposal service or the shop wher e yo u purc hased t he pr oduct .
Index I-1 Index A absolute value 11-5 add 11-3 algebraic en try 1-19 alpha characters typing 1-6 alphabetical so rting 17-6 angle measure 1-10 in statistics 8-12 setting 1-12 animation 15-5 creating 15 -5 annunciators 1-3 Ans (last answer) 1-24 antilogarithm 11-4, 11-9 aplet attaching notes 17- 4 clearing 17-3 copying 17-4 definition of R-1 deleting 17-6 Function 11-21 Inference 9-1 key 1-4 library 17-5 opening 1-16 Parametric 4-1 Polar 5-1 receiving 17-5 resetting 17-3 sending 17-4, 17 -5 Sketch view 15-1 Solve 7-1 sorting 17-6 statistics 8-1 transmitting 17-5 aplet commands CHECK 16-14 SELECT 16-14 SETVIEWS 16-17 UNCHECK 16-17 aplet variab les definition 12-1, 12 -8 in Plot view 16-30 new 12-1 aplet views canceling operations in 1-1 changing 1-19 note 1-18 Numeric view 1-17 Plot view 1-17 sketch 1-18 split-screen 1-17 Symbolic view 1-16 arc cosecant 11-19 arc cosine 11-4 arc cotangent 11-19 arc secant 11-19 arc sine 11-4 arc tangent 11-5 area graphical 3-10 interactive 3-10 variable 16-30 arguments with matrices 13-10 attaching a note to an aplet 15-1 a sketch to an aplet 15-3 auto scale 2-14 axes plotting 2-7 variable 16-30 B bad argument R-17 bad guesses error message 7-7 box-and-whisker plot 8-16 branch commands CASE...END 16-18 IF...THEN...ELSE...END 16-18 IFERR...THEN...ELSE 16-18 branch structures 16-17 build your own table 2-19 C calculus operations 11-7 catalogs 1-30
I-2 Index chronological sorting 17-6 circle dra wing 15-4 clearing aplet 17-3 character s 1-22 display 1-22 display history 1-25 edit line 1-22 lists 14-6 plot 2-7 cobweb graph 6-1 coeffi cients polynomial 11-10 columns changing position 16-25 combinations 11-12 commands aplet 16-14 branch 16-17 definition of R-1 drawing 16-19 graphic 16-20 loop 16-22 print 16-25 program 16-4, R-16 stat-one 16-28 stat-two 16-29 with matrices 13-10 complex number functions 11-5, 11-16 conjugate 11-7 imaginary pa rt 11-7 real p art 11-7 complex numbers 1-29 entering 1-29 maths functions 11-7 storing 1-29 confide nce inter vals 9-15 conjugate 11-7 connecting data points 8-18 variable 16-30 connectivity kit 17-4 constant? error message 7-7 constants 11-8 e 11-8 i 11-8 maximum real number 11-8 minimum real number 11-8 program R-15 contrast decreasing disp lay 1-2 increasing display 1-2 coordinate display 2-9 copying display 1-22 graphics 15-6 notes 15-8 programs 16-8 correlation coefficient 8-17 CORR 8-17 statistical 8-15 cosecant 11-19 cosine 11-4 inverse hyperbolic 11-8 cotangent 11-19 covariance statistical 8-15 creating aplet 17-1 lists 14-1 matrices 13-3 notes in Notepad 15-6 programs 16-4 sketches 15-3 critical value(s) displayed 9-4 cross product vector 13-10 curve fitting 8-12, 8-17 D data set definition 8-8 date, setting 16-26 debugging programs 16-7 decimal changing format 1-11 scaling 2-14, 2-16 decreasing display contrast 1-2 definite integral 11-6 deleting aplet 17-6 lists 14-6 matrices 13-4 programs 16-9 statistical data 8-11 delimiters, programming 16-1 deriva tives
