HP 39G User Manual

HP 39G/40G GR APHING CALCULATOR USER’S GUIDE Ve r s i o n 1. 1

Contents i Contents Pref ace Manual conventions... ....................... ................ ................. .................... P-1 Notice ............. ................. ...................... ................. ....................... ........ P-2 1 Getti ng starte d On/off, cancel operations...... ....................... ................. ................. .........1-1 The display ................ ....................... ................ ....................... ...............1- 2 The keyboard ........................ ................. ....................... ................. .........1-3 Menus ....... ................. ....................... ................ ....................... ...............1- 8 Input forms ................ ................. ...................... ................. ................. ....1-9 Mode settings................... ................. ..... ................. ...... ..... ................. ....1- 9 Setting a mode ..... ................. ...................... ................. ................. ..1-11 Aplets (E–lessons) ............................ ................ ....................... .............1-11 Aplet library .................... ...... ...... ..... ................. ...... ..... ................. ..1-15 Aplet views ................ ..... ................. ...... ..... ................. ...... ...... .......1-15 Aplet view configuration ................. ...... ..... ................. ...... .............1-1 7 Mathematical calculations ................ ................ ....................... .............1-18 Using fractions................. ...................... ................. ................. .............1-24 Complex numbers....................... ...................... ................. ................. ..1-27 Catalogs and editors ............. ................. ....................... ................. .......1-28 Differences between the HP 38G and the HP 39G/40G.......................1-29 2 Aplet s and their vi ews Aplet views ...................... ................. ...................... ................. ...............2-1 About the Symbolic view ........................... ................. .....................2- 1 Defining an ex pression (Symbolic view).......... ................. ...............2-1 Evaluating expression s ............... ...................... ................. ...............2-3 About the Plot view .............. ...................... ................. ................. ....2-5 Setting up the plot (Plot view setup) ................. ................. ...............2- 5 Exploring the graph .................... ..... ................. ...... ................. ..... ....2-7 Other views for scaling and splitting the graph ...... ...................... ..2-14 About the numeric view................... ................. ....................... .......2-16 Setting up the table (numer ic view setup) .............. ................. .......2-17 Exploring the table o f numbers ........ ................. ................. .............2-18 Building your own table of numbers .......... ....................... .............2-19 “Build Your Own” menu keys .................... ...... ...... ................. ..... ..2-20 Example: plotting a circle ...................... ................. ...................... ..2-21
ii Contents 3 Fun ct ion aplet About the Function aplet ... ................. ...................... ................. .............3-1 Getting started with the Function aplet ........................... ................. . 3-1 Function aplet interactive analysis ........... ...................... ................. .......3-8 Plotting a piecewise defined function example ................... ...........3-11 4 Par ametric apl et About the Parametric aplet ............................ ................. ................. .......4-1 Getting started with the Parametric aplet.................. ....................... . 4-1 5 Pol ar aplet Getting started with the po lar aplet ..................... ....................... .......5-1 6 Seq uence ap let About the Sequence aplet ................... ...................... ................. .............6-1 Getting started with the Sequen ce aplet .............. ................. .............6-1 7 Sol ve aple t About the Solve aplet .............. ...................... ................. ....................... . 7-1 Getting started with the Solve ap let .......................... ................. .......7-2 Use an initial guess ............ ....................... ................ ....................... .......7-5 Interpreting results ....... ....................... ................. ...................... .............7-6 Plotting to find guess es ................. ....................... ................. ..................7-8 Using variables in equ ations ......... ................. ................. ......................7-10 8 Sta tis tic s ap let About the Statistics aplet .............. ................. ....................... ................. . 8-1 Getting started with the Statistics aplet.......... ...................... .............8-1 Entering and editing s tatistical data .......... ...................... ................. .......8-5 Defining a regressio n model (2VAR) ................. ................. ...........8-11 Computed s tatistics ............ ................. ...................... ................. ...........8-13 Plotting ........................ ................. ................. ....................... ................8-15 Plot types........... ................. ...................... ................. ................. .....8-16 Fitting a curve to 2VAR data ......................... ................. ................8-17 Setting up the plot (Plot s etup view) ........ ................. ......................8-18 Trouble-shooting a plot ........... ....................... ................. ................8-19 Exploring the g raph ...................... ...................... ................. ...........8-20 Calculating predicted v alues .................... ....................... ................8-21
Contents iii 9 Infer ence a plet About the Inferen ce aplet ...................... ................. ................. ...............9- 1 Getting started with the Infere nce aplet ....................... .....................9- 2 Importing Sample Statistics from th e Statistics aplet .. ................. ....9-5 Hypothesis tests .......................... ................. ...................... ................. ....9-9 One–Sample Z–Test ................... ................ ....................... ...............9- 9 Two–Sample Z–Test ................... ..... ................. ...... ................. ..... ..9-10 One–Proportion Z–T est .............. ...................... ................. .............9-11 Two–Proportion Z– Test .............. ................ ................. ...................9-12 One–Sample T–Test ................... ................ ....................... .............9-13 Two–Sample T–Test ................... ..... ................. ...... ................. ..... ..9-14 Confidence intervals ......................... ................ ....................... .............9-16 One–Sample Z–Interval ........ ...................... ................. ...................9-16 Two–Sample Z–Interval . ...... ...... ..... ................. ...... ................. ..... ..9-17 One–Proportion Z–I nterval ......... ...................... ................. .............9-18 Two–Proportion Z– Interval ............. ................. ................. .............9-19 One–Sample T–Interval ........ ...................... ................. ...................9-20 Two–Sample T–Interval .................. ...... ................. ..... ................. ..9-21 10 Using mathemat ic al functi o ns Math functions ................. ...................... ................. ....................... .......10-1 The MATH menu............ ....................... ................. ................. .......10-1 Math functions by catego ry ................... ....................... ................. .......10-3 Keyboard function s ............... ................. ................. ...................... ..10-4 Calculus functions........... ................. ....................... ................. .......10-7 Complex number fu nctions ......... ................ ....................... .............10-8 Constants......................... ................. ....................... ................. .......10-9 Hyperbolic trigonom etry........................ ................. ...................... ..10-9 List functions .................. ................. ....................... ................. .....10-10 Loop functions ................ ....................... ................. ................. .....10-11 Matrix functions.................... ................. ...................... .................10-1 1 Polynomial functions .................. ..... ...... ..... ................. ...... ...........10-12 Probability functions ............. ................. ..... ................. ...... ...... .....10-13 Real-number fun ctions .......... ................. ...................... .................1 0-15 Statistics-Two ................. ....................... ................. ................. .....10-18 Symbolic functions ............... ................. ................. ......................1 0-19 Test functions........................ ................. ...................... .................1 0-20 Trigonometry functions ................... ....................... ................. .....10-21 Symbolic calculations ........... ...... ................. ..... ...... ................. ...... ..... 10-22 Finding derivatives ............... ...... ..... ................. ...... ..... .................1 0-2 3
iv Contents 11 Variables and memory management Introduction ................. ....................... ................. ................. ................11-1 Storing and recalling variables ................. ...................... ................. .....11-2 The VARS menu ............... ................. ...................... ................. ...........11-4 Memory Manager .................... ................. ................ ....................... .....11-9 12 Matri ces Introduction ................. ....................... ................. ................. ................12-1 Creating and s toring matrices ................... ................ ................. ...........12-2 Working with matr ices ....................... ................. ...................... ...........12-4 Matrix arithmetic ......... ....................... ................. ...................... ...........12-6 Solving systems of linear equations............... ...................... ...........12-8 Matrix functions and commands ................... ................. ...... ..... ...........12-9 Argument conven tions ........................ ................ ................. .........12-10 Matrix functions...................... ....................... ................. ..............12-10 Examples ................ ...................... ................. ................. ....................12-13 13 Lists Creating lists ...................... ....................... ................ ................. ...........13-1 Displaying and editing lists ........................... ................. ...... ..... ...........13-4 Deleting lists ...................... ................. ...................... ................. .....13-6 Transmitting lists .................... ....................... ................. ................13-6 List functions ........................... ................. ..... ...... ................. ..... ...........13-7 Finding statistical values fo r list elements ............................ ..............13-10 14 Notes an d sketches Introduction ................. ....................... ................. ................. ................14-1 Aplet note view............ ................. ....................... ................. ................14-1 Aplet sketch view .................... ................. ...................... ................. .....14-3 The notepad ....................... ................. ...................... ................. ...........14-6
Contents v 15 Pr ogram ming Introduction ............... ....................... ................ ....................... .............15-1 Program catalog .................... ...................... ................. ................. ..15-2 Creating and editing pro grams .............. ....................... ................. .......15-4 Using programs ............... ................. ...................... ................. .............15-7 Working with pro grams .............. ................. ...................... ................. ..15-8 About customizing an aplet .............. ..... ...... ................. ..... ................. ..15-9 Aplet naming convention ............................ ................. ...... ...........1 5-10 Customizing an aplet example .................... ................. .................15-1 0 Programming comm ands ....................... ................. ................. ...........15-14 Aplet commands ......................... ..... ................. ...... ................. .....1 5-1 4 Branch command s ...... ...................... ................. ................. ...........15-1 7 Drawing commands .................... ................ ....................... ...........15-19 Graphic commands ............... ...................... ................. .................15-2 0 Loop commands.............. ....................... ................. ................. .....15-22 Matrix commands ....................... ................ ....................... ...........1 5-23 Print commands .............. ................. ....................... ................. .....15-25 Prompt commands .......... ....................... ................. ......................1 5-25 Stat-One and Stat-Two commands ................... ...... ..... .................1 5-2 9 Storing and r etrieving variables in pro grams .......... ................. .....15-30 Plot-view variables ..................... ................ ....................... ...........15-30 Symbolic-view variables....... ...................... ................. .................15-3 7 Numeric-view variables .............. ..... ...... ..... ................. ...... ...........15-39 Note variables ............................. ................ ....................... ...........15-4 2 Sketch variables .................... ...................... ................. .................15-4 2 16 Ex te nding aple ts Creating new aplets based on existing aplets .................... ...................16-1 Resetting an aplet ............ ................. ................. ....................... .......16-4 Annotating an aplet with notes .............. ................. ...................... ..16-4 Annotating an aplet with sketches .............. ....................... .............16-4 Downloading e-lessons from the web .................... ................. .............16-4 Sending and receiving aplets ............................ ................. ...................16- 5 Sorting items in the aplet library menu list ............ ................. .............16-6
vi Contents Refere nce infor mation Regulatory inf ormation ...................... ...................... ................. ............ R-1 USA ....................... ................. ....................... ................. ................. R-1 Canada .............. ...................... ................. ................. ....................... R-1 LED safety .............. ...................... ................. ....................... ................. R-2 Warranty ................. ................. ...................... ................. ................. ...... R-2 CAS .................. ....................... ................. ................ ....................... ...... R-4 Resetting the HP 39G/40G ................. ...... ..... ................. ...... ................. R-4 To erase all memory and reset def aults .............. ...... ................. ...... R-5 If the calculator doe s not turn on .................. ................. ................. R-5 Glossary ............ ....................... ................. ...................... ................. ...... R-6 Operating details...................... ................. ...................... ................. ...... R-7 Batteries ............................. ................. ................ ....................... ...... R-7 Menu maps of the VAR S menu................ ...................... ................. ...... R-8 Home variables ............ ...... ...... ..... ................. ...... ..... ................. ...... ...... R-8 Function aplet variables...................... ................. ...................... ............ R-9 Parametric aplet variables........ ................. ...................... ................. .... R-10 Polar aplet variables ........................... ................. ...................... .......... R-11 Sequence aplet variables.......... ................. ...................... ................. .... R-12 Solve aplet variables .......... ....................... ................ ....................... .... R-13 Statistics aplet variables ..................... ................. ...................... .......... R-14 Menu maps of the MATH m enu ........ ...................... ................. .......... R-15 Math functions ................... ................. ...................... ................. .... R-15 Program constan ts ......................... ................. ................. ............... R-17 Program command s ................ ................. ................. ..................... R-18 Selected status messages .............. ................. ....................... ............... R-19 Index
Preface P- 1 Preface The HP 39G/40G is a feature-rich graphing calc ulator. It is also a powerful mathematics learni ng tool. The HP 39G/40 G is designe d so that you can us e it to explore mathem atical functi ons and their properties. You can get mor e informatio n on the HP 39G/40G f r om Hewlett- P ackard’s Calc ulators web site . You can download customized aplets fro m th e web site a nd lo ad the m on to yo ur calculat o r. Customized aplets are sp ecial applicati on s develop ed to perform c ertain func tions, and to demonstrat e mathema tical concepts. Hewlett P ackard’s Calcul ators web site can be found at: www.hp.com/calculators Manual conv entions The fol lowing conven tions are used in this ma nual to represent th e keys that you press and the menu options tha t you choo se to perform the d escribed oper at ions. • Key presses are rep resented as follows: >6,1@ , >&26@ , > 20(@ , etc. • Shift keys, that is the ke y functions th at you access b y pressing the >6 ,)7@ key first, are repre sented as follows: >6 ,)7@ CLEAR , >6 ,)7@ MODES , >6 ,)7@ ACOS , etc. • Numbers a nd letters are repres ented normally , as follows: 5, 7, A, B, etc . • Menu opt ions, that is, the function s that you select using the menu keys at the to p of the keypad ar e represente d as follows: 672 ?a ,  & $1&/ a , 2.a . • Input form fields and choose list items are represe nted as follows: Function , Polar , Parametric • Y our entries as t hey appear on the command l i ne or within input forms are represen ted as follows: 2*X 2 -3X 5
P-2 Pref ace Notice This manu al and any ex amples contain ed herein are provided as-is and are subj ect to change without not i ce. Except to the extent pro hibited by law, Hewlett-Packard Company mak es no expr ess or impl ied warran ty of any kind with re gard to t his manual a n d spe cific ally disclaims the i mplied warrant ie s and conditio ns of mercha ntaiblity an d fitness for a p articular purpose an d Hewlett-Packard Com pany shall not b e liable for any e rrors o r for incid ental or conse quential damage in connect ion with the fu rnishing, per formance or us e of this manual and t he ex amples herein.  Hewlett-Pa ckard Compan y 2000, all rig ht s reserved. The programs that control your HP 39G/40G are cop yrighted and all right s are reserv ed. Reproduction , adaptation or translation o f those prog rams without prior written permission of Hewlett P ackard is prohibited.
Getting st arted 1-1 1 Getting st arted On/off, cance l operations To turn on Press >21@ to turn o n the cal cula tor. To cancel When the c alculator is on, the >21@ key can cel s the current operatio n. To turn off Press >6 , )7@ OFF to turn the calculato r off. To save power, the calculator turns itself off after several minutes o f i na ctiv ity. All stored and d ispl aye d in form a tio n is saved. If you see the (( • )) annu nciator or the Low Bat message, then the calc ulator needs fresh batteries . HOME HOME is the calculator’s home view and is common to all aplet s. If you want to perf orm calcu lations, or you w ant to quit the current activity (such as an aplet, a program, or a n editor), press > 20(@ . Al l mathematical functions are available in the HOME. The name o f the current aplet is displ ayed i n the title of th e home vi ew.
1-2 G etting started The display To adjust t he contrast Simul taneous ly press >21@ and >@ (or >@ ) to in crease (or decrease) the contrast. To clear the display • Press CANCEL to clear th e edit line. • Press >6 ,)7@ CLEAR to clear the ed it line and the display history . Parts of t he display Menu ke y or soft key labels. The labels for the m enu keys’ current meani ngs. 67 2?a is the lab el for the first m enu key in this pictur e. “Press 672 ?a ” means to press the first me nu key , that is, the leftmost top -row key on th e calculator keyboard. Edit line. The line of current entry. History. The HOME displa y ( > 20(@ ) sho ws up to four lines of histo ry: the most rec ent input and output. Old er lines scrol l off the to p of the display but are retain ed in memory. Title. The na m e of th e c u r re nt a pl et is displ ayed at th e to p o f the HOME view. RAD, GRD, DEG specify whethe r Radians, Grads or Deg rees angle mode is set for HOME . The ' and ( symbols  indicate whether there is more h i story i n the HOME display. Pr ess the *e, and *k, to scroll in the HOME display. NOTE The HP 40G is pack aged with a computeri zed algebra system (CAS). Press &$6 _ to access t he comp uterized algebra s ystem. This User’s Guide con tains images from the HP39G an d do not display the &$ 6_ menu ke y la bel. Title Edit li ne History Menu key lab els
Getting st arted 1-3 Annuncia tors . Annunci ators are symbols that app ear above the title b ar and give you important status information. The keyboa rd Menu ke ys Annuncia tor Descrip tion Shift i n effect for next keyst roke. To cancel, p ress >6 ,)7@ again. α Alpha in eff e c t fo r ne xt ke ys tr oke. To cancel, press >$/3 $@ ag ain. (( • )) Low battery power. Busy. Data is being tr ansferred via infrared or cable. Alpha key Shift key Menu key labels Menu keys Aplet control keys keys Enter key Cursor
1-4 G etting started • On th e calcu lator keyboard , the top row of k eys are called m enu keys. Their mean ings depend o n the context—t h at’ s why their tops are blank. The menu keys are sometimes ca l led “soft keys”. • The botto m line of the display shows t he labels for the menu keys’ cu rrent meaning s. Aplet contr ol keys The apl et control k eys are: Key Meaning >6<0%@ Displays the Sy mbolic view for the current apl et . See “Symbolic vi ew” on page 1-15. >3/27@ Displays the Plo t vi ew for t he cu rrent aplet. See “P lot view” on page 1-15. >180@ Displays the Num eric view for the current apl et . See “Numeric view” o n page 1-15. > 20(@ Displays the HOME view. See “HOME” on p age 1- 1. >$3/(7@ Displays the Aple t Library menu. See “Apl et libra ry” on pa ge 1-15. >9,(:6@ Displays the VIEWS menu. See “Apl et views” on p age 1- 15 .
Getting st arted 1-5 Entry/E dit keys The ent r y and edit keys ar e: Key Meani ng >21@ ( CANCEL ) Cancels the cu rrent operation if the calculator is on by press ing >21@ . Pressing >6 ,)7@ , then OFF tur ns the calculator off. >6 ,)7@ Accesses the fun ction printe d in blue abov e a key. > 20(@ Returns to the HOME view, for performin g calc u lation s . >$/3 $@ Accesses the alp hab etical characters printed in orange bel ow a key. Hold down to enter a string of characters. >(17(5@ En t ers an input or executes an operation . In calculations, >( 17(5@ acts like “=”. When 2.a or 67$ 57a  is presen t as a menu key, >(17(5@ acts the sam e as pressing 2.a or 67 $57 a . >@ Enters a n egative num ber. To enter –25, press > @ 25. Note: this is not the same op er a tio n that the su btra ct butto n pe rforms ( >@ ). >;7 5 @ Enters the in dependent vari able by inserting X , T , θ, or N into the e dit line, depe nding on the cur rent a ctive aplet . >'(/@ Deletes the characte r under the cursor. Acts as a backspace key i f the cursor is at the end of the l i ne. >6 ,)7@ CLEAR Clears all data on the sc reen. On a settings screen, for ex ample Plot Setu p, >6 ,)7@ CLEAR returns all settings to their d efault values. *>, , *A, , *k, , *e, Moves the curso r around the displ ay. Press >6 ,)7@ first to move to the beginn ing, end, to p or bottom. >6 ,)7@ CHARS Displays a me nu of all av ailable characters. T o type one, use the arrow keys to high light it, an d press 2. a . To select mu ltiple characters, select each and press (& 2a , then press 2.a .
1-6 G etting started Shifted k eystrokes There are two shift keys t hat you use to access the operation s and char act ers printed above th e key s: >6 ,)7@ and >$/3 $@ . HELPWITH Th e HP 39G built -in help is a vailable in HOME only. It provid es syn tax help for bu ilt-in math fun c tion s. Access the HELPWI TH command by pressing >6 , )7@ SYNTAX and then th e mat h key for which you req ui r e syntax help. Example Press >6 ,)7@ SYNTAX >[  @ >(17(5@ Note: Remove the left par enthe sis fr om built-in comma nds such as sine , cosi ne, and tangent b efor e invoking th e HE LPWITH command. Key Description >6 ,)7@ Press the >6 ,)7@ key to access the operatio ns printed in blue above the keys. For insta nce, to access the Modes screen, press >6 ,) 7@ , the n press > 20(@ . ( MODES is labelled in blue ab ove the > 20(@ key). Yo u do n ot need to hold down >6 , )7@ when yo u press HOME. This a ction i s d epicted in this m anua l as “press >6 ,)7@ MODES .” To cancel a shift , press >6 ,)7@ again. >$/3 $@ The alphabet ic keys are also shifte d keystrok es. For in stance, to t ype Z, pres s >$/3 $@ Z. (The letters are printed in orange to th e lo wer ri gh t of each key.) To cancel Alph a, press >$/3 $@ again. For a lower case letter, pres s >6 ,)7@>$/3 $@ . For a s tring of letters, ho ld down >$/3 $@ while typi ng.
Getting st arted 1-7 Math key s HOME ( > 20(@ ) is the place to d o cal cu lations. Keyboa rd keys. The most common op erations are availab le from the k eyboard, such as the arithme tic (like >@ ) and trigonome tric (like >6,1@ ) functions. Press >( 17(5@ to complete the operati on: >6 ,)7@ √ 256 >(17(5@ displays 16 . . MATH menu. Press >0$7 @ to open the MATH menu. The MATH me nu is a comprehensiv e list of math functi ons that do not ap pear on the keyboa rd. It also includ es cate gories for a ll other fu nctions and constants. T he functio ns are grou ped by cate go ry, rangin g in alphabet i cal order fro m Calcul us to Trigonom etry. – The arrow keys scroll through th e list ( *e, , *k, ) an d move from the category list in the le ft column to the item list in t he right column ( *>, , *A, ). – Press 2.a to insert th e selected command onto the e dit line. – Press &$ 1 & /a to dismiss t he MA TH m enu without selectin g a com man d. – Pressing &2 16a  displa ys the l ist of Pr ogram Consta nts. Y o u can use these in program s that yo u develo p. – Pressing 0 7 a takes you to the be gi nning of th e MA T H menu. See “Ma th functio ns by categ ory” on pag e 10-3 f or detai ls of the math fu nctions. HINT When usin g the MA TH menu, or any men u on the HP 39G/ 40G , pressing an alpha key take s you straight to th e first menu option begi nning with that a lpha chara cter . W ith this m ethod , you do n ot nee d to pr e s s >$/3 $@ fi rst. Just press the key that corresp ond s to the command’s beginning alpha char a cter . Program commands Pressing > 6 ,)7@ CMDS displays the list of Program Com mands. See “ Program ming c ommand s” on pag e 15-14. Inactive keys If you pres s a key that doe s not operate in t he current contex t, a warning symb ol like this appears. There is no beep. !
1-8 G etting started Menus A menu o ffers you a choice of items. Menus are displayed in one or tw o co lumns. •T h e _ arrow in the display means more ite ms bel o w . •T h e A_  arrow in the display mean s mor e item s ab ove. To search a menu • Press *e, or *k, to scro ll throug h the li st. If yo u press >6 ,)7@ *e, or >6 ,)7@ *k, , you’l l go all the way to th e end or the be ginning of the list. Highli ght the item y ou want to select, th en press 2.a (or >(17( 5@ ). • If there are two column s, the l eft column shows general categories and the right column sh ows sp ecific contents within a categor y . High light a ge neral categ ory in the l eft column, then highligh t an item in the right co lumn. The list in the ri ght column changes whe n a different category is highligh ted. Press 2.a or >(17(5@ when yo u have highli ghted your sel e c tion. • T o speed-search a list (with no edi t line), type the first letter of t he word. For e xample, to fin d the Matrix category i n >0$7 @ , press > @ , the A lpha  “M” key . • T o go up a p ag e , yo u c an pr e ss >6 ,)7@ *>, . T o go down a page, pres s >6 ,)7@ *A, . To cancel a menu Press >21@ (for CANCE L ) or & $1&/ a . Th is can cels the cu rrent operation .
Getting st arted 1-9 Input fo rms An input form shows several fiel ds of information for you to examine and specify. Afte r highli gh tin g the field to edit, y ou can enter o r edit a number (or ex pression). You can also select options from a list ( & 226 a ). Some input forms i nclude items to check ( _& .a ). See bel ow for an example of an input form. Reset input form values To reset a d e fau lt field value in an input form, mo ve the cursor to th at fi eld an d pres s >'(/@ . To rese t all default field values in the input form, press >6 ,)7@ CLEAR . Mode settin gs You use the Modes input form to set the modes for HOME. HINT Although th e numeric set ting in Modes affects only HOME, the angle setting controls HOME and the current aplet. The angle setting se lected in Modes is th e angle setting us ed in both HOME and cu rrent aplet. To further configure an aplet, you use t he SETUP keys ( >6 ,)7@>3/27@ and >6 ,)7@>180@ ). Press >6 ,)7@ MODES t o access the HOME MODE S input form. Setting Options Angle Measure Angle va lu es are: Degrees . 360 degr ees in a circle. Radians . 2 π radians in a circl e. Grads . 400 grads in a cir cl e. The an gl e mod e yo u se t is th e an gle sett ing used in both HOME and the current aplet. This is done to ensure that trigono metric calculat i ons done i n the current ap let and HOME give t he same result.
1-10 Getting st arted Number Form at The number format mode you set is the number fo rmat used in bo th HOME and the current aple t. Stand ard . F ull-precisio n di sp lay. Fixed . Displays results r ounded to a number of decimal places. Exam ple: 123.45 6789 becomes 1 23.46 in Fix e d 2 format. Scientific . Disp lays results with an exponent , one digit to th e left of the decimal po int, and the specified num ber of decim al places. Example : 123.456789 become s 1.23E2 in Scienti fic 2 format . Engineering . Displays result with an exponent that is a multip le of 3, and the specif ie d number of si gnificant di gits beyond the first one. Exa mple: 123. 456E7 become s 1.23E9 in En gineering 2 f ormat. Fract ion . Displays results as fractions based on the sp ecified number of decima l place s. Exam ples: 12 3.4567 89 beco mes 123 in F ra ction 2 format , and .333 become s 1/ 3 and 0.142857 becomes 1/7. See “Using fractions” on page 1-24 . Decimal Mark Dot or Comma . Displ ays a number as 12456. 98 (Dot mod e) or as 12456, 98 (Comma mode). D ot mod e uses commas to separate elements in lists and mat rices, and to separ ate function arg uments. Comma mode use s periods (dot) as separators in these contexts. Setting Options (Continu ed)
Getting st arted 1-11 Setting a mode This examp le demonstra tes how to change t he angle measure from the defaul t mod e, radi ans , to degrees for the current aplet. The pro cedure is the same for cha nging number format and deci mal mark modes. 1. Press >6 ,)7@ MODES to open the HOME MODES in pu t form. The cursor (h ighlight ) is in the first field , Angle Measure . 2. Press & 226 a to dis play a list of choic es. 3. Press *k, to select Degrees ,  and pre s s 2 .a . The an gl e meas ur e changes to degre es. 4. Press > 20(@ to return t o HOME. HINT Whenever an inp ut form h as a list of choices for a field, you can pres s > @ to cycle through them instead of usi ng & 2 26 a . Aplets (E–lessons) Aplets ar e th e ap plication enviro nments where you exp lore different classe s of mathematical op erat ions. You select the aplet that y ou want to work wi th. Aplets co m e f rom a va r ie t y of so ur ces: • Built-in th e HP 39G/40G (initia l purchase). • Aplet s created by saving exi sting aplets, which ha ve been modified , wit h specific configurat io ns. See “Creating new ap lets bas ed on exis ting aple ts” on pa ge 16-1. • Downl oaded f rom HP’ s Calc ulators we b site. • Copie d from an other cal culator .
1-12 Getting st arted Aplets are store d in the Aplet library. See “Ap let library” on page 1-15 for further information. You ca n modify configurat ion settings for the graphical , tabular, and sym bolic views of th e aplets in the foll owing table. See “Aple t vi ew configura tio n ” on page 1-17 for further in formation. In additio n to these ap lets, which can be used in a v ariety of appl ication s, the H P 39G/ 40G is su pplied with two teach in g aplets : Quad Ex plorer and Trig Expl orer. You c annot mo dify configurati on settings for the se aplets. A great man y more tea ching aplets can be found a t HP’s web site and other web si tes created by educators, to get h er with accom panying docume ntation, o ften with studen t work sheets. The s e can be downloaded free of ch arge and transferred to the HP 39G/40G using the separately su pplied Conne ctivity Ki t. Aplet name Use this aplet to explore: Functi on Real-valu ed, rectangu lar funct io ns y in term s of x . Example: . Infere nce Confid ence interva ls and Hypoth esis tests based on th e Normal and St udents-t distri bu tions. Parametric Parametric re lations x and y in terms of t . Example: x = cos( t ) and y = sin( t ). Polar Polar f unct ions r in terms o f an angle θ . Example: . Sequenc e Seque nce functi ons U in te rms of n , o r in terms of previo us terms in the same or another seque nce, such as and . Exam ple: , and . Solve Equatio ns in one or more r eal -valued variables. E xample: . Statistics One-var iabl e ( x ) or t wo-vari able ( x and y ) sta tistic al d ata. 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 – =
Getting st arted 1-13 Quad Explorer aple t The Quad Expl orer aplet is used to inve stigate the behaviour of as the values of a , h and v ch ange, both by manipul ating the equat i on and seeing t he ch ange in the grap h, and by manipul ating th e grap h and s eeing the chang e in the eq uation. HINT More de tailed d ocument ation, a nd an a ccompany ing st udent work sheet ca n b e found at HP’s web si t e. When first sta rted, the aple t is in *53 a a mode, in which th e arrow keys, the >@ and >@ keys and t he >@ key are us ed to change t he shape of the graph. Thi s ch anging shape is reflec ted in the eq uation di sp layed at th e top right c or ner of the screen, while the or iginal graph i s retained for comparis on . In this mode the grap h controls the equa tion. It is a ls o possible to ha ve the equatio n control the graph . Pressing 6< 0%  a displa ys a sub-expr ession o f your equatio n (see ri gh t). Pressing the *A, and *>, key moves b et ween sub- expressi ons , while pressing the *k, and *e, key cha ng es their valu es. Pressing / (9( /a allows the user to select whether all three sub- expressions will b e explored at o nce or only one a t a time. A 7( 67 a butto n is provi ded to evalua te the stud ent’s know ledge. Pr essing 7 (67 a displays a target quad ra tic graph. The s tudent mu st manipulate th e equation’s pa rameters to make th e equation match the t arg et graph. When a stud ent feels that they ha ve correctly chosen the parame ters a & (&.a button evaluates t he answer and pro vide feedback. An $16: a button is provid ed for tho s e wh o give up! ya x h () 2 v =
1-14 Getting st arted Trig Explorer aplet The Trig Explorer aple t is used to investigate the b ehaviour of the graph of as the values of a , b , c and d change, both by m anipulati ng the e quation a nd seeing the change i n the graph, or by m anipulat ing the graph and seeing the ch an ge in the equation. When the user presses 67 $57 a in the $3 /(7 a view, the screen shown ri gh t is displaye d. In this mod e, the graph controls the e quation. Pressin g the *k,*e, an d *>,*A, keys transforms th e graph, with these transformat ions reflected in the e quation. The butt on la belled 2 5,*a a is a toggle b etween 25 ,*a a and ( ;75 a a . When 25 ,*a a is chosen , the ‘poin t of cont rol’ is at the origin (0,0) and the *k,*e, and *>,*A, keys control verti cal and horizont al transformatio ns. When ( ; 7 5a a is chosen the ‘po int of cont rol’ is on the first extremum of the graph (i . e. for the sine gra ph at . The arrow k eys change the amplitude a nd frequency of the graph. This is most easily seen by expe r im enting . Pressing >6<0%@ displa ys the equatio n at the t op of the screen. The equation is controls th e graph. Pressing the *A, and *>, ke y s moves fr om parameter to parameter. Pressing the *k, or *e, key cha ng e s the pa ra me te r ’s va lue s . The default a ngle setting for this aplet is radia ns. The angle setting can be chang ed to degree s by pressi ng 5$ 'a a . ya b x c () d sin = Origin π 21 , ⁄ () Extremum
Getting st arted 1-15 Aple t libra ry Aplets are stored in the Aplet library. To open an aplet Press >$3/(7@ to displa y the Aplet l ibrary menu. Select the aplet and press 67 $57 _ or >(17(5@ . From within an aplet, you can return to HOME any time by pressing > 2 0(@ . Apl et vie ws When you h ave configure d an aplet to define the re lation or data th at you want to ex plore, you c an di splay it in di fferent views. Here are illu st rations of the three major aplet views (Symbolic , Plot, and Numeric), the six supporting a plet views (from the VIEWS menu), and th e two user-defined views (Not e an d Sket ch ). Symb olic vi ew Press >6<0%@ to display th e aplet’ s Symb olic view . Y ou use this view to de fine the function(s) o r equation(s) that you want to explore. See “Ab out the Sy mbolic view” on pa ge 2-1 fo r furthe r informatio n. Plot view Press >3/27@ to display the aplet’ s Plot view . In this view , the function s that you hav e defined ar e displa yed graphic ally . See “Abou t th e Pl ot view” on page 2-5 for further informatio n. Numeric vi ew Press >180@ to display the aplet’s Nu meric view. In this view, the func tio ns tha t you hav e defined ar e displa yed in tabular fo rmat. See “About the num eric view” on page 2-15 for further informatio n.
1-16 Getting st arted Plot-Table view The VIEWS menu co nt ai ns the Plot-Table vi ew. >9,(:6@ Select Plot-Table 2. a Splits the screen into the plot and the da ta tab le. See “O t her views for scaling and splittin g the graph” on page 2-13 for futher information. Plot- Detail view The VIEWS menu co nt ains the Plot-Deta il vi ew. >9,(:6@ Select Plot-Detail 2.a Splits the screen into the plot and a close -u p . See “Oth er views for sc aling and splitting the gr aph” on page 2-13 for further information. Overlay Plot view The VIEWS menu co ntains the Overlay Pl ot view. >9,(:6@ Select Overlay Plot 2.a Plots the curren t expression(s) without eras i n g any pre - existin g plot(s). See “Oth er views for sc aling and splitting the gr aph” on page 2-13 for further information. Note view Press >6 ,)7@ NOTE to di splay th e aple t’s not e view. This note is tra nsferred with the aplet if it is sent to another calculator or to a P C . A no te view contai ns text to supplemen t an aplet. See “Notes and sketch es” on page 14 -1 for further information. Sketch vie w Press >6 ,)7@ SKETCH to display th e aplet’s sk etch view.
Getting st arted 1-17 Displa ys pictures to supplemen t an aplet . See “Notes and sketches” on page 14-1 for fu rth er informatio n. Aple t view co nfigurat ion You use the SETUP keys ( >6 ,)7@>3/27@ ,  and >6 ,)7@>180@ ) to configure t he ap let. For example, press >6 ,)7@ SETUP - PLOT ( >6 ,)7@>3/27@ )to display th e inpu t form f o r setting the aple t’s plot sett ings. Angle m easure is controlled u sing the MODES view. Plot Setup Press >6 ,)7@ SETUP - PLO T . Sets parame ters to plot a graph. Nume ric Se tup Press >6 ,)7@ SETUP - NUM . Sets parameters for b uild ing a table of num eri c values . Symbolic Setup This view is o nly available in the Statistics ap let in 2VAR mode, where i t plays an impor tant rol e in choo sing data models . P r ess ( >6 ,)7@ SETUP SYMB . To change views Each view i s a separate environm ent. To change a vi ew, select a diffe re nt view by pressin g >6 <0%@ , >180@ , >3/27@ keys or select a view from t he VIEWS menu. To change to HOME, press > 20(@ . You do not exp licitly close the cu rrent view, you jus t enter another on e—like passing from one room in to another in a h ouse. Data th at you enter is automati cally sav ed as you ente r it. To save aplet configuration You can save an apl et configurati on th at you have used, and transfer the aple t to other HP 39G/4 0G calcu lators. See “Sending and receiving ap lets” on page 16-5.