Index I-3 definition of 11-6 in Function aplet 11-22 in Home 11-21 determinant square matrix 13-11 differentiation 11-6 display 16-20 adjusting contrast 1-2 annunciator line 1-2 capture 16-20 clearing 1-2 date and time 16-26 element 13-5 elements 14-4 engineering 1-11 fixed 1-11 fraction 1-11 history 1-22 line 1-23 matrices 13-5 parts of 1-2 printing contents 16-25 rescaling 2-14 scientific 1-11 scrolling through history 1-25 soft key labels 1-2 standard 1-11 divide 11-3 drawing circles 15-4 keys 15-4 lines and boxes 15-3 drawing commands ARC 16-19 BOX 16-19 ERASE 16-20 FREEZE 16-20 LINE 16-20 PIXOFF 16-20 PIXON 16-20 TLINE 16-20 E e 11-8 edit line 1-2 editing matrices 13-4 notes 15-2 programs 16-5 Editline Program catalog 16-2 editors 1-30 eigenvalues 13-11 eigenvectors 13-11 element storing 13-6 E-lessons 1-12 engineering number format 1-11 equals for equations 11-17 logical test 11-18 equations solving 7-1 erasing a line in Sketch view 16-20 error messages bad guesses 7-7 constant? 7-7 exclusive OR 11-19 exiting views 1-19 exponent minus 1 11-9 of value 11-16 raisin g to 11-5 expression defining 2-1, R-1 entering in HOME 1-19 evaluating in aplets 2-3 literal 11-18 plot 3-3 extremum 3-10 F factorial 11-12 FastRes variable 16-31 fit a curve to 2VAR da ta 8-17 choosing 8-12 defining your own 8-13 fixed number format 1-11 font size change 3-8, 15-5 foreca sting 8-20 fraction number format 1-11 full-precision display 1-11 function analyse graph with FCN tools 3-4 definition 2-2, R-1 enteri ng 1-19
I-4 Index gamma 11-12 intersection point 3-5 math menu R-13 slope 3-5 syntax 11-2 tracing 2-8 Function aplet 2-21, 3-1 function variables area 16-30 axes 16-30 connect 16-30 fastres 16-31 grid 16-31 in menu map R-7 indep 16-32 isect 16-32 labels 16-33 Recent er 16-33 root 16-33 ycross 16-36 G glossary R-1 graph analyzing statistical data in 8-19 auto scale 2-14 box-and-whisker 8-16 capture cu rrent display 16-20 cobweb 6-1 compar ing 2-5 connected points 8-17 defining the independent variable 16-35 drawing axes 2-7 expressions 3-3 grid points 2-7 histogr am 8-15 in Solve aplet 7-7 one-var iable sta tistics 8-18 overlayin g 2-16 scatter 8-15, 8-16 split-screen view 2-15 splitting into plot and close-up 2-14 splitting into plot and table 2-14 stairsteps 6-1 statistical data 8-15 t values 2-6 tickmarks 2-6 tracing 2-8 two-variable statistics 8-18 Graphic commands → GROB 16-21 DISPLAY → 16-20 GROBNOT 16-21 GROBOR 16-21 GROBXOR 16-21 MAKEGROB 16-21 PLOT → 16-21 REPLACE 16-22 SUB 16-22 ZEROGROB 16-22 graphics copying 15-6 copying into Sketch view 15-6 storing and recalling 15- 6 , 16-20 H histogram 8-15 adjusting 8-16 range 8-18 setting min/max values for bars 16-31 width 8-18 history 1-2, 16-25 Home 1-1 calculating in 1-19 display 1-2 evaluating expressions 2-4 reusing lines 1-23 variables 12-1, 12-7, R-6 horizontal zoom 16-37 hyperbolic maths functions 11-9 hyperbolic trigonometry ACOSH 11-8 ALOG 11-9 ASINH 11-8 ATANH 11-8 COSH 11-8 EXP 11-9 EXPM1 11-9 LNP1 11-9 SINH 11-8 TANH 11-9 hypothesis alternative 9-2 inference tests 9-8 null 9-2 tests 9-2