1-18 Getting st arted Mathematical cal culations The most c ommonly used math operation s are available fro m the keybo ard. Access to the rest of the ma th functions i s via the MATH menu ( >0$7 @ ). To access programm ing commands, pr ess >6 ,)7@ CMDS . See “Programming commands” on page 15-14 for further information. Where to start The home base for the calcu lator is the HOME view ( > 20(@ ). You can do al l calculation s here, and yo u can access all > 0$7 @ operation s. Entering expressions • Enter an expre ssion into the HP 3 9G/40G in the same left-t o-right ord er that you woul d write the ex pr ession. This is called algeb raic ent ry . • T o enter f unctions, select t he key or MA TH m enu item for that fu nction. Y o u can also enter a functio n by using the Alpha ke ys to spell out it s name. • Press >(17(5@ to ev aluate the exp ression you ha ve in the edit line (whe re the blinkin g cursor is). An expr ession can contai n numbers, function s , and vari abl e s. Example Calc ulat e : Long results If the result is too long to fit on the display line, or if you want to see an expressi on in textbook format , press *k, to highlig ht it and then p ress 6 2 :a . Negati ve numbers Type > @  to start a negati ve numb er or to inse rt a negativ e sign. To raise a negati ve number to a power, enclo se i t in parenthe ses. For exam pl e, (–5) 2 = 25, wher eas –5 2 = –25. 23 2 14 8 – 3 – ------- -------- --------- --- - 45 () ln >@ 23 >[ , >@ 14 >;@>6 ,)7@ √ 8 >@ > j @>@ 3 >OQ@ 45 >@ >(17(5@
Getting st arted 1-19 Scientific notation (powers of 10) A number like or is written i n scientific notatio n , that is, in terms of p owers of ten. This is sim pler to work wi th than 5000 0 or 0.0000 00321. To e nter numbe rs like these, use EEX . (This is easier than us in g >;@ 10 >[ N @ .) Examp le Calculate >@ 4 >6 , )7@ EEX >@ 13 >@ >;@>@ 6 >6 , )7@ EEX 23 >@ > j@ 3 >6 ,)7@ EEX >@ 5 >(17(5@ Explicit and implicit multiplication Implied multiplic ation takes pl ace when two o perands appear with no o perator in between. If you enter AB , for example, the result is A*B . However, for c larity, it is b etter to include t he multiplicat ion sign where you expe c t multip lic a tion in an expression. It is clearest to enter AB as A*B . HINT Implied multip licatio n will not alway s work as expect ed. For example, entering A(B 4) will not giv e A*(B 4) . Instead an error mess age is displaye d: “Invalid User F unction”. This is because the c alculator interprets A(B 4) as meaning ‘evaluat e func tion A at th e va lue B 4 ’, and function A doe s not exist. W hen in dou bt, insert the * sign manually. 51 0 4 × 3.21 10 7 – × 41 0 13 – × () 61 0 23 × () 31 0 5 – × ------- -------- --------- -------- --------- -------- ---
1-20 Getting st arted Parentheses You need to u se par enthes es to en close argume nts for functi ons, such as SIN( 45). You can om it the final parenthesis at the end of an edit line . The calculator insert s it automa tically. Parent h eses are also im portant in specifying the order of operation . Without parentheses, the HP 39G /40G calcul ates accord ing to th e order o f algebr aic precedenc e (the ne xt topic) . Follow ing are some ex amples using pa renthes es. Algebraic precedence order of evalua tion Function s wi thin an expression are evalu ated in the following order of p recedence. Fun ctions with the same preced ence are evaluated in order from left to right. 1. Expressions within pare ntheses. Nested parenthese s are evaluated from inner to outer . 2. Prefix functi ons, such a s SIN and LO G . 3. Postfi x functions , su ch as ! 4. Power function, ^, NTHROOT . 5. Negat i on, multip li cation, and division. 6. Addition and subtractio n. 7. AND and NOT . 8. OR and XOR. 9. Left argume nt of | (where) . 10. Equals, =. Largest and smallest numbers The smallest numb er t he HP 3 9G/40G can represent is 1×1 0 –499 (1E–49 9). A sma ller result is displaye d as zero. Th e large st number is 9. 999999999 99 × 10 –49 . A larger resu lt is still display ed as this number. Entering... Calculates... >6,1@ 45 >@ >6 ,)7@ π sin (45 π ) >6,1@ 45 >@ >@ >6 ,)7@ π sin (45) π >6 ,)7@ √ 85 >;@ 9 >6 ,)7@ √ >@ 85 >;@ 9 >@ 85 9 × 85 9 ×
Getting st arted 1-21 Clearing numbers • >'(/@ clears the character un der t he cursor . When the cursor is posi t io ned after the last character, >'( /@ deletes the charact er to the l eft of th e cu rsor , that is, it performs the same as a back space key . • CANCEL ( >21@ ) cl ears the edit line. • >6 ,)7@ CLEAR clears all in put and outpu t in the disp lay , includi ng the disp lay history . Using previous results The HOME disp lay ( > 20(@ ) shows yo u f our lines of input/ output history. A n unlimited (except by memo ry) number of previo us lines can be displ ayed by scrolli ng. You can retriev e and reuse any of t hese values or expressio ns. When yo u hi ghlight a pre vious input or re sult (by pressing *k, ), the &2 3< a and 6 2: a menu labels appear. To copy a previous line Highlight the line (press *k, ) and press &2 3<a . The num ber (or expressi on) i s copied into the edi t l ine. To reuse the last result Press >6 , )7@ ANS (last answer) to put the last re sult from the HOME display into an expression. ANS is a variable that is updat ed each time you pr e ss >(17(5@ . To repeat a previous line To repeat the very last line, just press >(17(5@ . Otherwise, highlig ht the line (press *k, ) first, and then press >(17(5@ . The highlig hted exp ression or number is re-en tered. I f the previo us line is an expressio n co ntaining the ANS , the calculat ion is repeated ite ra tively. Output Last output Input Last input Edit line
1-22 Getting st arted Example See ho w >6 ,)7@ ANS retrieves and reuses the last result (50), and >(17(5@ updates ANS (from 50 to 75 to 100). 50 >(17(5@ >@ 25 >(17(5@>(17(5@ You can use the last resu lt as the first expression in the ed it line with out pressing >6 ,)7@ ANS . Pressing >@ , >@ , >;@ , or > j@ , (or ot her operators th at require a p receding argument ) automatic a lly enters ANS be fore the op erato r. You can reu se any other e xp ression or valu e in the HOME displa y by high lighting the expre ssion (usi ng the ar row keys), then pre s si ng & 23< a . See “U sing previo us results” on pa ge 1- 21 for more details. The variable ANS is different from the numbers in HOME’s displa y history. A value in ANS is stored int ernally with the full precis io n of the calcul ated result , whereas the disp layed numb ers ma tc h the dis p la y mo de . HINT When yo u r et r ie ve a numb er from ANS , y ou obtain the re sult to its ful l precision. When you retriev e a number fro m the HOME’s disp l ay history, yo u obtain exact ly what was displa yed. Pressing >(17(5@ evaluates (or re-evaluates) the last input , whereas press i ng >6 , )7@ ANS copies the last result (as ANS ) into the edit line.
Getting st arted 1-23 Storing a value in a variable You can save an ans wer in a variable and use the variable in later calcu lations. There are 27 variable s available for stori ng real values . Thes e are A to Z and θ . See Chapter 11, “Varia bles and memory management” f or more inform ation on variables. Fo r exam ple: 1. Perfo rm a ca lcu lat ion. 45 >@ 8 >[ 8 @ 3 >(17(5@ 2. Store the result in the A varia ble. 672 a? a >$/3 $@ A >(17(5@ 3. Perform anot her calc ula tio n usin g the A va ri a b le . 95 >@ 2 >;@ >$/3 $@ A Access ing the display history Pressing *k, enables the hi ghlight bar in the di splay history . While the highlight bar is active, th e following menu and keyboard keys are very usefu l: Key Func tion *k, , *e, Scrolls throug h the displa y histo ry. &2 3<a Copie s th e highlighte d expression to the position o f the cursor in th e edit line. 6 2:a Displays the current exp r ession in standard mathematica l form. >'(/@ Deletes the highlig hted expression from the di spla y histo ry, un less the re is a c ursor in th e edit l ine. >6 ,)7@ CLEAR Clears al l li ne s of display hi st ory and the edit l ine.
1-24 Getting st arted Clearing the display history It’s a good ha bit to c lear th e displa y history ( >6 ,)7@ CLEAR ) whenever yo u have finishe d wor k ing in HOME. It saves calculator mem ory to clear the display hist ory. Remember that all your prev ious inputs an d results ar e saved until yo u clear them. Using fra c tions To work with fra ctions in HOME , you set the numbe r format to Fraction s, as follows: Setting Fraction mode 1. In HOME, open the HOME MODES input form. >6 ,)7@ MODES 2. Select Numb er Format and press & 2 26a to display the options, th en select Fr action. *e, & 226 a *e,*e,*e,*e, 3. Press 2. a to select the option , then select th e precision value. 2. a *A, 4. Enter th e precision that you wan t to use, and press 2. a to set the pr ecision. Press > 20( @ to return to HOME. See “Setting fract i o n precision” below for more informatio n.
Getting st arted 1-25 Setting fraction precision The fraction precision setting determines th e precision in which the HP 39 G/40G converts a decimal valu e t o a fractio n. The greater the precision value that is set, the closer the fraction is to the decimal value . By choo si ng a precisio n of 1 you are saying that the fr act ion only has to mat ch 0.234 to at leas t 1 dec imal place (3/13 is 0.2307 6...). The fra ctions us ed are foun d using the techniqu e of continue d fractions. When conve r tin g recurring decimals this can be i mportant. For examp le, at precisi on 6 the decimal 0.66 66 becomes 3333/ 5000 (6666/ 10000) whe re as at precis ion 3, 0.66 66 becomes 2/ 3 , which is prob ably what yo u wou ld want. For example , when converting .234 to a fraction, the precisio n value has the f ollowing effect : • Precision set to 1: • Precision set to 2: • Precision set to 3: • Precision set to 4
1-26 Getting st arted Fraction calcul ations When e ntering fracti ons: • Y ou use t he > j @ key to separate the num erator p art and the deno minator par t of the fracti o n. • T o ent er a mi xed fraction, for example, 1 1 / 2 , you ent er it in the for mat (1 1 / 2 ). For examp le, to perform th e following c alculation: 3(2 3 / 4 5 7 / 8 ) 1. Set the mode Number format to fraction. >6 ,)7@ MODES *e, & 22 6a Select Fraction >(17(5@ *A, 4 2. a 2. Return to HOM E and en ter the calcu la tio n. 3 >;@>@>@2 >@3 > j@ 4 >@>@>@ 5 >@ 7 > j@ 8 >@>@ 3. Evaluate the ca lculation. >(17(5@ Converting decimals to fractions To conver t a de cimal value to a fraction : 1. Set t he number mode to Fraction . 2. Eithe r retrieve the va lue from the Histo ry , or enter the value on th e com mand line. 3. Press >(17(5@ to conv ert the num ber to a frac tion.
Getting st arted 1-27 Converting a number to a fract ion When conv erting a num ber t o a fr action , keep the follow ing points in mind: • When con verting a recurring decima l to a fraction, set the frac tion precision to about 6, and ensure th at you inclu de more than six dec imal places in the recu rring decimal that you en te r . In this example, th e fraction precision is set to 6. The top calcula tio n returns the correct result. The bot tom one doe s not. • T o convert an exact decimal to a fracti on, set th e frac tio n precision to at lea st two more than the n umber of decim al places in the deci ma l. In this example, th e fraction precision is set to 6. Complex n umbers Complex r esults The HP 39G/40 G can ret urn a complex num ber as a result for some math func tions. A complex numb er appears as an order ed pair ( x, y ), where x is the real part and y is the imaginary part. For example, enterin g returns (0,1). To enter co mp lex numbers Enter the number in either of these form s, where x is the real part, y is the imagin ary part, an d i is the imaginary cons tant, : • (x, y) or • x iy . To enter i : • press >6 ,)7@>$/3 $@ I or • press >0$7 @ , *k, or *e, keys to select Constant , *A, to move to the right c olumn of the menu , *e, to  sel ect i , and 2.a . 1 – 1 –
1-28 Getting st arted Storing complex numbers There are 10 variable s av ailable for storing com plex numbers: Z0 to Z9. To stor e a com plex number in a varia ble: • Enter t he complex nu mber , pre ss 6 72a ?a ,  enter the variable to sto re the number in and press >(17(5@ . >@ 4 >@ 5 >@ 67 2a? _ >$/3 $@ Z 0 >(17(5@ Catalogs and editors The HP 39G/40G has se v er a l ca ta lo gs an d ed ito r s . You us e them to create an d manipulate objects. They access features and st ored va lues (nu mbers or text or other item s) that a re indepe ndent of ap lets. •A catalog lists i tems, which you c an delete or transm it, for example an aple t. •A n edi tor lets you create or modi fy items and numbers, for exam pl e a note or a matr ix. Catalog/ Editor Contents Aplet library ( >$3/(7@) Aplets. Sketch edit or ( >6 ,)7@ SKETCH ) Sketches an d diagrams, See Chapter 14, “No t es and sketches” . List ( >6 ,)7@ LIS T ) L ists. In HOME, lists are enclosed in {}. See Chapter 13, “Lists”. Matr ix ( >6 ,)7@ MATRIX ) One- and t w o- dimension al arrays. In HOME, arrays are encl osed in []. See Chapter 12, “M at rices”. Notepa d ( >6 ,)7@ NOTEPA D ) Notes (short te xt entries). See Chapter 14, “No t es and sketches” . Progr am ( >6 ,)7@ PROGR AM ) Programs that yo u create, or associated with user-defined aplets. See Cha pter 15, “Pro gramm ing”.
Getting st arted 1-29 Differences b etween the HP 38G and the HP 39 G/40 G CAS The HP 40G is pack aged with a compute r algebra system (CAS). Refer to the CAS Manual for further information. Memory manager The HP 39G/ 40G incorporat es a memory manager t hat you can use to s ee ho w much memory the objects t hat you have created o r loaded are occupy ing. See “Memory Manager” on page 11-9 for m ore information. Plot Goto function In Plot vi ew, you can use the *272 a menu key to j ump to a value on t he plot instead of havi n g to trace the plot to locate values . See “Explor i ng the graph” o n pa ge 2-7 fo r more informatio n. Statistic s Pred function When yo u choose the ) ,7a option in the Statistic s aplet’s Plo t view screen, it is now possible to 75$ &( a along the regressio n curve. Onc e a dat a set and regression curv e is displayed, press ing the up an d down a rrow s wi ll move betwe en the data and the curve of regress ion. When the regressi on curve is selected, the values display ed in the Plot view stat us line are the PREDY values. On the HP 38G, the Trace functio n would select kn ow n data po ints on ly. Inference aple t To complement the St atistics aplet, a new Infe rence aple t has been added. Use th is aplet to perform h ypothesis tests and determin e confidence in tervals. See “About th e Inference aplet” on page 9-1 for more information. Trig Explorer and Quadra tic Explorer aplets The te aching a plets Trig Explorer and Qua dratic Exp lorer have been added to the cal cul ator. These two apl ets add powerfully t o the capab ilities of the cal culator in the classroo m.

Aplet s and th eir v i ews 2-1 2 Aplet s and their views Aplet views This section e xamines the o ptions and func tionality of the three main views for the Function, Polar, Parametric, and Sequen ce ap lets: Symbolic, Pl o t, and Numeric views. About the Symbolic view The Sy mbolic view is the defining v iew for th e Function, Parametric , Polar, and S equence aplets. The other v iews are deriv ed from th e symb olic expr ession. You can create up to 10 different de finitions for each Function , Parametric , Polar, and Sequence a plet. You can graph any of the relatio n s (in the same aplet) simulta n eously by selecting them. Defining an expression (Symbolic view ) Choose the ap let from the Aplet Library. >$3/(7@ Press *k, or *e, to select an aplet. 67$ 57_ The Functio n, Parametri c, Polar , and Sequence aplets start in the Symb olic view . If the hi ghlight is on a n existing e xpression, scrol l to an empty line—un less yo u don’ t mind writing o ver the expre ssion—or, clear one line ( >'( /@ ) o r all lines ( >6 ,)7@ CLEAR ). Expressio ns are se lected (check marked) on ent r y . T o desele ct an ex pression , press _  & ._ . All  selected expre ssions are plotted.
2-2 Aplets an d their views – For a Function definition , ente r an expression to d efine F(X) . The only indepe ndent variabl e in the expression is X. – For a Parametr ic definition , ente r a pair of e xpr e ssions to define X(T) and Y(T) . The only indepe ndent variabl e in the expressions is T . – For a Polar definition , ente r an expression to d efine R ( θ ). The only indepe ndent variabl e in the expression is θ . – For a Sequence definition , either: Enter the first and second terms for U (U1 , or . .. U9, or U0 ). Define the n th term of the s e qu ence in terms of N o r of the prior terms, U(N–1) and U( N–2) . The expression s should produce re al-valued sequences w ith inte ger domains. Or define t he n th term as a non-recursive expression in terms o f n only . In this case, the calculator in serts the first two te rms based on th e express ion that you def i ne.
Aplet s and th eir v i ews 2-3 Evaluating expressions In aplets In th e Symbolic v iew, a variab le is a sy mbol only, an d does not repre sent one specifi c value. To e valuate a func tion in Symbol i c view, pre ss ( 9$/ _ . If a functio n calls anothe r function, th en ( 9$/_ resolves all references to other functio ns in terms of their indepe nd e nt varia b le . 1. Choo se the Function aplet. >$3/(7@ Select Function 67$ 57_ 2. Enter the expressions in the Func tion aplet’ s Symbolic view . >$/3 $@ A >;@ _;_ _ >[  @ _ _2._ _ >$/3 $@ B _ _2._ __ >$/3 $@ F1 >@ _; __ >@ >@ >$/3 $@ F2 >@ _; __  >@ _ _ 2 . __ _ 3. Highlight F3 (X). *k, 4. Press (9 $/_ Note how the values for F1(X) and F2(X) are substituted i nto F3(X). In HOME You can also eval uate any expressi on in HOME by entering it into the edit line a nd pressi ng >(17 (5 @ . For example, defi ne F4 as below. In HOME, type F4(9) and press >(17(5@ . Th is evaluates the expre ssion, substituting 9 in place of X into F4 .
2-4 Aplets an d their views SYMB view keys The foll owing tabl e details th e menu keys that y ou use to work with the Sy mbolic view. Key Meaning ( ',7_ Copi es the h ighlighted expres sion to th e edit line for edi tin g. Press 2._ when done. _& ._ Checks/unch ecks the current express ion (or set of expressio ns). Onl y checked expression(s) are ev aluated in the Plot and Numeric vi ews. __ ; _ __ Enters the independent v ariable in the Funct ion apl et. Or, you can use the >;7 5 @ key on th e keyboard . __ 7 _ __ Enters the independent v ariable in the Parametric a plet. Or, you can use the >;7 5 @ key on th e keyboard . __  _ __ Enters the independent v ariable in the Polar ap let. Or, you can use the >; 7 5 @ key on the key board. __ 1__ _ Enters the independent v ariable in the Sequenc e aplet. Or, y ou can use the >;7 5 @ key on th e keyboard . 6 2: _ Displays the cu rrent expression in text book f orm. ( 9$/_ Resolves all references to other definit ions in terms of variab les and evaluates all arithmetric expressions. >9$56@ Displays a menu for entering variable names or content s of vari ables. >0$7 @ Displays t he menu for entering math operation s. >6 ,)7@ CHARS Displays special characters. To ente r one, pl ace the curso r on it a nd press _ _ 2 . __ _ . To rema in in the CHARS me nu and enter anot h er spec ial character, press (& 2_ . >'(/@ Deletes the hig hlighte d ex pr essio n or the current charact er i n the edit line. >6 ,)7@ CLEAR Deletes all ex pressions in the list o r clears the edit line.
Aplet s and th eir v i ews 2-5 About the Plot view After entering and selecting (check marking ) the expression in the Sym bolic view, pres s >3/27@ . To adjust the appearance of the graph or the interv al that is disp laye d, yo u can chang e the Plot view se ttings. You can plot up t o ten expres sions at the sam e time. Sel ect the expres sions you want to be p lotted toget her. Setting up the pl ot (Plot view setup) Press >6 , )7@ SETUP - PLO T to d efine any of the settings shown in the ne xt two tables . 1. Highlight the field to edit. – If there is a number to ente r , type it in a nd press >(17(5@ or 2._ . – If there is an optio n to choose, press & 2 26_ , highlig ht your ch oi ce, and pre s s >( 17( 5 @ or 2. _ . As a shortcut to & 226 _ , just h ighlight th e field to change a nd press >@ to cycle thro ugh the options. – If there is an option to select or deselect, press _& ._ to chec k or uncheck i t . 2. Press 3 $ *( _ to view more settings. 3. When do ne, press >3/27@ to vie w the new plot . Plot view settings The plot v iew settings are: Field Mea ning XRNG, YRNG Speci f ies the minimum and maximum h orizontal (X) and v ertical (Y) values for the plotti ng window. RES For fu nction plot s: Resolut ion; “Faster” plo ts in alternate pixel columns; “Det ai l” plots in every pixel c olumn. TRNG Parametric aplet: S pecifies the t- values (T) for the graph. θ RNG Polar aplet: Specifies the a ngle ( θ ) value range for the grap h.
2-6 Aplets an d their views Those it ems with space for a check mark are settin gs you can turn on or o ff. Press 3 $*(_ to display the se con d pa ge . Reset plot settings To reset the default values for a ll plot settings, pre ss >6 ,)7@ CLEAR in the Plot Setu p view. To re set the default valu e for a fiel d, highlight the f i eld, and press >'(/@ . NRNG Sequ ence aplet: Specifi es t he index (N) values for the graph . TSTEP For Parametric plo ts: the increment for the in dependent v ariable. θ STEP Fo r Polar plots: the increment va lue for the in dependent v ariable. SEQPLOT For Sequence a plet: Stairstep or Cobweb types. XTICK Horizontal spacing for tickmarks. YTICK Vertical spacing for tickmarks. Field M eaning (Continued) Field Meaning SIMULT If more t han one rel ation is be in g plotted , plots them simul taneously (otherwise sequentia lly). INV. CROSS Cursor crosshairs invert the status of the pi xels they cove r. CONNECT Connect the plotted points. (The Sequenc e aplet always con nec ts them.) LABELS Label the axes with XRNG and YRNG valu es. AXES Draw the axes. GRID Draw grid points using XTICK and YTICK spacing.
Aplet s and th eir v i ews 2-7 Exploring the graph Plot vi ew gi ves you a selec ti o n of keys and men u ke ys to explore a grap h further. The options vary from apl et t o aplet. PLOT view keys The fol lowing table details the keys tha t you use to work with the grap h. Key Meani ng >6 ,)7@ CLEAR Erases th e plot and axes. >9,(:6@ Offe rs additional pre -defined view s for splitting the screen and fo r scaling (“zo om in g” ) the ax es . >6 ,)7@ *>, >6 ,)7@ *A, Moves c ursor to far left or far right. *k, *e, Moves cursor b etween relations. 3$8 6(_ or >21@ Inter rupts plott ing. &217 _ Continues p lotting if in terrupted. 0 ( 18 _ Turns me nu-key label s on and off . When the labe ls are off, pre ssing 0 ( 18 _ turns them back on. • Pressing 0 (18_ once displays the full row of labels. • Pressing 0 (18_ a second time removes the ro w of labels to d isplay only th e graph. • Pressing 0 ( 18 _ a third tim e disp la ys the coo r dinate mode. =22 0_ Displays ZOOM m enu list. 75$ &(_ Turns trace mode on/off. A white box appears over the (_ on 75$ &(_ . *272 _ Opens an input form for you to enter an X (or T or N or θ ) v alue. Enter the value and press 2. _ . The cursor jump s to the point on the grap h tha t yo u en te r e d. )&1_ Function aplet on ly: Turns on menu list for root-finding fu nctions ( see “Analyse grap h wi th FC N func tions” on pag e 3-3. '() 1_ Displ ays t he cu rrent , defini ng expression . Pr ess 0 (18_ to restore the menu.
2-8 Aplets an d their views Trace a graph You can t race along a fu nction using the *>, or * A , key which moves t he cursor along the graph. T he display a lso shows th e current coordinat e position ( x, y ) of th e cursor. Tr ace mode and the coordina te display are automatically set when a p lot is drawn. Note: T racing mi ght not appear to e xactly follow your plot if the resolu tion (in Plot Setup view) is set to Faster. T his is because RES: FAS TER plo ts in only every othe r column, whereas tra cing always uses every col umn. In Fu nction a nd Sequ ence Ap lets: Y ou can also scrol l (move the cu rsor) lef t or right be yond the edge of the display window in t race mode, giving yo u a view of more of the pl ot. To move betw e en relations If there is m ore than one rela tion displaye d, press *k, or *e, to move b etween relation s. To jump directly to a value To jump straight to a val ue rather than u sing the Trace functi on, use the *2 72_ menu key. Press *2 72_ , then ente r a value. P ress 2._ to jump to the value. To turn trace on/ off If the menu labels are not display ed , press 0( 18_ first. • T urn o ff tr ace mode by pres sing 7 5$& _ . • Turn on tr ace mode by pressing 7 5$& (_ . • T o turn the coo rdinate di splay off, p ress 0 ( 18 _ . Zoom within a graph One of the men u key optio ns is = 220 _ . Zo oming red r aws the plot on a larger or sm aller scale. It is a shortcut for ch anging the Plot Setup . With the Set Facto r s optio n yo u can specify the factor s that determine t he extent of zooming, and whether the zoom is centered abou t the cursor. ZOOM options Press = 220 _ , select an opt ion, and press 2._ . (If =22 0_ is not displayed, press 0 (18_ .) Not all =22 0_ options are availa ble in all aplets. Opti on Meanin g Center Re-centers t he plot around the current positi o n of the cur s o r withou t changing the scale. Box ... L ets you draw a box to zoom in on. See “Other vie ws for scaling an d splitting the gr aph” o n page 2-13.
Aplet s and th eir v i ews 2-9 In Divides hori zontal and vertical scal es by the X-fact or and Y-facto r. For instance , if zoo m factors are 4, then zooming in results in 1/ 4 as many units depicted per pixel. (se e Set Factors ) Out Multiplies h orizontal and vertical scales by th e X-fact or an d Y-factor (see Set Factors). X-Zoom In Divi des horiz ontal s cale only, using X–factor. X-Zoom Out Multiplies horizonta l scale , using X–factor. Y-Zoom In Divi des vert ical scal e only, using Y–factor. Y-Zoom Out Multiplies v ertical scale only, using Y–factor. Square Changes the vertical scale to match the horizontal scale. (Use this after doing a Box Z oom , X–Zoom , or Y–Zoom .) Set Factors... Sets the X–Zoom and Y–Zoom factors for zooming. Includes o ptio n to recent er the plot befo re zooming. Auto Scale Rescales the v ert ical axis so that the display sh ows a representat ive piece of the plot, for the supplie d x axi s settings. ( For Sequence a nd Statistics aplets, autoscaling rescal es both axes.) The autoscale pro cess uses the first sele cted fu nctio n only to de termi ne the best scale to us e. Decimal Res cales both axes so ea ch pixel = 0.1 units. Resets d efault values for XRNG (–6.5 t o 6.5) and YRNG (–3.1 to 3.2). (Not in Sequence or S tatistics aplets.) Option Meanin g (Continued )
2-10 Aplets an d their views ZOOM ex amples The follo wing screens show th e effects of zooming o ptions on a plot of . Plot of Zoom In : 0 (18_ =2 20_ In 2. _ Un-zoom : = 220 _ Un-zoom 2._ (Press *k, to move to the botto m of the Zoom l ist.) Zoom Out : = 220 _ Out 2._ Now un-zoom. Integer R escales hor izontal ax is only, m aking each pixe l =1 unit. ( Not availa bl e in Sequence or S tatistics aplets.) Trig Re scal es hor izon tal a xis so 1 pixel = π /24 radia n, 7.58, or 8 1 / 3 grads; rescal es vertical axis so 1 pixel = 0.1 un it. (Not in Sequen ce or Statistics aplets.) Un-zoom Returns the display to the previou s zoom, or if there has been only one zoom, un -zoom displa ys the graph with the o riginal plot settin gs. Opti on Meaning ( Continued ) 3 x sin 3 x sin
Aplet s and th eir v i ews 2-11 X-Zoom In : =22 0_ X-Zoom In 2._ Now un-zoom. X-Zoom Out : =22 0_ X-Zoom Out 2._ Now un-zoom. Y-Zoom In: =22 0_ Y-Zoom In 2._ Now un-zoom. Y-Zoom Out: =22 0_ Y-Zoom Out 2._ Zoom Sq uare: =22 0_ Square 2. _
2-12 Aplets an d their views To box zoom The Box Z oom optio n lets yo u draw a box arou nd the are a you want to zoom in on by sele cting the e ndpoints of one diag onal of the zoom rect angle. 1. If necessary , press 0 (18_ to turn on the menu-key l abels. 2. Press = 220 _ and select % 2;_ . 3. Positi on th e curs or on o ne cor ner o f the recta ngle. Press 2._ . 4. Use the cu r s or ke y s ( *e, , etc.) to drag to the opposi te corn er . 5. Press 2. _ to zo om in on the boxe d area . To set zoom factors 1. In the Pl ot view , pr e ss 0 (18_ . 2. Pres s = 220 _ . 3. Select Set Factors... a nd pre ss 2._ . 4. Enter the zoom fact ors. There is one zoom factor for the horizont al scale ( XZOOM ) and on e for the vertical scale ( YZOOM ). Zoomin g ou t multiplie s the scale by the factor, so that a greater scale dist ance appears on the s creen . Zooming in divides the scale by the factor, so that a shorter scale distance ap pears on the screen.
Aplet s and th eir v i ews 2-13 Other views for scaling and splitting the graph The p reset view ing opt ions menu ( >9,(:6@ ) contain s options for dra wing the plot us ing certain pre-defin ed configura tions. This is a short cut for changi ng Plot view se ttings. For insta nce, if you hav e defined a t r igonometr ic functio n, then you coul d select Trig to plot your func tion on a trigonomet ric scale. It also contains sp lit-screen options . In certai n aplets, for example those that you down load from the world wide web, the p reset viewing op tions menu can also contain options that re late to the a plet. VIEW S menu options Press >9,(:6@ , sele ct an optio n, and press 2. _ . Option Meanin g Plot- Detail Splits the sc reen into the plo t and a close-up . Plot-Table Splits the sc reen into the plo t and the data t able. Overlay Plot Plots the c urrent expre ssion(s) without erasi ng an y pre-exist ing plot(s) . Auto Scale Rescales the v ert ical axis so that the display sh ows a representat ive piece of the plot, for the supplie d x axi s settings. ( For Sequence a nd Statistics aplets, autoscaling rescal es both axes.) The autoscale pro cess uses the first sele cted fu nctio n only to de termi ne the best scale to us e. Decimal Res cales both axes so ea ch pixel = 0.1 unit. Rese ts de fa ult values for XRNG (–6.5 t o 6.5) and YRNG (–3.1 to 3.2). (Not in Sequence or S tatistics aplets.) Integer Res cales horizontal axis only, making each p ix el = 1 un it. (Not ava ilable i n Sequence or S tatistics aplets.) Trig Rescales hori zon tal axis so 1 pixel = π /24 radi an, 7.58, or 8 1 / 3 grad s; re scales ver tical axis so 1 pixe l = 0.1 unit . (Not in Sequence or S tatistics aplets.)
2-14 Aplets an d their views Split the screen The Plo t-Detail view can g ive you tw o simult aneous vi ews of the plot. 1. Press >9,(:6@ . Sele ct Plot-Detail a n d pres s 2._ . The graph is pl otte d twice. Y ou can now zo om in on the ri gh t side. 2. Press 0 (18_ =2 20 _ , sele ct the zoom method a nd press 2. _ or >(17(5@ . This zoom s the right side. Here is an example of split scre en with Zoom In . . – The Plot men u ke ys are available as for th e ful l plot (for tra cing , co ordin ate d ispla y , equation disp lay , and so on). – >6 ,)7@ *>, moves the leftmost cursor to the screen’s left edge and >6 ,)7@ *A, mov es the rightm ost cursor to the screen’ s right edge. – The menu ke y copies the righ t pl ot to the left plot . 3. T o un-split the s c r een, press >3/27@ . The left si de takes over the whole scree n. The Plo t-Table vie w gives yo u two simult aneous vie ws of the plot . 1. Press >9,(:6@ . Select Plot-Table and press 2. _ . The screen disp lays the plot on the left sid e and a table of numbers on t he right side. 2. T o move up and dow n the tabl e, use the *>, a nd *A, cursor keys. Th ese keys m ove the tra ce point lef t or right along the plot, and in the ta ble, the co rresponding va lues are hi ghlighted. 3. T o mo ve between functio ns, use th e *k, and *e, cursor keys to mo ve the curso r fr o m one graph to another . 4. T o return to a full Numeric (or Plot) vi ew , press >180@ (or >3/27@).
Aplet s and th eir v i ews 2-15 Overlay plots If y ou want to plot ov er an ex isting plo t with out erasi ng that plot, then us e >9,(:6@ Overlay Plot instead of >3/27@ . Note that tr acing follo ws only the cu rrent f unctio ns fro m the current apl et . Decimal sc aling Decimal scaling is the default scaling. If yo u have change d the scaling to Trig or Integer, you can c hange it bac k with Decimal. Integer scaling Integer scal ing compresses t he axes so that each pixel is and the or ig i n is near the screen cent e r. Trigonometric scaling Use trigono met ric scaling whenev er you are plotting an expres sion that incl ud es trigonome tric functi on s. Trigonom etric plots are more likel y to i nt ers ect the axis at points f actored by π . About the numeric view After entering and selecting (check m arking) the expres sion or e xpressions that yo u want t o explore in the Symb ol ic view, pre ss >180@ to view a table of data values fo r the indepen dent variable ( X , T , θ , or N ) an d depende nt variabl es. 11 ×
2-16 Aplets an d their views Setting up the table (numeric view setup) Press >6 ,)7@ NUM to define any of th e tab le set tings. Use the Nume ric Setup inpu t form to c onfigure the ta ble. 1. Highligh t the field to edit. Use the ar row keys to move from field to field. – If the re is a number to enter , typ e it in and press  >(17(5@ or 2._ . T o modi fy an exi sting number , press (' ,7_ . – If there is an option to choos e, press & 226 _ , highl ight your ch oi ce, and pres s > (17(5@ or 2. _ . – Shortcut: Press the 3 /27 ?_ key to co py values fro m the Plot S etup into NUMSTART and NUMSTEP . Effectively , the 3 /27 ?_ menu key al lows you t o make the table match the p ixel columns in the graph view . 2. When done, p ress >180@ to view the table of nu mbe rs. Numeric view settings The follo wing table details the field s on the Numeric S etup input f orm. Reset numeric settings To reset the default values fo r all table settings, press >6 ,)7@ CLEAR . Field Meaning NUMSTART The independent v ariable’s starting valu e. NUMSTEP The size of the increm ent from one indepe ndent varia ble value to t he next. NUMTYPE Type o f numeric t able: Autom atic or Build You r Own. To bu ild your own table, yo u must type each indepe ndent value into the ta ble yourself . NUMZOOM Allows you to zoom in or ou t on a selected v alue of the independen t varia ble.
Aplet s and th eir v i ews 2-17 Exploring the table of numbers NUM v iew menu keys The fol lowing tabl e details th e menu keys th at you use to wor k with the table of numbers. Zoom within a tabl e Zooming redraws the table of numbers in grea ter or lesser detail. ZOOM options Th e following table lists the zoom options: Key Meani ng =22 0_ Displays ZOOM m enu list. %,*_ Toggles between two character sizes. '() 1_ Displays the defining func ti on expre ssion for the highli ghted co lumn. To cancel th is display, press ' () _ . Option Meaning In Decreases th e intervals for th e independent variable so a narrower range is sh own. Uses the NUMZOOM factor in Numeric Setup. Out Increases the interval s for the indepen den t vari able so that a wider range is sh own. Uses the NUMZOOM factor in Numeric Setup. Decimal Ch anges inte rvals for t he independe nt variab le to 0.1 units. Sta rts at zero. (Shor tcut to c hanging NUMSTART and NUMSTEP .) Integer Ch anges inte rvals for t he independe nt variable to 1 unit. Starts at zero. (Shortcut to changing NUMSTEP .) Trig Changes interval s for in de pendent variable to π /24 radi an or 7.5 degr ee s or 8 1 / 3 grads. Sta rts at zero. Un-zoom Returns the display to the previou s zoom.
2-18 Aplets an d their views The display on the right is a Zoom In of the display on the left. The ZOOM factor i s 4. HINT To jump to a n independ ent variable value in the tabl e, use the arrow keys to place t he cu rsor in the independen t variable column , then enter th e value to jump to. Automatic recalculatio n You can enter an y new value in the X col umn. Wh en you p ress >(17(5@ , the values for the depe ndent variables are recalculated , and the entire tab le is regenerated wit h the same interval be twee n X value s. Building your own table of numbers The defaul t NUMTYPE is “A utomatic”, wh ich fills the ta ble with data for regular in tervals of the in dependent ( X , T , θ , or N ) va riab le. Wi th th e NUMTYPE option set to “Build Your Own”, you fill the table yourself by typ ing in the inde pendent- variabl e values you want . The depende nt values are then calculat ed and displaye d. Build a table 1. Star t with an e xpressio n define d (in Sym bolic vie w) in the aplet of you r choice. Not e: Func tion, Polar , Parametric, a nd Sequence aplets only . 2. In the Numeric Setup ( >6 ,)7@ NUM ), choose NUMTYPE: Build Your Own . 3. Open the Nu meri c vi ew ( >180@ ). 4. Clear exis tin g data in the table ( >6 ,)7@ CLEAR ). 5. Enter th e indepen dent values in the left-hand column. T y pe in a n umber an d press >(17(5@ . Y ou do not hav e to enter them in order, because the 625 7_ functi on can rearrange th em. T o i nsert a number between two o thers, use ,1 6 _ . F1 and F2 entries are generated au tomatica lly You enter numbers into the X column
Aplet s and th eir v i ews 2-19 Clea r data Press >6 , )7@ CLEAR , < (6_ to erase the data from a table. “Build Your Own” menu keys Key Meanin g (', 7_ Puts the hi ghlighted independe nt value ( X , T , θ , or N ) into the e dit line. Pressing >( 17(5@ replaces this variable with its current va lue. ,16_ Inserts a row of zero values at th e position of the hig hlight. Repla ce a zero by typi ng the number yo u want and pre ssi ng >(17(5@ . 625 7_ Sorts the in dependent v ariable values into asce nding or d escending order . Press 6257 _ and se lect the ascendi ng or descendi ng option from the menu, and press 2._ . %,*_ Toggle s between t wo char acter sizes. '() 1_ Displa ys the defining function expre ssion for t he highlig hted column. >'(/@ De le tes the high lighted r ow. >6 ,)7@ CLEAR Clears all data from the ta ble.
2-20 Aplets an d their views Example: plotting a circle Plot the circle, x 2 y 2 = 9 . First rea rrange it to read . To plot b oth the positiv e and negativ e y values, you ne e d to define two equations as fo llows: and 1. In th e Func tio n aple t, spec ify the fun ction s. >$3/(7@ Select Function 67$ 57_ >6 ,)7@ √>@ 9 >@>;7 5@>;  @>@>(17(5@ >@>6 ,)7@ √>@ 9 >@>;7 5@ >;  @>@>(17(5@ 2. Reset the graph setup to the default sett ing s. >6 ,)7@ SETUP - PLOT >6 ,)7@ CLEAR 3. Plot the two functi on s and hi de the menu so that you can see all the circle. >3/27@ 0(18 _  0 (18_ 4. Reset the numeri c setup to the default set ting s. >6 ,)7@ SETUP - NUM >6 ,)7@ CLEAR 5. Display the fu nctio ns in numer ic for m . >180@ y 9 x 2 – ± = y 9 x 2 – = y 9 x 2 – – =
Function aplet 3-1 3 Function aplet About t he Function aple t The Func tion aplet e nables you to explore up to 10 real –valued, rect angular f unction s y in terms of x . For example . Once you ha ve defined a fu nc tion you can : • create g raphs to find roots, intercept s, slope, si gned area, and ext rema • creat e t ables to evaluat e fu nc tions at particu lar values. This chapter de monstrates the ba sic tools of the F unction aplet by steppi ng you through an exa mple. See “Aplet vi ews” on page 2-1 for further information about the function ality of the Symbol i c, Numeric, a nd P lot views. Getting started with the Function aplet The following ex a mple invo lv es two funct ion s: a line ar function and a quad ratic equation . Open the Function aplet 1. Open the Functio n aplet. >$3/(7@ Select Function 6 7$5 7_ The Func tion aplet starts in the Symboli c view . The Symb oli c vie w is the de fining view for Fu nction, Param etric, P ol ar, and Se quence aplet s. The othe r views are derived from the s ymbol ic expr essi on. y 2 x 3 = y 1 x – = yx 3 () 2 2 – =
3-2 F unction aplet Define the expressions 2. There are 10 function defin itio n fie lds on the Func tio n aplet’ s Symbolic view screen. They are la beled F1(X) to F0(X). High light the fu nction defin ition fie ld you want to use, and ent er an ex pression. (Y ou can press >'(/@ to dele te an ex is ting l ine, or >6 ,)7@ CLEAR to cl ear al l lines.) 1 >@>;7 5 @>(17(5@ >@ >;7 5 @>@ 3 >@ >; @ >@ 2 >(17(5@ Set up the plot You can chan ge t he scales of the x and y axes, grap h resolution , and spacing of axis ticks. 3. Display p lot settings. >6 ,)7@ SETUP - PLOT Note: Fo r our exa m ple , y o u c a n l eave t he p l ot s ett ing s at their defa ult va lue s sin ce we will b e usin g th e Aut o S cale featur e to choose an appr opriate y axis for o ur x ax is settings. If your set tings do not match this e xample, pr ess >6 ,)7@ CLEAR to r estor e the de fault value s. 4. Specify a grid fo r the grap h. 3$ *(_ *A,*e,*e, __ & ._  Plot the functions 5. Plot the func tions. >3/27@
Function aplet 3-3 Change the scale 6. Y ou can chan ge the scale to see mor e or l ess of your graphs. In thi s exam ple, choose Auto Scale. (See “VIEWS menu opt ions” o n page 2- 13 for a description of Auto Scale). >9,(:6@ Select Auto Scale 2. a Trace a graph 7. T race the line ar function. *>, 6 times Note: By d efault, the tracer is active. 8. Jump from the line ar function to the qua dratic func tion. *k, Analyse gr aph with FCN function s 9. Displ ay t he Plot view menu. 0( 18a From the Plot view m enu, y ou can use the functions on the FCN me nu to find roo ts, intersections, slo pes, and are as for a f u n ction d efined in the Fu nc tion ap let (an d any Fun ction-base d apl ets). The FC N fu nc tions act on the current ly sel ected graph. See “FCN funct i ons” on page 3-9 for further information.