Index I-5 I i 11-8 implied multiplication 1-21 importing graphics 15-6 notes 15-8 increasing display contrast 1-2 indefinite integral using symbolic variables 11-23 independent values adding to table 2-19 independent variable defined for Tracing mode 16-32 inference confidence intervals 9-15 hypothesis tests 9-8 One-Proportion Z-Interval 9-17 One-Sample Z-Interval 9-15 One-Sample Z-Test 9-8 Two-Proportion Z-Interval 9-17 Two-Proportion Z-Test 9-11 Two-Sample T-Inte rval 9-19 Two-Sample Z-Interval 9-16 infinite result R-17 infrared transmission of aplets 17-5 initia l guess 7-5 input forms resetting default values 1-9 setting Modes 1-12 insufficient memory R-17 insufficient statistics data R-17 integer rank matrix 13-12 integer scaling 2-14, 2-16 integral definite 11-6 indefinite 11-23 integration 11-6 interpreting intermediate guesses 7-7 intersection 3-11 invalid dimension R-17 statistics data R-17 syntax R-17 inverse hyperbolic cosine 11-8 inverse hyperbolic functions 11-9 inverse hyperbolic sine 11-8 inverse hyperbolic tangent 11-8 inverting matrices 13-8 isect v ariable 16-32 K keyboard editing keys 1-5 entr y keys 1-5 inactive keys 1-8 list keys 14-2 math functions 1-7 menu keys 1-4 Notepad keys 15-8 shifted keystrokes 1-6 L labeling axes 2- 7 parts of a sketc h 15-5 letters, typing 1-6 library, managing aplets in 17-5 linear fit 8-13 list arithmetic with 14-7 calculate sequence of e lements 14-8 calculating product of 14-8 composed from differences 14-7 concatenating 14-7 counting elements in 14-9 creating 14-1, 14-3, 14- 4 , 14-5 deleting 14-6 deleting list items 14-3 displaying 14-4 displaying list elements 14-4 editing 14-3 finding statistical values in list ele- ments 14-9 generate a series 14-8 list function syntax 14-6 list variables 14-1 returning positi on of element in 14-8 reversing order in 14-8 sending and receiving 14-6 sorting elements 14-9 storing e lements 14-1 , 14-4 , 14-5 storing one element 14-6 logarithm 11-4
I-6 Index logarithmic fit 8-13 functions 11-3 logical operators AND 11-19 equals (logical test) 11-18 greater than 11-18 greater than or equal to 11-19 IFTE 11-19 less than 11-18 less than or equal to 11-18 NOT 11-19 not equal to 11-18 OR 11-19 XOR 11-19 logistic fit 8-13 loop commands BREA K 16-23 DO...UNTIL...END 16-22 FOR I= 16-23 WHILE...REPEAT...END 16-23 loop func tions ITERATE 11-9 RECUR SE 11-10 summation 11-10 low battery 1-1 lowercase letters 1-6 M mantissa 11-14 math functions complex number 11-7 hyperbolic 11-9 in menu map R-13 keyboard 11-3 logical operators 11-18 menu 1-7 polynominal 11-10 probability 11-12 real-number 11-13 symbolic 11-17 trigonometry 11-19 MATH menu 11-1 math operations 1-19 enclosing arguments 1-21 in scientific notation 1-20 negative numbers in 1-20 matrices adding rows 16-23 addition and s ubtraction 13-6 arguments 13-10 arithmetic operations in 13-6 assembly from vectors 13-1 changing row position 16-25 column norm 13-10 comma 14-7 commands 13-10 condition number 13-10 create identity 13-13 creating 13-3 creating in Home 13-5 deleting 13-4 deleting columns 16-24 deleting rows 16-24 determinant 13-11 display eigenvalues 13-11 displaying 13-5 displaying matrix elements 13-5 dividing by a square matrix 13-7 dot product 13-11 editing 13-4 extracting a portion 16-25 finding the trace of a square ma- trix 13-13 inverting 13-8 matrix calculations 13-1 multiplying and dividing by scalar 13-7 multiplying by vector 13-7 multiplying row by value and add- ing result to second row 16-24 multiplying row number by value 16-24 negating elements 13-8 opening Matrix Editor 16-27 redimension 16-24 replacing portion of matrix or vec- tor 16-24 sending or receiving 13-4 singular value decomposition 13-13 singular values 13-13 size 13-12 spectral norm 13-12 spectral radius 13-12 start Matrix Editor 16-24 storing elements 13-3, 13 -5 storing matrix elements 13-6 swap column 16-25 swap row 16-25 transposing 13-13