3-4 F unction aplet To find the greater of t he two roots of the quadratic function 10. Fi nd the greate r of the two roots of the qu adratic functio n. Note: Mo ve the cursor to th e graph of th e quadratic equat ion by pr essi ng the *k, or *e, k ey . Then move the cursor so that it is near by pressing the *A, or  *>, key . )& 1a Select  Root  2. a The root va lu e is displ a ye d at the bott om of the screen. To find the intersection of the two functi ons 1 1. Find the intersec tion of the two functions. 0 (18a )& 1a *e, 2.a  12. C h oos e the line a r func tio n whose int ersec tio n with the quadra tic functio n yo u wish to find . 2. a The c oordinate s of the intersecti on point are displ a ye d at the bott om of the sc reen. Note: If ther e is mor e than one int ersection (as in our example ), the c oor dinates of the intersection po int closest t o the cur r ent curso r position ar e displa yed. x 1 – =
Function aplet 3-5 To find the slope of the quadratic function 13. Find the slope of th e quadratic functi on at the intersection point. 0( 18a )&1a Select  Sl ope  2.a  The sl ope val u e i s displayed at the botto m of the screen. To find the signed area o f the t wo functions 14. T o fi nd the area between the t wo functions in the rang e –2 ≤ x ≤ –1, first move the cursor to and select the si gned area option. 0( 18a )&1a Select Signed area 2.a 15. M ov e the cursor to by pressin g the *A, or *>, key . 2.a 16. Press 2. a to accep t using F2 ( x ) = ( x 3) 2 – 2 as the other bounda ry for th e integra l. 17. Choos e the end value fo r x . *272 a >@ 2 2.a The cu r s or j um p s to x = –2 on the lin ear function. F 1 x () 1 x – = x 1 – =
3-6 F unction aplet 18. Display t he numerical va lue of th e integral. 2. a Note: Se e “Shading area” on page 3-1 0 f or anoth er met hod of calc ul ating area. To find the extremum o f the quadratic 19. Mo ve the cursor to the qu adra tic equation an d find the extremum of the quadratic. *k, 0(18 a ) &1a Sele ct Extremum 2. a The c oordinate s of the ext r em u m ar e di s p l a ye d at the b ottom of th e screen. HINT The Root and Ext remum functions retu rn one value only even if the func tio n has more than one roo t or ex t remum. The functi on finds the va lue closest to th e position of t he cursor. You need to re -locate the cursor to find oth er roots or extrema that ma y exist. Displa y the numeric vi ew 20. Display the numeric vi ew . >180@ Set up th e table 21. Display the numeric set u p. >6 ,)7@ SETUP - NUM See “Settin g up the table (nume r ic vi ew set up)” on page 2-16 for more information.
Function aplet 3-7 22. M atch the table set tings to the pixel columns in the g raph view . 3/2 7a 2.a Explor e the tabl e 23. Displa y a tabl e of nu meric va lues. >180@ To navigate around a table 24. Move to X = –5 .9. *e, 6 times  To go directly to a valu e 25. M ove directly to X = 10 . 1 0 2. a To acce ss the zoom options 26. Zoom i n on X = 10 by a factor of 4. Note: NUMZOOM has a sett ing of 4 . =22 0a  In 2.a
3-8 F unction aplet To change font size 27. Display table numb ers in large fon t. %, *a To displa y the symbolic definition of a column 28. Display the symbol ic definitio n for the F1 colu mn. *A, '() 1a The symboli c defin itio n of F1 is disp layed at the bo ttom of the screen. Function aplet interactive a nalysis From the Plot view ( >3/27@ ), you can use the function s on the FCN menu to find roots, intersectio ns, slopes, and area s for a functio n defin ed in the Functi on aplet (and any Funct ion- base d aplets). See “FC N functi ons” on page 3-9. T he FCN operation s act on t he currently selected graph. The result s of the FCN fu nctions are save d in the fol lowing variables: •A R E A •E X T R E M U M •I S E C T • ROOT •S L O P E For exam ple, if you use the ROOT fun ction to find the root of a plot, y ou can use th e result in calc ulations in Home.
Function aplet 3-9 Access FCN variables The FCN variabl es are contained in the VARS men u. To access FCN variab le s in HOME: >9$56@ $3 /( 7a Select Plot FCN *A, *k, or *e, to choo se a varia ble 2.a To access FCN vari ab le in the Function aple t’s Symbolic view: >9$56@ Select Plot FCN *A, *k, or *e, to choose a vari able 2.a FCN functions The FCN fu nc ti on s are: Function Descri ption Root Se lect Root to find the root of the current function nea rest the cursor. If no root is found, but only an extremum, then the result is label ed EXTR: instead of ROOT: . (T he root-finder is also used in th e Solve aplet. See also “Inter preting results ” on page 7-6. ) The cursor is moved to the root value o n the x-axis and the resulting x -value i s save d in a variable nam ed ROOT. Extremum Sele ct Extremum to fi nd the maximum or min imum of the current functio n nea rest the cursor. This displays the coordina te values and moves the cursor t o t he extremum. T he resulting value i s saved in a va riable named EXTREMUM. Slope Se lect Slope to find the nu meric derivative at the cu rrent position of the cursor. Th e result is saved in a variabl e nam ed SLOPE.
3-10 Function aplet Shading ar ea You can shad e a selected area between functions. This process also gives yo u an approximat e measurement of the are a shaded. 1. Open th e Func tion a plet. The F unct ion a plet o pen s in th e Symbolic view . 2. Select the ex pressions whose curve s you want to study . 3. Pres s >3/27@ to plot the f u nctions. 4. Press *>, or *A, to pos ition the cursor at the start i ng point of th e area yo u want to shade . 5. Press 0 (18a . 6. Press ) &1a , then select Signed area and pre ss 2. a . 7. Press 2. a , choose the funct i on that will act as the boundary of he shaded area, an d press 2.a . 8. Press the *>, or *A, k ey to shade in the area. 9. Press 2. a to calculate th e area. The area measurement is displaye d near the bott o m of the screen. To remove t he shading, pres s >3/27@ t o re-draw the plot. Signed area Select Signed area to find the numeric integral. (If there are two or more expressio ns checkmarked, then yo u will be asked to choos e the second express ion from a list that incl udes the x -axis.) Select a start ing point, then mov e the cursor to sele ction ending point. The resu lt is saved in a va r ia bl e named AREA . Intersection Select Intersection to fin d th e intersection of two gra phs nearest the cu rsor. (You need to have at le ast two sele cted expressi ons in Symboli c vi ew. ) Displays the coordi nate values and mo ves the cursor to the int ersection. (Uses Solve fun ction.) The re sulting x - value is saved in a variab le named ISECT. Function Descripti on (Continued)
Function aplet 3-11 Plotting a piecewise defined function example Suppos e y ou wanted to graph t he following piece wise defined function. 1. Open the Functio n aplet. >$3/(7@ Select Function 67$ 57 a 2. Highlight the lin e you want to use, and e nter the expre ssion. (Y ou can pr e ss >'(/@ to de lete an existing line, or >6 ,)7@ CLEAR to clear all lin es.) >@ ;a >@ 2 >@ > j @ >@ ;a >6 ,)7@ CHARS ≤ >@ 1 >@>(17(5@ ;a >[  @ > j @>@ ;a >6 ,)7@ CHARS > >@ 1 >6 ,)7@ AND ;a >6 ,)7@ CHARS ≤ 1 >@ > ( 17(5@ >@ 4 > @ ;a >@> j @>@ ;a >6 ,)7@ CHARS > 1 >@>(17(5@ Note : Y o u can use the ;a menu key to assi st in the entry of equation s. It has the same effect as pr essi ng >;7  5 @ . f x () x 2 x 1 – ≤ ; x 2 1 – x 1 ≤ < ; 4 xx 1 ≥ ; –      =

Parametric aplet 4-1 4 Parametric aplet About t he Parametric aplet The Parametric aplet allows you to explore pa rametric equat ions . The se are eq uati on s in whic h both x and y are defin ed as fu nction s of t . They take the forms an d . Getting started with the Parametric aplet The foll owing example uses the pa rametric equa tions Note: This example will pro duce a circle. For this example to work, the an gle measure must be set t o de grees. Open the Parametri c aplet 1. Open the Parametric a plet. >$3/(7@ Select Parametric 67 $57 _ Define the express ions 2. Ente r ea ch equation. 3 >;@>6,1@>;7 5 @> @ >(17(5@ 3 >;@>&26@>;7 5 @>@ >(17(5@ xf t () = yg t () = xt () 3 t yt () 3 t co s = sin =
4-2 Parametric aplet Set angle measure 3. Set the ang le measure to degrees . >6 ,)7@ MODES & 226 _ Sele ct Degrees 2. _ Set up the plot 4. Display the graphin g options. >6 ,)7@ PLOT Y o u can see the Plot Setup input f or m has two fields no t incl uded in the Fu nc tion a plet, TRNG and TSTEP . TRNG specifies the rang e of t values . TSTEP specifies the step valu e be tween t values. 5. Set the TRNG an d TSTEP so that t steps from 0 ° to 36 0 ° in 5 ° steps. *A, 360 2. _ 5  2. _ Plot the expression 6. Plot the expres si on . >3/27@ 7. T o see all the circle, press 0 ( 18 _ twic e. 0 (18_0( 1 8 _
Parametric aplet 4-3 Overlay plot 8. Plot a triangle gra ph over the existing circ le graph. >6 ,)7@ PLOT *e, 120 2._ >9,(:6@ Select Overlay Plot 2._ 0( 1 8 _  0 (18_ A triangle is displayed rather than a circle (without cha nging th e equatio n) because the chang ed value of TSTEP ensures that point s being plotte d are 12 0 ° apart i nstead of nearl y contin uous. Y ou are able to exp lore the graph using trace, zoom, split screen, and scaling functio n ali ty ava ilabl e in the Functio n aplet. See “E xploring the grap h” on pa ge 2-7 for further information. Display t he numbers 9. Displ a y t he table of numer i c values. >180@ Y ou can see there is a colu mn of t -values. This column i s active in the sense th at you can highli ght a t -value, t ype in a replacement val ue , and see the tabl e j ump to that value. Y ou can also zoom in or zoom out on any t -value in the table. You are able to exp lore the table using = 220 _ , *272 _ , build you r own table, a nd split scree n functiona lity availabl e in the Fun ction aplet. S ee “Explorin g the table of nu mbers” on page 2-18 fo r furt her info rmati on.

Polar aplet 5-1 5 Polar aplet Getting started wi th the polar aplet Open the Pola r aplet 1. Open the Polar ap let. >$3/(7@ Select Polar 5(6 (7 a< (6 a 67$ 57a Like the Functio n aple t, the Polar aple t opens in the Symboli c view . Define the expr ession 2. De fine the polar eq uation . 2 >6 ,)7@ π > &26@ >;7 5 @> j@ 2 > @ >&26@>;7 5 @>@ >[ @>(17(5@ Specify plot settings 3. Specify the plot set ting s. I n this example , we wil l u s e the default se ttings, except f or the θ RNG fields. >6 ,)7@ SETUP - PLOT >6 ,)7@ CLEAR *A, 4  >6 ,)7@ π 2. a Plot the expr ession 4. Plot t he ex pression. >3/27@ r 2 πθ 2 ⁄ () θ () 2 cos cos =
5-2 Polar aplet Explore the graph 5. Display the Pl ot view m enu key lab els. 0 (18a The Plot vi ew options available are the same as those foun d in the Funct io n ap let. See “Explor ing the graph” on page 2-7 for further info rmation. Displa y the numbers 6. Display t he table of values θ for and R1. >180@ The Numeric view options availa bl e are the same as thos e found in the Func tion aplet. See “Explor ing the table of numbers” on page 2-18 for further information.
Seque nce aplet 6-1 6 Sequence a plet About the Seq uence aplet The Sequen ce ap let allows you to exp lore sequences. You can defi ne a sequenc e nam ed, for example , U1: • in terms of n • in terms of U1 ( n -1) • in terms of U1 ( n -2) • in te rms of an other s equenc e, for e xample, U2( n ) • in any com bi na tio n of the abov e. Getting started with the Sequence aplet The fo llowing e xample defin es and t hen plots an expression in the Se quence aplet. Open the Sequence aplet 1. Open the Seq uence aplet. >$3/(7@ Select Sequence 67$ 57_ The Seq uence aplet starts in the Symbolic view .
6-2 Sequ ence aplet Define the expression 2. Define the Fibonacci sequ ence, in which each term (after the first tw o) is the sum of the prec eding two terms: , , for . In th e Symb olic vi ew of the Seq uence a plet, highlig ht th e U 1 (1) fie l d and begin defin ing your seque nce. 1 >(17(5@ 1 >(17(5@ 8 _  > 1@ _ >@ 8_  >1 @_ Note: Y ou can use the 1_ , 8 _ , and 8_ menu keys to assist in the entry of equati ons . >(17(5@ Speci fy pl ot settings 3. In Pl ot Setup, first se t the SEQPLOT option t o Stairstep . Reset the de fault plot settings by clearin g the Plot Setup view. –A St a i r s t e p s gr aph plots n on t he h orizo ntal ax is and U n on the vertical axis. –A Cobw eb graph plots U n- 1 on th e ho rizonta l axis and U n on th e ve rtical axi s. >6 ,)7@ SETUP - PLOT >6 ,)7@ CLEAR *e,*A, 8  >(17(5@ *A, 8  >(17(5@ U 1 1 = U 2 1 = U n U n 1 – U n 2 – = n 3 >
Seque nce aplet 6-3 Plot the sequen ce 4. Plot the Fibo nacci sequenc e. >3/27@ 5. In Pl ot Setup, set t he SEQPLOT option t o Cobwe b . >6 ,)7@ SETUP - PLOT  & 2 26_ Sele ct Cobweb 2._ >3/27@ Display t he tabl e 6. Display the table of n umeric values for this exampl e. >180@

Solve aplet 7-1 7 Solve aplet About the So lve aplet The Solve aplet so lves an equation or an expressi on for its unkno w n va r ia ble . You define an equa tion or express ion in the symbolic v iew, then supply values for all th e variables except one in the numeric vie w. Solve works onl y with real numbe rs. Note the differen ces between an equation and an expression: •A n equa tion cont ains an equals sign. It s solution is a value fo r the unknown var iable that makes b ot h sides have the sa m e va lu e. •A n expression does not c ont ain an equals sign . Its solution is a ro o t , that is, a value for the unk no wn variable th at make s the expression have a va lue of zero. You can use the Solve aplet to solve an equation for any on e of its variables. When the Solve a ple t is started, it opens in the So lve symbolic view. • In Sy mbo lic vi ew , you spec ify the expr ess ion o r eq uati on to solve. Y ou ca n define up to t en equations (or expre ssions), named E0 to E9. Each equ ation can cont ain up to 2 7 real va riables, named A t o Z and θ . • In N umeric vi ew , you sp ecify the values of the known variables, hi ghlight the variable t hat you want to sol ve for, and press 62 /9 ( a . You can sol ve the equati on as many tim es as you want, using new valu es f or the knowns and hi ghlighting a di fferent unknown . Note: It i s no t p o ssible to so lv e fo r more th an o ne variab le a t once. S imultaneous lin ear equations, fo r example, should be solved using matrice s or graph s in the Func tio n ap let.
7-2 Solve ap let Getting star ted with the Solve aplet Suppose you want to find the accel eration ne eded to increase the s peed of a car fr om 16.67 m/sec (6 0 kph) to 27.7 8 m/sec (100 kph) i n a distance of 100 m. The equa tion to solve is: Open t h e Solve aplet 1. Open the Solve aplet. >$3/(7@ Select Solve 67 $5 7a The Solv e aplet starts in the Symbo lic view . Define the equation 2. Define the equation. >$/3 $@ V >;  @ a >$/3 $@ U >;  @ >@ 2 >[@ >$/3 $@ A >[@ >$/3 $@ D >(17(5@ Note: Y ou can us e the _ menu key to assist in the entry of equatio ns. Define known variables 3. Display t he Solve numeri c view sc reen. >180@ 4. Enter th e values for the known variab les. 2 7 >@ 7 8 >(17(5@ 1 6 >@ 6 7 >(17(5@ *e, 1 0 0 >(17(5@ HINT If the Dec imal Mark setting i n the Modes inp ut form ( >6 ,)7@ MODES )is set to Comma, use > @ instead of >@. v 2 u 2 2 ad =
Solve aplet 7-3 Solve the unknown variable 5. Solve for the unknown variable (A). *e,*e, 62/ 9(a Therefore , the acceleration nee ded to increase the speed of a car from 16.67 m/se c (60 kph) to 2 7.78 m/sec (100 kph) in a dista nce of 100 m is appro ximatel y 2.47 m/s 2 . Because the v ariable A in t he equation is lin ear , once values are su bstituted into V , U and D, we know that we need no t look for an y other solutio ns. Plot the equation The Plot view shows one graph for each member of the select ed equatio n. Y ou can choose any of the va riables in the Numeric vi ew to be t he independent vari abl e. The othe r variables take on th e values a ssigned to th em in the Nume ric vi ew . The curre nt equation is . W ith the variable A high lighted, t he Plot view will show two grap hs. One of these is , with , or . This g raph will be a h o riz on tal lin e . T he other graph will be , with and , or . Thi s graph is also a line . The desired so lution is the v alue of A whe re these two lin es intersect. 6. Plot the equation fo r variable A. >9,(:6@ Select Auto Scale 2.a 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 277.88 89 =
7-4 Solve ap let 7. Trace along the grap h representing th e left member of the equation u ntil the cursor n ears the intersection . *A, ≈ 20 times Note the value of A displaye d near t he bottom left corne r of the screen. The Plot vi ew pro vides a convenient way to find an approxima tion to a solu tion before u sing the Nu meric view So lve option. See “Plottin g to find gue sses” on page 7-8 for more information. Solve aple t’s NUM vie w keys The Solv e aplet’s NUM view ke ys are: Key Mea ning ( ',7a Copies th e highlig hted value to the edit line for e diting. Press 2. _ when do ne . ,1) 2a Displays a mes sage about the solu t io n (see “I nterpretin g results ” on p age 7- 6). 3 $*(a Displa ys other pages of va riables, if any. ' ()1a Displays th e symbolic defini tion of the current express ion. Press 2. _ when done. 6 2/9 (a Finds a soluti on for th e highli ghted variabl e, based on t he va lues of the other variable s. >'(/@ Clears highl i gh ted variable to zero or deletes cu rre nt character in edit li ne, i f edit line is active. >6 ,)7@ CLEAR Resets all variable values to zero or clears the edit l ine, if cursor is in edit line.
Solve aplet 7-5 Use an initial guess You can usuall y obtain a faster an d m ore acc u rate sol utio n if you supp ly an estima ted value for t he unknown var i able before pressing 62 /9 ( a . Solve star ts looking for a solution at the initial guess. Before plo tting, make sure the unknown variable is highlig hted in the nume ric view . Plot the equa tion to help you select an ini tial guess when you don’t k now the range in which to look fo r the solution. See “Plottin g to find g uesses” on page 7-8 for further information. HINT An initial guess is especially import ant in th e case of a curve that cou ld have m ore than on e solution . In thi s case, only the solution closest to the in itial guess is returned. Numb er form at You can chan ge the number format for the S olve aplet in the Numeric Setup view. Th e opt ions are the same as in Home MODES: St andard, Fixed, Sc ientific , and Engi neering. Fo r the latt er three, yo u also specify how many digits of accurac y you want. See “Mode settin gs” on page 1-9 for more informatio n. You might find it handy to set a different number format for the Solve ap let if, for e xam pl e, yo u defin e equa tio n s to solv e for the val ue of money. A n umber format of Fixed 2 would be appr o p ri ate in thi s case .
7-6 Solve ap let Interpreting results After Solve has return ed a solution, press ,1)2 a in the Numeric view for more information. You wil l see one of the followin g three messages. Pres s 2.a to cle ar the message. Messa ge Condition Zero The Solv e aplet found a point where the valu e of the equa tion (or the ro ot of the expressi on) i s zero within the calculator’s 12 -digit accuracy. Sign Reversal Solve fo und two points where th e value of the equatio n has opposite signs, but it cannot find a point in between wh ere the value is zero. This might be because ei ther the two points are neighb ours (they d iffer by one i n the t welfth digi t), or the equa tion is not real-value d between the two points. Solve returns the point where the value is closer to zero. If the value of the equati on is a conti nuous real fu nction, this point is Solve’s best approxi mat ion of an actual ro ot . Extremum Solve found a point where the v alue of the equati o n approximates a l ocal minimum ( for positive va lues) or maximum (for negative values). This point may o r may not be a r oo t. Or: Solve sto pped searching at 9.9999 9999999E 49 9, the larges t number t he calculator can represent.
Solve aplet 7-7 If Solve c ould not find a solution, y ou will see one of the follo wing two messag es. HINT It is impo rtant to che ck the informatio n relating to the solve process. For ex ample, the solutio n that the Solve aplet finds i s not a solu tion, but th e closest tha t the functio n gets to ze ro. Only by ch ecking the i nformation will you know t hat this is the ca s e . The Root- Finder at work You can watc h the process of th e root-find er calculating an d searchin g for a root. Im mediately after pressing 62/ 9( a to start the root - finder, press an y key except >21@ . You will see two intermediate gue sses and, to the left, the sign of the expre ssion evalua te d at each guess. For exampl e: 2 2. 219330 55574 5 – 1 2 1.311111 11149 You c an watch a s the roo t-finde r either f inds a si gn reversal or converge s on a local extr ema or does not conv erge at all. If there i s no conver gence in pro cess, you might want to canc el the operation ( press >21@ ) and start ov er with a different initial gues s. Message Condition Bad Guess(es) The ini tial guess lies outside th e domain of the eq uation. Therefore, the so lution was not a real number or it caused an error. Constant ? The value of the equation is the same at every poi nt sampled.
7-8 Solve ap let Plotting to find g uesses The main rea son for p lott ing in the Solve ap let is to help you find initia l guesses and solution s for those equatio ns that hav e difficult-to -find or multiple solutions. Consider the eq ua tion of motion for an accel e rating body: where x is dis tance, v 0 is initial velocity, t i s ti me, and a is accelerati on . This is actually two equation s, y = x an d y = v 0 t ( at 2 ) / 2 . Since th is equation i s quadratic for t , ther e can be bo th a positiv e and a ne gative solu tion. Howeve r, we are con cerned only with p ositive solu tions, since on ly positive dista nce makes sense. 1. Select the Solv e aplet and enter the equat ion. >$3/(7@ Select Solve 67 $57 a >$/3 $@ X _ >$/3 $@ V >;@>$/3 $@ T  >@>$/3 $@ A  >;@>$/3 $@ T >;  @> j @ 2 2.a 2. Find the solution for T (time) wh en X =3 0 , V =2 , a n d A = 4. Enter the va lues for X , V , and A ; then h ighlight th e indepe ndent variab le, T . >180@ 30 >(17(5@ 2 >(1 7(5 @ *e, 4 >(17(5@ *e,*e, to high light T xv 0 t at 2 2 ----- - - =
Solve aplet 7-9 3. Use the Plot view to find an initial guess for T . Fir st set appropriat e X and Y ranges in the Plot Setu p. Since we have an equation, , the pl ot will produc e tw o gr a p hs : on e for and one for . Sinc e we hav e set in this example , on e of the graph s will be . There fore, make the YRNG –5 to 35. Keep the XR NG defaul t of –6.5 to 6.5. >6 ,)7@ SETUP - PLOT  *e, >@ 5 >(17(5@ 35 >(17( 5@ 4. Plot t he graph. >3/27@ 5. Move the cursor ne ar the positive (right-side ) intersection. This c u rsor val ue will b e an initia l g uess for T . *A, to move cursor to the intersect ion. The two po ints of intersectio n sho w that there are two so lu t io ns for th is equati on. However, only pos itive va l ues for x make sense, so we want to find th e solution for the intersectio n on the righ t side of th e y -axis . 6. Return to the Numeric view . >180@ Note: the T -value is fill ed in with the position of t he cursor from the Plot view . 7. Ensure that the T value is highlig hted, and solve t he equa tion. 62/ 9( a XV T A T 2 × × 2 ⁄ = YX = YV T A T 2 × × 2 ⁄ = X 30 = Y 30 =
7-10 Solve aplet 8. Use this equ ation to solve f or another variable, su ch as velocity . How fast must a body’ s initial veloci ty be in order for it to travel 50 m within 3 second s? Assume the same accel eration, 4 m/s 2 . Leave th e last value of V as an initial guess. 3 >(17(5@ *k,*k,*k, 50 >(17(5@ 62 /9 (a Using variables in equations You can use any of the real va riable nam es, A to Z and θ . Do not use variable names defined for other types, such as M1 (a matrix varia ble). Home variables All home variables (othe r than those for ap let settings, lik e Xmin and Ytick ) are global , which mean s they are shared throug hout the dif ferent ap lets of the c alculator . A value that is assigned to a home variab le anywhere remain s with that var iable wher ever i ts na me is used. Therefo r e, if you have def ined a value for T (as in the above example ) in another aplet or even anothe r Solve equatio n, that value shows u p in the Num eric view for this S olve equation. When you then redefine the value fo r T in this Solve equat ion, that val ue is applied to T in all other con texts (until it is changed ag ain). This sharing allows you to work on the sam e problem in different places (suc h as HOME and the Solve aple t) without having to update th e value eve rywhere when ever it is recalculated . HINT As the Solv e aplet uses any existing variab le values, b e sure to check for existin g varia ble va lues th at may a ffect th e solve proc es s. (Y ou ca n use >6 ,)7@ CLEAR to reset all va lues to zero in the So lve aplet’s Numeric v iew if you wish.) Aplet variable s Func tions defined in other aplets can al so be referenced in the Solve aple t. F or e x amp le , if, i n th e Fu nc tio n a p let, y ou de fin e F1(X)=X 2 10 , you can enter F1(X)=50 in th e Solve a plet to solve t he equation X 2 10=50 .
Stati stic s apl et 8-1 8 St atis tic s aplet About the Sta tistics aplet The Statistics aplet can store up to t en separate data sets at one time. It can do one-var iable or two-variable statisti cal analysis of on e or more sets of data. The Statistics aplet st arts with the Nume ric view which is used to enter data . The Symbolic v iew is used to specify which columns c ontain dat a and which co lumn contains frequencies. You can also co mpute statistics values in HOME and re cal l the values of specific statistics variables. The values computed in the S tatistics aplet are sav ed in variables , and many of thes e variables are listed by the 6 7$7 6_ function acce ssible from the Statist i cs aplet’s Numeric view screen. Getting started with the Statist ics aplet The followi ng example asks you to enter and analyze th e adverti sing and sal es da ta (in the ta ble below) , compute statistics, fit a curve to the data, and p redict the e ffect of more advertising on sales. Advertising min utes (independe nt , x ) Resulting Sales ($) (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 S tatistics aplet Open t h e Statist ics aplet 1. Open the Statistics aple t and clear existin g data by pressing 5(6 (7_ . >$3/(7@ Sele ct Statistics 5( 6(7 _  <(6_ 67 $57 _ The S tatistics aplet starts in the Numerical view . At any time the Sta tistics aplet is conf igured for only one of two types of statistical explor atio ns: on e-va ria ble ( 9$ 5_ ) or two- varia ble (  9$5 _ ). The 5th me nu key label in the Numeric view to gg le s be twe e n the s e tw o op tio ns and sh ow s the current optio n. 2. Select  9$5 _ .  Y o u need to select 9$ 5_ beca use i n this examp le we are analyzin g a dataset comprisin g two variables: advertising minutes and resultin g sales. Enter data 3. Enter the data i nto the columns. 2 >(17(5@ 1 >(17(5@ 3 >(17(5@ 5 >(17(5@ 5 >(17(5@ 4 >(17(5@ *A, to move to the next column 1400 >(17(5@920 >(17(5@ 1100 >(17(5@ 2265 >(17( 5@ 2890 >(17(5@2200 >( 17(5@ 1VAR/2VA R menu key label
Stati stic s apl et 8-3 Choose fit and data columns 4. Select a fit in the Symbolic setup vie w . >6 ,)7@ SETUP - SYMB *e, & 226 _ Select Linear 2._ Y ou can d e f ine up to fiv e ex ploratio ns of two-vari abl e data, nam ed S1 to S5 . In this exampl e, we will create just one : S1 . 5. Speci f y the columns that ho ld the data you want t o analyz e. >6<0%@ Y ou could h ave en tered your da ta into colum ns other than C1 and C2. Explore statis tics 6. Find the mean ad vertising time ( MEANX ) and the mean sales ( MEANY ). >180@ 67$ 76_ MEANX is about 3 .3 minu tes and MEANY is about $1 79 6 . 7. Scroll down to di splay the va lue for the c orrelation coefficient ( CORR) . The CORR value ind icates how we l l the line ar model fit s the data . *e, 9 times The va lue is 0. 8995 to four si gnifica nt digits. 2._ Setup plot 8. Change the plott ing range to ensure all the d ata points are plotted (a nd select a di fferent po int mark, if y ou wish). >6 ,)7@ SETUP - PLOT *A,  7 >(17(5 @ >@ 100 >(17(5@ 4000 >(17(5@
8-4 S tatistics aplet Plot the graph 9. Plot t he graph. >3/27@ Draw t he regress ion curve 10. Draw the regression curve (a curve to fit the data points). 0 (18_ ),7 _ This draws the regression line f or the best linear fit. Displa y the equation for best linear fit 1 1. Return to the Symbolic view . >6<0%@ 12. Display the equa tion for the b est linear fit. *e, to move to the FIT1 field 6 2:_ The full FIT1 expressio n is shown. The slope (m) i s 425.87 5. The y -inte rcept (b) is ab out 376.25 .
Stati stic s apl et 8-5 Predict va lues 13 . T o find the predicted sales figure if adverti sing were to go up to 6 minutes: 2._ > 20(@ >0$7 @ S ( to hi ghlight Stat-Two) *A,*e, (to hi ghlight PREDY ) 2._ 6 >(17(5@ 14. R eturn to the Pl ot view . >3/27@  15. Jump to the indi cated point o n the regr ession line . *e, *27 2_ 6 2._ Observe the pred i cted y - value in the left bottom corner o f the screen. Entering and editing statistical data The N um e r i c vi ew ( >180@ ) is used to enter data into the Statistic s aplet. Each colum n represents a variabl e named C0 to C9. After en te ring t he d at a, y ou m ust de fine th e data set in the Symbol ic view ( >6<0%@ ). HINT A data colu mn must hav e at least fou r data poin ts to provide valid t wo-variable statistics, or two da ta points for one - variable sta tistics. You can al so store stat istical dat a values by copying lis ts from HOME into Statis tics data colum ns. For example, in HOME, L1 672 ?_ C1 stores a copy o f the list L1 into the data-c olumn variab le C1 .
8-6 S tatistics aplet Statist ics aplet’s N UM view keys The Statistics apl et ’ s Nume ric view keys are: Key Meaning ( ',7_ Copies t he highlight ed item into the edit line. ,16_ Inserts a zero va lu e abo ve the highlig hted cell. 6 257_ Sorts the specified i ndependent data column i n ascending or desc ending order, and rearra ng es a specifie d dependent (or frequency ) data column accordin gly. %, * _ Switches bet ween larger and smaller font sizes.  9$5 _  9$5 _ A togg le switc h to sel ect one- va riabl e or two-varia ble statistics. This setti ng affects the statistical calculatio ns and plots. Th e label indicat es which setting is current. 6 7$76 _ Computes descript ive statistics for each dat a set specifi ed in Symbolic view. >'(/@ Deletes the currentl y highlighte d valu e. >6 ,)7@ CLEAR Clears the current co l umn or all columns of data. P ress >6 ,)7@ CLEAR to display a menu list, then se lect the curren t column or all column s option, and press 2._ . >6 ,)7@  FXUVRU NH\ Moves to the first or last row, or first or last column .
Stati stic s apl et 8-7 Examp le You are me asur ing the hei ght of students in a cla ssroom to find the mean height. The first fiv e students have the follow ing mea sureme nts 160c m, 165c m, 170 cm, 175c m, 180cm. 1. Open th e S t a t i stics ap l e t . >$3/(7@ Select Statistics 5(6 (7_<( 6_ 67$ 57_ 2. Enter the measure ment data. 160 >(17(5@ 165 >(17(5@ 170 >(17(5@ 175 >(17(5@ 180 >(17(5@ 3. Find th e mean of the sample. Ensure the 9$ 5_ /  9$5 _ menu ke y labe l re a ds 9$ 5_ .  Pres s 67$ 76_ to see the statistics calculated from the sample data in C1. Press the *e, ke y  to scroll to further statistics. Note that t he title for the column of statisti cs is H1. There are 5 da ta set definitions ava ila ble f or one-varia ble statistic s: H1–H5. If data is entere d in C1, H1 is automaticall y set to use C1 for data, and the frequency o f each dat a point i s set to 1. Y ou can select other col umns of data from the Statisti cs Symboli c setup view .
8-8 S tatistics aplet 4. Press 2. _ to close the statistics window an d press >6<0%@ key to see the data se t definitions. The first column indicates t he as sociated column of data for e ach data set definition, a nd the second col umn indicat es t he constant frequency , or the column t hat holds th e frequencies. The keys you ca n use from this wi ndo w are: Key Meaning ( ',7_ Copies the column variable (or variable e xpression) to the edit l ine for editing. Press 2._ when done . _& ._ Checks/u nch ecks the current data se t. Only the che ckmarked data set(s) are comput ed an d plotted. &_ RU ;_ Typing ai d for the colum n va riables ( &_ ) or for the Fit expressions ( ;_ ). 6 2: _ Displays the cu rrent variable expression in stan dard mathematical form. Press 2. _ when done. ( 9$/_ Evaluates th e variables in th e highlig hted c olumn (C 1, etc.) expression. >9$56@  Displays the menu for entering varia bl e names or cont en ts of variabl es. >0$7 @ Displays t he menu for entering math operation s. >'(/@ Deletes the highligh ted variable or the current cha racter in the edit line.
Stati stic s apl et 8-9 To cont inue ou r ex a m ple , su ppose th at the heig h ts of th e res t of th e students in the class a re measured, but each o ne is rounded t o the nearest of the five values first recorded . Instead of entering a ll the new data in C1, we sha ll simply add another column, C2, th at ho lds the fre quenc ies of our fiv e data point s in C1. 5. Move the hi ghlight ba r into the ri ght colum n of the H1 de finition an d replace the frequ ency value of 1 wi th the name C2. &_ 2 6. Return to the num eric view . >180@ 7. Enter the frequen cy data show n in the ab ove table. *A, 5 >(17(5@ 3 >(17(5@ 8 >(17(5@ 2 >(17(5@ 1 >(17(5@ >6 ,)7@ CLEAR Resets default specifications for the data sets or clears the edit l ine (if it was active). Note: If >6 ,)7@ CLEAR is used th e data sets will need to be sele cted again before re -use. Key Me aning (Conti nued) Height (cm ) Frequency 160 5 165 3 170 8 175 2 180 1
8-10 Statistics aplet 8. Display th e co mputed statistics. 67 $76 _ Y o u can scroll do wn to the mean. T he mean heig ht is approx im ately 167.63 cm. 9. Setup a hi stogram p lot fo r the data . 2._ >6 ,)7@ SETUP - PLOT Enter set up information approp r i ate to your data. 10. Plot a hi stogram of t he da ta. >3/27@  Angle Setting You can ig nore the angl e measurement mode unless your Fit definit ion (in Symbolic view) invo lves a trigon ometric function . In this case, yo u should specify in the mode scree n whether th e trigonometric units are to be interpreted i n degrees , radians, or grad s. Save dat a The d ata th at you ent er is automat ically saved . When you are finishe d entering data values , you c an press a key for anoth er Statistics view (like >6<0%@ ), or y ou ca n switch to anot h er aplet or HOME. Edit a data set In the Numeric v ie w of th e Sta tistic s aplet, highlight th e da ta value to change. Type a new value a nd press >(17(5@ , or pres s ( ',7_ to copy the va lu e to t he edit line for m odific a tio n. Press >(17(5@ afte r modifying t he value on the edit li ne. Delete data • T o dele te a single dat a item, high light it an d press >'(/@ . The valu es below the deleted cell will scroll up on e row . • T o delete a column of d ata, highlig ht an en try in that column and pr ess >6 ,)7@ CLEAR . Sel ect th e col umn n ame. • T o delete a ll columns of data, pre ss >6 ,)7 @ CLEAR . Select All columns .
Stati stic s apl et 8-11 Insert data Hig h lig ht the entry fo llowing the point of insertion. Press ,1 6_ , then enter a number. It will write over the zer o that was inserted. Sort data values 1. In Numeric view , highl ight the c olumn yo u want t o sort, and press 6 257_ . 2. Select the SORT ORDER op tion. Y ou can c hoose eith er Ascending or Descending . 3. Specify the INDEPENDEN T an d DEPENDEN T data columns. Sort ing is by the inde pendent column. For instance , if Age is C1 and Income is C2 an d you want to sort by Incom e, then y ou make C2 the inde penden t column for th e sorting an d C1 the depe ndent column . – T o sort just one column , choose None for the depen dent colum n. – For one-varia ble statistics with two data columns, specify t he frequenc y column as t he dependen t colu mn. 4. Press 2._ . Defining a regression model (2VAR) The Sym bolic view inc ludes an expression (Fit1 through Fit5) that defin es the regre ssion model, o r “fit”, to use for the regres sion anal ysis of e ach two-va riable da ta set. There are three way s t o sel ec t a regression model: • Accept th e default op tion to fit t he data to a straight line . • Select o ne of the availa ble fit option s in Symbolic Setup view . • Ente r your o wn mathema tical expre ssion in S ymbolic view . This expression will be plotted, but it will not be fitted to th e data poin ts . To choose the fit 1. In Numeric v iew , make sure  9$5 _ is set. 2. Press >6 ,)7@ SETUP - SYMB to display the Symb olic Se tup view . Highlight the Fit numb er ( S1FIT to S5FIT ) you want to define. 3. Press & 226 _ and selec t from the foll owing list. Pre ss 2._ when done. The regression formula for th e fit is displayed in Symbolic v iew .