Index I-7 variables 13-1 matrix functions 13-10 COLNORM 13-10 COND 13-10 CROSS 13-10 DET 13-11 DOT 13-11 EIGENVAL 13-11 EIGENVV 13-11 IDENMAT 13-11 INVERSE 13-11 LQ 13-11 LSQ 13-11 LU 13-11 MAKEMAT 13-11 QR 13-12 RANK 13-12 ROWNORM 13-12 RREF 13-12 SCHUR 13-12 SIZE 13-12 SPECNORM 13-12 SPECRAD 13-12 SVD 13-13 SVL 13-13 TRACE 13-13 TRN 13-13 maximum real number 1-22, 11-8 memory R-17 clearing all R-3 organizing 12-9 out of R-18 saving 1-25, 17-1 viewing 12-1 menu lists searching 1-8 minimum real number 11-8 modes angle measure 1-10 decimal mark 1-11 number format 1-11 multiple solutions plotting to find 7-7 multiplication 11-3 implied 1-21 N name conflict R-17 naming programs 16-4 natural exponential 11-3, 11-9 natural log plus 1 11-9 natural logarithm 11-3 negation 11-5 negative numbers 1-20 no equations checked R-18 Normal Z-distribution, confidence i n- tervals 9-15 note copying 15-8 editing 15-2 importing 15-8 printing 16-25 viewing 15-1 writing 15-1 Notepad 15-1 catalog keys 15-7 creating notes 15-6 writing in 15-6 nrng 2-6 n th root 11-6 null hypothesis 9-2 number format engine ering 1-11 fixed 1-11 fraction 1-11 in Solve aplet 7-5 scientific 1-11 Standard 1-11 numeric prec ision 12-9 Numeric view adding values 2-19 automatic 2-17 build your ow n table 2-19 display defining function for col- umn 2-18 recalculating 2-19 setup 2-17, 2-19 O off automatic 1-1 power 1-1 on/can cel 1-1 One-Proportion Z-Interv al 9-17 One-Sa mple T-In terval 9- 18 One-Sa mple T- Test 9-12 One-Sa mple Z-I nterval 9-15 One-Sa mple Z-Te st 9-8
I-8 Index order of precedence 1-21 overlaying plots 2-16, 4- 3 P π 11-8 paired columns 8-11 parametric variables axes 16-30 connect 16-30 grid 16-31 in menu map R-8 indep 16-32 labels 16-33 recent er 16-33 ycross 16-36 parentheses to close arguments 1-21 to specify order of operation 1-21 pause 16-28 permutations 11-12 pictures attaching in Sketch view 15-3 plot analyzing statistical data in 8-19 auto scale 2-14 box-and-whisker 8-16 cobweb 6-1 compar ing 2-5 connected points 8-17, 8-18 decimal scaling 2-14 defining the independent variable 16-35 drawing axes 2-7 expressions 3-3 grid points 2-7 histogr am 8-15 in Solve aplet 7-7 integer scaling 2-14 one-var iable sta tistics 8-18 overlay plot 2-14 overlayin g 2-16, 4-3 scaling 2-14 scatter 8-15, 8-16 sequence 2-6 setting up 2-5, 3-2 split-screen view 2-15 splitting 2-15 splitting into plot and close-up 2-14 splitting into plot and table 2-14 stairsteps 6-1 statistical data 8-15 statistics parameters 8-18 t values 2-6 tickmarks 2-6 to capture current display 16-20 tracing 2-8 trigonometric scaling 2-15 two-variable statistics 8-18 plotting resolution and tracing 2-8 plot-view variables area 16-30 connect 16-30 fastres 16-31 function 16-30 grid 16-31 hmin/hmax 16-31 hwidth 16-32 isect 16-32 labels 16-33 recenter 16-33 root 16-33 s1mark-s5mark 16-33 statplot 16-34 tracing 16-32 umin/umax 16-34 ustep 16-34 polar variables axes 16-30 connect 16-30 grid 16-31 in menu map R-9 indep 16-32 labels 16-33 recenter 16-33 ycross 16-36 polynomial coefficients 11-10 evaluation 11-11 form 11-11 roots 11-11 Taylor 11-7 polynomial functions POLYCOEF 11-10 POLYEVAL 11-11 POLYFORM 11-11 POLYROOT 11-11 position argument 16-20 power (x raised to y) 11-5
Index I-9 preced ence 1-22 predicted values statistical 8-20 print contents of display 16-25 name and contents of variable 16-25 object in history 16-25 variables 16-25 probability functions ! 11-12 COMB 11-12 RANDOM 11-12 UTPC 11-12 UTPF 11-13 UTPN 11-13 UTPT 11-13 program commands 16-4 copying 16-8 creating 16-4 debugging 16-7 deleting 16-9 delimiters 16-1 editing 16-5 naming 16-4 pausing 16-28 printing 16-25 sending and receiving 16-8 structured 16-1 prompt commands beep 16-25 create choose box 16-26 create input form 16-27 display item 16-26 display message box 16-28 halt program execution 16-28 insert line breaks 16-28 prevent screen display being up- dated 16-27 set date and time 16-26 store keycode 16-27 Q quadratic extremum 3-6 fit 8-13 function 3-4 quotes in program names 16-4 R random numbers 11-12 real number maximum 11-8 minimum 11-8 real p art 11-7 real-number functions 11-13 % 11-15 %CHANGE 11-15 %TOTAL 11-15 CEILING 11-13 DEGtoRAD 11-13 FNROOT 11-14 HMSto 11-14 INT 11-14 MANT 11-14 MAX 11-15 MIN 11-15 MOD 11-15 RADtoDEG 11-15 ROUND 11-16 SIGN 11-16 TRUNCATE 11-16 XPON 11-16 recalc ulation fo r table 2-19 receive error R-18 receiv ing aplet 17-5 lists 14-6 matrices 13-4 programs 16-8 redra wing table of numbers 2-18 reduced row eche lon 13-12 regression analysis 8-17 fit models 8-13 formula 8-12 user-defined fit 8-13 relative error statistical 8-17 resetting aplet 17-3 calculator R-3 memory R-3 result copying to edit line 1-22 reusing 1-22 root
I-10 Index intera ctive 3-10 n th 11-6 variable 16-33 root-finding displaying 7-7 intera ctive 3-9 operat ions 3-10 variables 3-10 S S1mark-S5mark variables 16-33 scaling automatic 2-14 decimal 2-10, 2-14 integer 2-10, 2-14, 2-16 options 2-14 resetting 2-14 trigonometric 2-15 scatter plot 8-15, 8-16 connected 8-17, 8-18 SCHUR decomposition 13-12 scientific number format 1-11, 1- 20 scrolling in Trace mode 2-8 searching menu lists 1-8 speed searche s 1-8 secant 11-20 sending aplets 17-4 lists 14-6 programs 16-8 sequence definition 2-2 sequence variables Axes 16-30 Grid 16-31 in menu map R-10 Indep 16-32 Labels 16-33 Recent er 16-33 Ycross 16-36 setting date 16-26 time 16-26 sign reve rsal 7-6 sine 11-4 inverse hy perbolic 11-8 singular value decomposition matrix 13-13 singular values matrix 13-13 sketches creating 15-5 creating a blank graphic 16-22 creating a set of 15-5 erasing a line 16-20 labeling 15-5 opening view 15-3 sets 15-5 storing in graphics variable 15-5 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 16-30 connect 16-30 fastres 16-31 grid 16-31 in menu map R-11 indep 16-32 labels 16-33 recenter 16-33 ycross 16-36 sorting 17-6 aplets in alphab etic order 17-6 aplets in chronological order 17- 6 elements in a li st 14-9 spectral norm 13-12 spectral radius 13-12 square root 11-5 stack history printing 16-25 stairsteps graph 6-1 standard number format 1-11 statistics analysis 8-1 analyzing plots 8-19 angle mode 8-12 calculate one-variable 16-29 calculate two-variable 16-29 data set variables 16-39