8-12 Statistics aplet Fit models Eight fit model s are availa ble : To define your own fit 1. In Numeri c view , ma ke sure 9$ 5_ is set. 2. Display t he Symbolic v iew . 3. Highli ght the Fit e xpression ( Fit1 , etc.) for the desired data set. 4. T y pe in an expressio n and press >(17(5@ . The inde pendent vari able must be X , an d the expression must not con tain any unkn own variable s. Example: . This autom atically change s the Fit type ( S1FIT , etc.) in the Symb ol ic Setu p vi ew to User Defined . Fit model Meanin g Linear (Default.) Fi ts the data to a stra ight line, y = mx b. Uses a least-sq ua res fit. Logarithmic Fits to a logarithmi c curve, y = m ln x b. Exponential Fits to an exponentia l curve, y = be mx . Power Fits to a p ower cu rve, y = bx m . Quadratic Fits to a quadrati c curv e, y = ax 2 bx c. Needs at leas t three points. Cubic Fits t o a cu bic curve, y = ax 3 bx 2 cx d. Needs at lea st four po int s. Logistic Fits to a logisti c 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 comput ed au tomatically . User Defined Define you r own expressi on (in Symbolic view.) y L 1 ae bx – () ------ -------- --------- -- - = 1.5 x cos × 0.3 x sin ×
Stati stic s apl et 8-13 Computed statistics One-varia ble When th e data set c ontains an odd number of values, the data set’s median value is not use d when calculating Q1 an d Q3 in the table a bove. For e xample, for th e following data set: {3,5,7,8,15,16,17} only the fi rst three items, 3, 5, and 7 are used to calcul ate Q1, and onl y t he last three term s, 15, 16, and 17 are used to calculat e Q3 . S ta tisti c De finit ion N Σ Number of d ata points. TOT Σ Sum of da ta values (with th eir frequencies ) . MEAN Σ Mean valu e of data set. PVAR Σ Population variance of data set. SVAR Σ Sample va riance of data se t. PSDEV Population stan dard de viat ion o f data set. SSDEV S ample stand ard deviatio n of data set. MIN Σ Minimum d ata value in data set. Q1 First quart ile: median o f ordinals to left of me dian. MEDIAN Me d ian valu e of data s e t. Q3 Third quartile : median of ordinal s to right o f medi an. MAX Σ Maximum data value i n data set.
8-14 Statistics aplet Two-variable S tatistic Defi nition MEANX Mean of x - (independent) values. Σ X Sum of x -values. Σ X2 Su m of x 2 -values. MEANY Mean of y - (dependent) values. Σ Y Sum of y -values. Σ Y2 Su m of y 2 -values. Σ XY Sum of each xy. SCOV S ample covarian ce of i ndependent and d ependent data colum ns. PCOV P opulatio n covariance of i ndependent and d ependent data c olumns CORR Correlation coefficient of the indep endent and d ependent data colu mns 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 o f accuracy for the fit.
Stati stic s apl et 8-15 Plotting You can plot: •h i s t o g r a m s (  9$5 _ ) • box -and-whisker plots ( 9 $5 _ ) • scat ter plots of da ta ( 9$ 5_ ). Once you ha ve entered you r data ( >180@ ), def i ned your da ta set ( >6<0%@ ), and def ined your Fi t model for t w o- variable statistics ( >6 ,)7@ SETUP - SYMB ), you can plot your dat a . You can selec t up to five sc atter or box -and-wh isker plots a t a time. You can pl ot only one histog ram at a time. To plot statistical data 1. In Symbolic vie w ( >6<0%@ ), select ( _ & ._ ) the da ta sets you want to plot. 2. For one-v ariabl e dat a (  9$5 _ ), select th e plot type in Plot Setup ( >6 ,)7 @ SETUP - PLOT ). Highlight STATPLOT , press & 2 26_ , select ei ther Histogram or BoxWhisker , and press 2._ . 3. For an y pl ot, but espec ially for a hi st ogram, adjust th e plotting scale an d rang e in the Pl ot Setup v iew . If you find hi stogram ba r s too fat or too t hin, you c an ad just them with t he HWIDTH setting. 4. Press >3/27@ . I f you have no t a dj usted the Plo t Setup your sel f, you can tr y >9, (:6@ selec t Auto Scale 2._ . HINT Auto Scal e can be relied upon to gi ve a g ood starting scal e which can th en be adjusted in the Pl ot Setup view.
8-16 Statistics aplet Plot t ypes Histogram One-va riable statist i cs . The numbers belo w the plo t mean that the current bar (where the cursor is) starts at 0 and ends at 2 (not in cluding 2), and the frequency for this column, (that is, t he number of da ta elements that fall betwee n 0 and 2) is 1. You ca n see information about the ne xt bar by pressin g the *A, key. Box and Whisker Pl ot One-vari ab le statistics . The left whisker marks the minimum da ta value. The box marks the first quartile, the median , and the th ird quartile. The right whisker marks the maximum dat a va lue. Scatter Plot Tw o-vari able stat istics . The numbers belo w the plo t indicate th at the cursor is at the first data point fo r S2, at (1, 6). Press *A, to mov e to the ne xt data point and displa y information about it. To conn ect the da ta points as they are plot t ed, checkmark CONNECT in the seco nd page of the P l ot Setup. T his is not a regression cur ve.
Stati stic s apl et 8-17 Fitting a curve to 2VAR data In th e Plot view, pre ss ) ,7_ . This draws a curve to fit the checked two - vari able data set(s). See “To cho ose the fit” on page 8-11. >3/27@ 0 ( 18 _ ),7_ >6<0%@ 6 2 :_ The expres sion i n Fit2 shows that the slope = 1. 9808219178 1 and the y -interce pt = 2. 2657. Correlat ion coeff icie nt The c orrelat ion coe fficie nt is sto red in th e CORR vari able . It is a measure of fit t o a linear curve only . Regardless of the Fit mode l y ou have chos en, CORR relates to the linear model. Relative Error The relative erro r is sto red in a variable named RELERR . The relative error provides a measure of fit accuracy for all fi ts, and it does depen d on the Fit mo d el you have ch os e n . The relative e rror is a measure of t he error between predict ed values and act ual values based on the specifi ed Fit. A smaller number means a bet t er fi t. HINT In order to access t he se variables after you plo t a set of statistics, you must pre ss >180@ to access the numeric view and the n 6 7$7 6_ to display the corre lation values. The va lues are stor ed in the v ariables when you access the Symbolic view.
8-18 Statistics aplet Setting up the plo t (Plot setup view) The Pl ot Setup v iew ( >6 ,)7@ SETUP - PLOT ) sets most of the same plottin g paramet ers as it does for th e other built -in aplets . See “Settin g up the plot (Plot vi ew set up)” on page 2-5. Settings unique to the Statistics aplet are a s follows: Plot type (1V AR) STATPLOT enables you to specify ei th er a hi stogram or a box-an d-whisker pl ot for one-va riable s tatistics (w hen 9$ 5_ is set). Press & 226 _ to cha nge the hig hlighted setti ng Histogram width HWIDTH enables you to s pec ify the wid th of a hi st ogr am bar. This determin es how many bars will fit in the displa y, as well as how the da ta is distri bu ted (how man y va lues each ba r represents). Histogram range HRNG enables yo u t o specify the ra n ge of values fo r a set of histogr am bars. The ra ng e runs from th e left edge of t he leftmost b ar to the righ t edge of th e rightmost ba r. You can limit the range to exclude any val ues you suspect are outliers . Plotting mark (2VAR) S1MARK through S5MARK enables you to specify on e of five symbols to use to plot ea ch data set. Pres s & 226 _ to change the highli ghted setti ng. Connected poi nts (2VAR) CONNECT (on t he seco nd pa ge), w hen che ckmar ked, connec ts t he data points as they ar e plotted. The resulting line is not the regression curve. The orde r of plotting is accordin g to the ascendi ng order of indepen dent values. For instan ce, the data set (1,1), (3,9), (4,1 6), (2,4) would be plotted and traced in the order (1 ,1), (2,4), (3,9 ), (4,16).
Stati stic s apl et 8-19 Trouble-shooti ng a plot If you h ave proble ms plotting, check tha t you ha ve the foll owing: • Th e co r r e ct 9 $5 _ or 9 $5 _ menu la bel on (Nume ric view). • The correct fit (regression mode l), if the data se t is two- varia ble. • Only t he data sets to comput e or plot are checkm arked (Sym bolic view ) . • The correct plott ing rang e. T ry u sing >9,(:6@ Auto Scale (instead of >3/27@ ), or adjust the plotting parameters (in Plot Setup) for the ranges of the axes an d the wid t h of histogram bar s ( HWIDTH ). •I n 9$ 5_ mode, ens ure that bo th paired col umns contain data, an d that the y are the sa me length. •I n 9$ 5_ mode, ensure t hat a paired column of frequency values is t he same le n gth a s the d ata co lum n that i t refers to.
8-20 Statistics aplet Exploring the graph The Pl ot view h as men u keys for zoomin g, trac ing, and coordin at e display. There are also scal ing options under >9,(:6@ . T hese optio ns are des cribed in “Explori ng the gr aph” on pa ge 2-7. Statist ics aplet’s P LOT view key s Key Meaning >6 ,)7@ CLEAR Erases the pl ot. >9,(:6@ Offers ad ditional pre-defined views for splitting th e screen, ove rlaying pl ots, and autoscal ing the axes. >6 ,)7@ *>, >6 ,)7@ *A, Moves cursor to far left o r far right. = 220 _ Displays ZOOM menu. 7 5$&( _ Turns trace mod e on/off. The white box appears next t o the option when Trace mode is activ e. ) ,7_ Turns fit mode o n/off. Turning  ),7_ on draws a curve to fit the data points accordin g to t he cu rrent regression model. *27 2_ (2var statistics on ly) Enables yo u to specify a valu e on the line o f b e st fi t to jum p to o r a da ta po i nt number to jum p to. ' ()1_ Displays the e quation of the re gression curve. 0 (18_ Hide s and displays the men u key la bels. When the la bels are hi dden, any menu key disp lays the (x,y ) coordinat es. Pressing 0(18 _ redispl a ys t he menu labels.
Stati stic s apl et 8-21 Calculating p redicted values The fu nctions PREDX a nd PREDY estimate (predi ct ) val ues for X or Y given a hypo th et ical valu e f or the oth er. The estimat ion is made based on th e curve that has been cal culated to fit the data accordin g to the specified fi t. Find predicted values 1. In P lot view, draw th e regressi on curve f or the data set. 2. Press *e, to move to the regression curve. 3. Press *2 72_ and enter the value of X . The cursor jumps to the desir ed point on curve an d the coordinat e display shows X and the pred icted value of Y . In HOME, –E n t e r PREDX ( y-value ) >(17( 5@ to find th e predicted (estimated) value for the indepe nd e nt variable give n a hy pothet ica l de p en de n t value. –E n t e r PREDY ( x-value ) to find the p redicted valu e of the de pendent variab le given a hypo thetical indepe ndent va riable. Y ou ca n type PREDX and PREDY into the edit line, or you can copy the s e func tio n na m es f rom the MA TH menu under the Stat-T wo category . HINT In cases where more th an o ne fit curve is displayed, the PREDY function us es the most recently calcul ated curve. In order to avo id errors with this func tion, uncheck all fi ts except the one tha t yo u w an t to wo rk w ith, or use the Plot View method .

Infe rence ap let 9-1 9 Inference aple t About the In ference aplet The Inferenc e capabilities in clude calculatio n of confi dence interv al s and hypothesi s t ests based on the Nor mal Z–distribu tion or Stud ent’s t–distrib ution. Based on th e s ta tistics from one or two samples, you ca n tes t hypothes es and find confidence interval s for the following quantitie s: • mean • prop ortion • difference b etween two mean s • difference b etween two proportions Examp le data When you first access an input fo rm for an Inference test, by default t he i np ut form contains exam ple data. This ex amp le data is designed to return meaningful re sults that relate to the test. It is useful for ga ining an u nderstanding o f what the test does, and for de monstrating t he test. The calculat or’s on–line help p rovides a descri ption of what t he examp le data represents.
9-2 Inference ap let Getting started with the Inference aplet This exa m pl e describes th e Inference a pl et’s options an d functio nality by stepp ing yo u throug h an ex ample us ing the example data for the Z–Test on 1 mean. Open t h e Inference aplet 1. Open the Inference aplet. >$3/(7@ Sele ct Inferential 67 $5 7a . The Inferenc e apl et opens in the Sy mbolic view . Inferen ce aplet’s SYMB v iew keys The tabl e below summa rizes the options a vailable in Symbolic v iew . Hypot hesis T e s ts Confi dence Int ervals Z: 1 µ , t he Z– Test on 1 m ean Z–Int: 1 µ , the confidence interval for 1 mean, based on th e Normal distribution Z: µ 1 – µ 2 , the Z–Test on t he diff erence of two means Z–Int: µ 1 – µ 2 , the confid en ce interval for the difference of two means, base d on the Normal distribu tion Z: 1 P, th e Z–Test on 1 p roport ion Z–Int: 1 P, the confide nce interval for 1 pro portion, bas e d on the No rmal distribu tion Z: P 1 – P 2 , the Z–Test on t he differenc e in two prop orti ons Z–Int: P 1 – P 2 , the confid en ce interval for the difference of two proporti ons, based on the N ormal distribu tion T: 1 µ , t he T– Test on 1 m ean T–Int: 1 µ , the confidence interval for 1 mean, based on th e Student’s t–d istrib ut ion T: µ 1 – µ 2 , the T–Test on t he diff erence of two means T–Int: µ 1 – µ 2 , the confid en ce interval for the difference of two means, base d on the Studen t’s t–distribu tion
Infe rence ap let 9-3 If you ch oose one of the hypothesi s tests, you c an choose t he alternative hypothesis to test against the null hypoth esis. For each test, there are t hree possible choices fo r an alternative hypothe sis based on a quantita tive comparison of two quantitie s. The null hy pothesis is alway s that the two quantities are equal.Thus, the alternative hyp otheses cover the various cases for th e two quantities being unequal: <, >, a nd ≠ . In this sectio n, we will use the examp le data for the Z–Test on 1 mean to illustrate h ow the aplet works and what features the various v iews present. Define the inferential method 1. Select the Hypothesis Te st inferential method. & 2 26 a Select HYPOTH TEST 2. Define the ty pe of test. 2.a  *e, & 2 26 a Z–Test: 1 µ 3. Select an alternative hypo th esis. 2.a  *e, & 2 26 a µ< µ 0 2.a
9-4 Inference ap let Enter data 4. Enter the sample statistics and populatio n parameters that define t he chosen test or in terval. >6 ,)7@ SETUP - NUM The tabl e below lists the fie lds in this vie w for our cur rent Z–Test : 1 µ example. By default, each field already contai ns a va lue. These values con s titu te th e e xa mpl e datab ase a n d are expl ained in the ( /3a feature of th is aplet. Display on-line help 5. Display the on-lin e help. ( /3 a 6. T o clos e the on-lin e help, press 2. a . Display test results in numeric format 7. Display t he test results in numeric format. >180@ The test dist r ibution val ue and its associ ated proba bili ty are disp la ye d, along wit h t he cri t ical value(s) of the test an d the associated crit ic al value (s) of the statistic. Note: Y ou c an access t he on-line help in Numeric view . Field n ame Definition µ 0 Ass umed popu la tion mea n σ Popula tion standa rd devia tion Sample mean n Sample size α Alpha level for the test x
Infe rence ap let 9-5 Plot test results 8. Display a graphic view of the test resu lts. >3/27@ Horizontal axes are presented fo r both the distr ibu tio n va r ia bl e and the test sta tistic. A generi c bell curve repres ents the prob abili ty distributio n function. V ertical lines ma rk the critical value(s) of the test, as well as the value o f the test sta tistic. Th e rejectio n region is mar ked and the test n umeric results are display ed between the ho rizontal axes. Importing Sample Stati sti cs from the Statistics aplet The Inference ap le t supports the calculati on of con fidence intervals and the testing of hypotheses ba sed on data i n the Statistics aple t. Computed sta tistics for a sample of da ta in a column in an y Statistics-based aplet can be i mported for use in the Inference aple t. T he fol l o wing example illustrates the proces s. A calcu lator p roduces th e follow ing 6 r andom num bers: 0.529, 0.295, 0.952, 0.259, 0.925, and 0 .592 Open the Statistics aplet 1. Open Statistics a plet. Note: Reset curr ent settings. >$3/(7@ Select Statistics 5(6 (7 a< (6 a 67$ 57 a The S tati stics ap let op e n s in the Numeric view . R
9-6 Inference ap let Enter data 2. In th e C1 co lumn , ente r the random numb ers pr oduc ed by the calcu lator . >@ 529 >(17(5@ >@ 295 >(17(5@ >@ 952 >(17(5@ >@ 259 >(17(5@ >@ 925 >(17(5@ >@ 592 >(17(5@ HINT If the Dec imal Mark setting i n the Modes inp ut form ( >6 ,)7@ MODES ) is set to Comma, use >@ instead of >@ . 3. If necessary , select 1–variable statistics. Do this by pressing the fifth menu key un til 9$ 5a a is displayed as its menu label. Calculat e stati st ics 4. Calcul ate st atist ics. 67 $7 6a The mean of 0.5 92 seems a little la rge c ompared to th e expected value of 0.5 . T o see if the diff erence is statistically significant, we will use the statist i cs co mputed here to con s t ruct a confidence interval for the true mean of the population of random number s and see whether or no t this inter val contains 0. 5. 5. Press 2. a to close the comp uted statistics win do w . Open Inference aplet 6. Open the In ference aplet and clear current settings. >$3/(7@ Select Inference 5( 6( 7a <(6 a 67 $5 7a
Infe rence ap let 9-7 Choose inference method and type 7. Choose an inference method. & 2 26 a Select  CONF INTERVAL 2.a 8. Choo se a distributio n statistic ty pe. *e, & 22 6a Select T-Int: 1 µ 2.a Set up the interval calculati on 9. Set up the interv al calcula tion. Note: The defa ult v alu es ar e sample d ata fr om the on -line help e xample. >6 ,)7@ SETUP - NUM Import the data 10. Import the data from the Statistic s aplet. Note: The data fr om C1 is display ed by defau lt. ,03 57a Note: If there ar e other col umns of da ta in th e S tatistics aplet, y ou could select a column and press 2.a to see the sta tistics befor e importing them into the Numeric Setup view . Also, if ther e is mor e than one aple t based on t he S tatis tics aplet, yo u ar e prompted to choose one. 2.a
9-8 Inference ap let 1 1. Speci fy a 90% co nfide nc e inte r v al in the C: field. *e, *e, *e, to move to the C: fiel d 0.9 >(17(5@ Display Numeric view 12. D i s pl ay the confidence int e rval in the Numeric vi ew . Note: The interval setting is 0.5. >180@ Display Plot view 13. D i splay the confide nce interval in the Plo t vi ew . >3/27@ Y o u can see, from the second te xt row , that the mean is con t ained within the 90 % confidence inte rval (CI) o f 0.3469814 to 0.8370 186 . Note: T he g raph is a simple , generic bell- c urve. It is not meant to a ccurately r epr esent t he t-distribution with 5 degrees of fr eedom.
Infe rence ap let 9-9 Hypothesi s tests You us e hypothesis te sts to test the va lidity of hypothese s that relate to th e statistical pa rameters of on e or two popu lations. The tests are based on statistics of samples of the popula tions. The HP 39G/40G hypothesis te sts use the Normal Z–distri bution or Stud e nt’ s t- di s tr ibu tio n to c alc u la te probabilities. One–Sample Z–Test Menu name Z–Test: 1 µ On the basis of statistics from a single sample, the 1 mean Z–Test measure s the strength of the eviden ce for a selected hypothe sis against t he n ull hypothe sis. The n ull hy pothesis is that the population m ean equals a specified va lue Η 0 : µ – µ 0 . You select on e of the fo llowing alternat ive hypotheses against which to te st the null hy pothesis: Inputs The input s ar e: H 1  µµ 0 < H 1 : µµ 0 > H 1 : µµ 0 ≠ Field na me Defini tion Sample mean. n Sam p l e s i z e. µ 0 Hypo thet i ca l po pu la tio n me a n. σ Popul ation standa rd deviation. α S ignificance level. x
9-10 Inference aplet Results The re sult s are: Two–Sample Z–T e st Menu name Z–Test: µ 1–µ 2 On the basi s of two sample s, each from a separa te population, this test measures t he strength of the evidenc e for a select ed hypoth esis against the null h ypothesis . The null hypothes is is that the mean of th e two popu lations are e qual ( H 0 : µ 1 = µ 2 ). You sel ect one of th e following altern ative hypo theses against which to t est the null hyp othesis: Inputs The inputs are: Result Description Test Z Z–tes t stat istic. Prob Probability associated with t he Z–Test statistic. Crit ical Z Bou ndar y value s of Z asso ciated wit h the α level that you suppli ed. Critical Boun dary values o f re quired by the α value that yo u supplied . x x H 1  µ 1 µ 2 < H 1  µ 1 µ 2 > H 1  µ 1 µ 2 ≠ Field na me Defini tion Sample 1 mean. Sample 2 mean. n1 Sample 1 size . n2 Sample 2 size . σ 1 Popul a tion 1 stan dar d deviatio n. σ 2 Popul a tion 2 stan dar d deviatio n. α Signif ic ance le vel. x 1 x 2
Infe rence ap let 9-11 Results The results are: One–P r opor tion Z– Tes t Menu name Z–Test: 1 P On the ba sis of statistics from a sing le sample, this test measures th e st rength of the evidence for a se le cted hypothe sis against t he n ull hypothe sis. The n ull hy pothesis is that the proportion of su ccesses in the t wo popula tions is equal . You select on e of the fo llowing alternat ive hypotheses against which to te st the null hy pothesis: Inputs The input s ar e: Result Description T est Z Z–T est statistic Prob Probabili ty associated with th e Z–T est statistic. Critical Z Boundary va lue of Z associated with the α lev el that yo u supp lied. H 0 ππ 0 = H 1 : ππ 0 < H 1 : ππ 0 > H 1 : ππ 0 ≠ Field na me Definition x Nu mber of succ esses in the s ample. n S amp le size. π  Populatio n proportion of successes. α Signific anc e level.