Index I-11 data structure 16-39 define one-variable sample 16-29 define two-va riable data set’s de- pendent column 16-29 define two-variable data set’s in- dependent column 16-29 defining a fit 8-12 defining a regression model 8-12 deleting data 8-11 editing data 8-11 frequency 16-29 inserting data 8-11 plot type 8-18 plotting data 8-15 predicted valu es 8-20 regression curve (fit) models 8-12 saving data 8-10 sorting data 8-11 specifying angle setting 8-12 toggling between one-variable and two-variable 8-12 tracing plots 8-19 troubleshooting with plots 8-18 zooming in plots 8-19 statistics variables Axes 16-30 Connect 16-30 Grid 16-31 Hmin/Hmax 16-31 Hwidth 16-32 in menu map R-12 Indep 16-32 Labels 16-33 Recenter 16-33 S1mark-S5mark 16-33 Ycross 16-36 step size of independent variable 16-35 storing list elements 14-1, 14 -4 , 14-5 , 14-6 matrix el ements 13-3, 13-5, 13-6 results of calculation 12-2 value 12-2 strings literal in symbolic operations 11-18 subtract 11-3 summation function 11-10 symbolic calculations in Function aplet 11-21 defining expressions 2-1 differentiation 11-21 displaying definitions 3-8 evaluating variab les in view 2-3 setup view for statistics 8-12 symbolic functions | (where) 11-18 equal s 11-17 ISOLATE 11-17 LINEAR? 11-17 QUAD 11-17 QUOTE 11-18 Symbolic view defining expressions 3-2 syntax 11-2 syntax errors 16-7 T table navigate around 3-8 numeric values 3-7 numeric view setup 2-17 tangent 11-4 inverse hyperbolic 11-8 Taylor polynomial 11-7 tickmarks for plotting 2-6 time 11-14 setting 16-26 time, converting 11-14 times sign 1-21 tmax 16-35 tmin 16-35 too few arguments R-18 tracing functions 2-8 more than one curve 2-8 not matching plot 2-8 plots 2-8 transmitting lists 14-6 matrices 13-4 programs 16-8 transposing a matrix 13-13 trigonometric functions 11 -19 scaling 2-10, 2- 15 , 2-1 6 trigonometry functions
I-12 Index ACOT 11-19 ACSC 11-19 ASEC 11-19 COT 11-19 CSC 11-19 SEC 11-20 trng 2-6 truncating values to decimal places 11-16 tstep 2-6 , 16-35 Two-Pr oportion Z- Interva l 9-17 Two-Pr oportion Z- Test 9-11 Two-Sample T-Inte rval 9-19 Two-Sample T-tes t 9-14 Two-Sample Z-Interval 9-16 typing letters 1-6 U undefined name R-18 result R-18 un-zoom 2-11 upper-tail chi-squared probability 11-12 upper-tail normal probability 11-13 upper-tail Sned ecor’s F 11-13 upper-tail student’s t-probability 11-13 user defined regression fit 8-13 V value recal l 12-3 storing 12-2 variables aplet 12-1 categories 12-7 definition 12-1, 12-7, R-2 in equation s 7-10 in Symbolic view 2-3 independent 16-35 local 12-1 previous result (Ans) 1-23 printing 16-25 root 16-33 root-finding 3-10 step size of independent 16-35 types 12-1, 12 -7 use in calculations 12-3 VARS menu 12-4 , 12-5 vectors column 13-1 cross product 13-10 definition of R-2 views 1-18 configuration 1-18 definition of R-3 W warning symbol 1-8 where command ( | ) 11-18 X Xcross variable 16-35 xrng 2-6 Y Ycross variable 16-36 yrng 2-6 Z Z-Interval 9-15 zoom 2-1 8 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 2-18 out 2-9 redrawing table of numbers op- tions 2-18 square 2-10 un-zoom 2-11 within Numeric view 2-18 X-zoom 2-9 Y-zoom 2-10