9-12 Inference aplet Results The re sult s are: Two–Proportion Z –Test Menu name Z–Test: P1 – P2 On the basis o f statistics from two samples, ea ch from a diffe rent popu lation, the 2 propo rtion Z–Tes t measure s the strength of the ev idence for a selected h ypo thesis agains t the null hy pothesis. Th e null hy pothesis is th at the pro portion of successes in the two po pulations is equal. ( H 0 : π 1 = π 2 ). You sel ect one of th e following altern ative hypo theses against which to t est the null hyp othesis: Inputs The inputs are: Result Description Test P Proportion of successes in the sam ple. Test Z Z– Test statisti c. Prob Probabili ty associated with the Z–Test statistic. Crit ical Z B ounda ry value of Z associ ated wi th the level y ou supplie d. H 1  π 1 π 2 < H 1  π 1 π 2 > H 1  π 1 π 2 ≠ Field na me Defini tion ; 1 Sample 1 mean. X2 Sample 2 me an. n1 Sample 1 size . n2 Sample 2 size . α Signif ic ance le vel.
Infe rence ap let 9-13 Results The results are: One–Sample T–Test Menu name T–Test: 1 µ The One–sample T– Test is used when the popu lation standard deviatio n is not known. On the basis of statisti cs from a single sample, this te st measures the strength of the evidence for a sele ct ed hypothes is agains t t he null hypot hesis. Th e nu ll hypothesi s is that the samp le mean has some assum ed value , Η 0 :µ = µ 0 You select on e of the fo llowing alternat ive hypotheses against which to te st the null hy pothesis: ) Inputs The input s ar e: Result Description T est P1–P2 Differe n ce between the proportions of su ccesses in the two samples. T est Z Z–Test statistic. Prob Probabili ty associated with th e Z–Test statisti c. Critical Z Boundary va lu es of Z associated with the α lev el that yo u supplied . H 1 : µµ 0 < H 1 : µµ 0 > H 1 : µµ 0 ≠ Field na me Defini tion Sample mean. S x S amp le standard de viatio n. n Sam p l e s i z e. µ0 Hyp othetical population m ean. α S ignificance level. x
9-14 Inference aplet Results The re sult s are: Two–Sample T–T e st Menu name T–Test: µ 1 – µ 2 The Two–sam ple T–Test is use d when the po pulation standard de vi ation is not known. On the basis of statistics from two sa mples, each sam ple from a diffe rent popu la tion, this test measures t he strength of the evidenc e for a select ed hypoth esis against the null h ypothesis . The null hypothes is is that the two p op ulations means are equal ( H 0 : µ 1 = µ 2 ). You sel ect one of th e following altern ative hypo theses against which to t est the null h ypothesis Result Description T est T T–Test statistic. Prob Probability associated with t he T–Test statistic. Critical T Boundary valu e of T as sociated wit h the α level that you suppli ed. Critical Boun dary valu e of require d by the α value that yo u sup plied. x x H 1 : µ 1 µ 2 < H 1 : µ 1 µ 2 > H 1 : µ 1 µ 2 ≠
Infe rence ap let 9-15 Inputs The input s ar e: Results The results are: Fiel d name Defi ni tion Sample 1 me an. Sample 2 me an. S1 Sample 1 st an dard deviat ion. S2 Sample 2 st an dard deviat ion. n1 Sa mple 1 s ize. n2 Sa mple 2 s ize. α Si gnific ance le vel. _Poole d? Check thi s optio n to pool sa mples based on their standard deviations. x 1 x 2 Result Description Te s t T T–T est statistic. Prob Probability associated with the T– T est sta tistic . Criti cal T Boun dary values of T assoc iated with the α le vel that yo u supplied .
9-16 Inference aplet Confidenc e intervals The conf idence interval calculations t hat the HP 39G/40G can perfor m are based on t he Normal Z –distributi on or Student ’s t–distri bution. One–Sample Z–I nterval Menu name Z–INT: 1 µ This option uses the Normal Z–distribution to calculate a confidence interv al for µ , the true mean of a pop ulation, when the true popula tio n st and ard devia tio n, σ , is known. Inputs The inputs are: Results The re sult s are: Field n ame Definition Sample mean . σ Popu lation st andard devia tion. n Sample si ze. C C onfidenc e level. x Result Descrip ti on Critical Z Critical value f or Z. µ min Lower bo un d f or µ . µ max Upper bound for µ .
Infe rence ap let 9-17 Two– Sample Z –Int erval Menu name Z–INT: µ1 – µ2 This opt i on u ses the Normal Z–distri bution to calcul at e a confidence interval for the differenc e between the means o f two popu lations, µ 1 – µ 2 , when the p opulation stand ard devia tions, σ 1 and σ 2 , are known. Inputs The input s ar e: Results The results are: Fiel d name Defi ni tion Sample 1 me an. Sample 2 me an. n1 Sa mple 1 s ize. n2 Sa mple 2 s ize. σ 1 Popula tion 1 stan dar d devia t ion. σ 2 Popula tion 2 stan dar d devia t ion. C C onfidence level. x 1 x 2 Result Description Critical Z Critical va lue for Z. µ Mi n Lower bo und for µ 1 – µ 2 . µ Max Upper bound for µ 1 – µ 2 . ∆ ∆
9-18 Inference aplet One–Proportion Z–Interval Menu name Z–INT: 1 P This option uses the Normal Z–distribution to calculate a confidence i nterv al for the proportion of success es in a population for the case in whic h a sample of size, n , has a number o f successes, x . Inputs The inputs are: Results The re sult s are: Field n ame Definition x Sample succ ess count. n Sample si ze. C C onfidenc e level. Result Descrip ti on Critical Z Critical value f or Z. π Min Lower bo un d f or π . π Max Up per bound for π .
Infe rence ap let 9-19 Two–Proportion Z–In terval Menu name Z–INT: P1 – P2 This opt i on u ses the Normal Z–distri bution to calcul at e a confidence interval for the difference between the proportions of successes in two populations. Inputs The input s ar e: Results The results are: Fiel d name Defi ni tion Sample 1 succes s cou nt. Sample 2 succes s cou nt. n1 Sa mple 1 s ize. n2 Sa mple 2 s ize. C C onfidence level. x 1 x 2 Result Description Critical Z Criti cal value for Z. π Mi n Lower bound for t he di fferen ce between the proportio ns of successes. π Max Upper bou nd for the di f fe rence betwee n the proporti ons of successes. ∆ ∆
9-20 Inference aplet One–Sample T–I nterval Menu name T–INT: 1 µ This option uses the S tudent’s t–distrib ution to ca lculate a confidence interv al for µ , the true mean of a popu lation, for the ca se in wh ich the tru e p opulati on stan dard d eviatio n, σ , is unknown . Inputs The inputs are: Results The re sult s are: Field n ame Definition Sample mean . S x Sample sta ndard dev iation. n Sample si ze. C C onfidenc e level. x Result Descrip ti on Critical T Critical value f or T . µ Min Lo w er bo und for µ . µ Max Upper boun d for µ .
Infe rence ap let 9-21 Two– Sample T –Int erval Menu name T–INT: µ 1 – µ 2 This option uses the Studen t’s t–distributio n to calcu late a confidence interval for the differenc e between the means o f two popu lations, µ 1 − µ 2 , when the popu lation standard devia tions, σ 1 and σ 2 , are unk now n. Inputs The input s ar e: Results The results are: Fiel d name Defi ni tion 1 Sample 1 me an. 2 Sample 2 me an. s1 Sampl e 1 standard dev i ation. s2 Sampl e 2 standard dev i ation. n1 Sa mple 1 s ize. n2 Sa mple 2 s ize. C C onfidence level. _Poole d Wheth er or no t to pool t he samples based on their st an dard deviat ions. x x Result Descrip tion Critical T Criti cal value for T . µ Mi n Lower bo und for µ 1 – µ 2 . µ Max Upp er bo und for µ 1 – µ 2 . ∆ ∆

Using m athematical fun ctions 10-1 10 Using mathematical functions Math funct ions The HP 39 G/ 40G contain s man y math function s. The functi ons are groupe d in categor i es. For example, t he Matrix category c ontains func tions for mani pulating matric es. The Probability category (sho wn as Prob. on the MATH men u) contains f unctions for workin g with probab ility. To use a m ath functio n, you en ter the functio n onto the command li ne, and include the argume nts in parentheses aft er the function. You can also select a math func tion from the MATH men u. The MA TH menu The MAT H menu provide s access to m ath functions an d progra mming consta nt s. The MATH menu is or ganized by ca tegory . For each category of functions o n the left, there is a list of function names on the right . The highlig hted catego ry is the curr e nt category . • When yo u press >0$7 @ , you see the m enu list of Math functi on s. The menu ke y 0 7  _  indica tes that the MA TH FUNCTIONS menu list is active.
10-2 U sing mathemat ical functions To select a function 1. Press >0$7 @ to di splay the MA TH menu. The c atego ries appear in alp habetical order . Press *e, or *k, to scroll through the cat egories. T o skip directly to a categ ory , press the first letter of the cate gory ’ s name . Note: Y ou do not need to pr ess >$/3 $@ first . 2. The list of fu nctions (on the right) applies to the cu rrently highlig hted catego ry (on the le ft). Use *A, and *>, to switch betwee n the catego ry list and t he function list. 3. Highl ig ht the name of the fu nct ion you want an d pr e ss 2._ . This copi es the fu nction nam e (and an initial parenthesi s, if appropriate) to the ed it line. Function categories • Calcul us • Compl ex numbers •C o n s t a n t • Hyper bolic trig • Lists • Loop •M a t r i c e s • Polyn omial • Probabili ty • Real– numbers • Sta t–T wo (T wo –variable sta tistic s) • Symb olic •T e s t s • Trigonometry
Using m athematical fun ctions 10-3 Math functions by category Following a re definition s for all c ategories of fun ctions excep t List, Matrix, and Statistics, each of which appears in its own chapte r. Except f or the keyboard ope rations, whi ch do not appear in the MATH me nu, all othe r functions are listed by their category in the MATH menu. Syntax Each functi on’s definition includes its syntax, that is, the exact orde r and spelling of a function ’s name, its delim iters (punct uati on), and its argumen ts. Note that the syntax for a functi on does not requir e spaces. Functions common to keyboard and menus These functi ons are common to the ke yboard and me nus. >6 ,)7@ π For a description, see “p” on page 10-9. >6 ,)7@ ARG For a descr iption, see “ARG ” on page 10-8. >GG[@ F or a descripti on , see “D” on page 10-7. >6 ,)7@ AND For a description, see “AND” on page 10-21 . >6 ,)7@ ! For a des c r i ption, see “!” on page 10-13 . >6 ,)7@ ∑ For a d escrip tion, see “S” on page 10-11. >6 ,)7@ EEX For a desc ript ion, see “S cien tifi c notati on (powers of 10)” o n page 1-19. >6 ,)7@ ) For a d escr iptio n, se e “S” on page 10-7. >6 ,)7@ The multi plicative inve rse function finds the inverse of a squa re matrix, and the m ultiplicative in verse of a real or co mplex numbe r. Also works on a li s t containing only these object types. x 1 –
10-4 U sing mathemat ical functions Keyboard functions The most frequently used fu nctions are available direct ly from the keyboard . Many of the keyboard functions also accep t complex n umbers as a r guments. >@ , >@, >[@, >@ Add, Subtrac t, Mu ltiply, Divide. Also accepts complex numbers, lists an d matrices. value1 va lue2 , etc. >6 ,)7@ e x Natural exponen tial. Also accepts comp lex numbers. e^ value Example e^5 returns 148.413159103 >OQ@ Natural logarit hm. Al so accepts complex nu mbers. LN ( value) Example LN(1) returns 0 >6 ,)7@ 10 x Exponential (antilogarithm). Also accepts complex numbers. 10^ value Example 10^3 returns 1000 >ORJ@ Common lo garithm. Also accepts comp lex numbers. LOG ( value) Example LOG(100) returns 2 >6,1@ , >&26@, >7$1@ Sine, co sine, ta ngent. I nputs a nd output s depen d on the current angl e format (Degrees, Radians, or Grads). SIN ( value) COS ( value) TAN ( value) Example TAN(45) returns 1 (Degrees mode).
Using m athematical fun ctions 10-5 >6 ,)7@ ASIN Arc sine: sin –1 x. Output rang e is from –90° to 90 ° , – π /2 to π /2, or – 100 to 100 gr ads. Inputs and outpu t s depend on the current angl e form at. Also accepts compl ex n umbers. ASIN ( value) Example ASIN(1) returns 90 (Degrees mode). >6 ,)7@ ACOS Arc cosin e: cos –1 x . Ou tput ran ge is fro m 0° to 18 0°, 0 to π , or 0 to 200 gra d s . Inputs an d outputs dep end on the curre nt angle format. Al so accepts complex numbers. Output will be comple x for valu es ou tside the nor m a l COS domain o f . ACOS ( value) Example ACOS(1) ret urns 0 (Degrees mo de). >6 ,)7@ ATAN Arc tangent: tan –1 x . Output range is from –90° to 90°, 2 π /2 to π /2, or – 100 to 100 gr ads. Inputs and outpu t s depend on the current angl e form at. Also accepts compl ex n umbers. ATAN ( value) Example ATAN(1) ret urns 45 (Degrees mo de). >[  @ Square. Also accepts co mpl ex numbers. value 2 Example 18 2 returns 324 >6 ,)7@ √ Square root. Also ac cep ts complex numbers. √ value Example returns 18 >@ Negation. Also accept s complex numbers. – value Example -(1,2) returns (-1,-2) 1 – x 1 ≤≤ 324
10-6 U sing mathemat ical functions * ;N, Power ( x raised to y ). Also ac cep ts complex numbers. value ^ po wer Example 2^8 returns 256 >6 ,)7@ ABS Absolute value. For a com plex number, this is . ABS ( value) ABS (( x , y )) Example ABS( –1) returns 1 ABS((1,2)) returns 2.236067 9775 >6 ,)7@ Takes the n th ro ot of x . ro o t NTHROOT value Example 3 NTHROOT 8 returns 2 x 2 y 2 n
Using m athematical fun ctions 10-7 Calculu s functions The symbols fo r differentiati on and integratio n are availabl e directly form the keybo ard— >GG[@ and ) respectively —as well as from the MATH menu . % Differentiates expressio n with respect to the variable of differentia tion. From the command line, use a fo rmal name (S1, etc .) for a non-num eric result. See “Finding derivati ves” on pa ge 10-23. % vari able ( expr ession ) Example % s1(s1 2 3*s1) returns 2*s1 3 ) Integrates expression fro m lowe r to uppe r lim its with respect to the var iable of integra tion. To find the definite in tegral, both limits must have nume ric values (that is, be numbers o r real varia b les). To find the indefinite integra l, one of the limits must be a formal variable (s1, etc.). ) ( low er ,up per ,exp r ession, variable ) See “Using formal variables” on page 10-22 for further details. Example ) (0,s1,2*X 3,X) >(17(5@ *k, &2 3<_ >(17(5@ finds the indefinite result 3*s1 2*(s1^2/2) See “T o find th e indefini t e integra l using form al variables” on page 10-25 for more information on finding ind efinite integ rals. TAYLOR Calculates the n th order Tay lor poly no mial of expressio n at the po int where th e given variab le = 0. TAYLOR ( expression,variab le,n) Example TAYLOR(1 sin(s1) 2 ,s1,5) with Radians ang le measure and Fraction number format (set in MODES) returns 1 s1^2-1/3*s1^4.
10-8 U sing mathemat ical functions Complex number function s These func tions are for complex numb ers only. You ca n also use complex nu mbers with all trigono metric and hyperbol i c functi ons, and with som e real-numbe r and keyboa rd function s. Enter comp lex numbers in the form ( x,y ), where x is the real part an d y is the imag ina ry part. ARG Argumen t. Finds the ang le defined by a comp lex number. Inputs and ou tputs use the curre nt angle format set in Mo de s. ARG (( x,y)) Example ARG((3,3)) returns 45 (Degrees mode) CONJ Complex co njugate. C onjugatio n is the negat i on (sign reversal) of the imag in ary part of a com plex number. CONJ (( x,y)) Example CONJ((3,4)) returns (3,-4) IM Imaginary part, y, of a compl e x number, ( x,y ). IM (( x,y)) Example IM((3,4)) returns 4 RE Real part x, of a com pl ex number, ( x,y ). RE (( x,y)) Example RE((3,4)) returns 3
Using m athematical fun ctions 10-9 Constants The HP 39G/40G has an inte rnal numeric representa t ion for these con s t ants. e Natural logarith m base. Inter nally repres ent ed as 2.71 82 81828 46 . e i Imagin ary value for √−1 , the co mplex number (0,1). i MAXRE AL Maximum real numb er. Internally represent ed as 9.99 9999999 99 x 10 499 . MAXREAL MINREAL Minimu m real number. I nt ernally repre sented as . MINREAL π Intern ally repre sented as 3.141592 65359. π Hyperbol ic trigonometry The hyperb olic trigono metry functions can also take complex numbers as argume nts. ACOSH Inverse hyperbolic c osin e : cosh –1 x . ACOSH ( value) ASINH Inverse hy pe rb olic sine : sinh –1 x . ASINH ( value) ATANH Inver se hyper bolic ta ngent : ta nh –1 x . ATANH ( value) COSH Hyperbol ic cosine COSH ( value) SINH Hyperbolic sine. SINH ( value) TANH Hyperbo lic tangent. TANH ( value) 11 0 499 – ×
10-10 Using ma thematical functi ons ALOG Antilogarithm (exponential ). This is more a ccurate than 10^x due to limitation s of the power functi on . ALOG ( value) EXP Natural exponentia l. This is more accu rate than due to limitati ons of the po wer function. EXP ( value) EXPM1 Expone nt minus 1 : e x –1. This is m ore accurate than EXP when x is close to zer o. EXPM1 ( value) LNP1 Natural log p lus 1 : ln( x 1). This is more accurate than the natural l ogarithm fun ction when x is clos e to zero. LNP1 ( value) List functions These fun ctions work o n list data. S ee “List func tions” on page 13-7. e x
Using m athematical functions 10-11 Loop functions The loop functions di sp lay a result af ter evaluati ng an expressi on a g iven number of times. ITERATE Rep eatedly for #times evaluate s an expres sion in terms of variabl e . The value for variabl e is updated each time, starting with initia lvalue. ITERATE( expre ss ion , va riabl e , initialv alue , #times ) Example ITERATE(X 2 ,X,2,3) returns 256 RECURSE P r ov ides a method of defi ni n g a sequence without usi ng the Symbolic v iew of the Sequence aplet. If used with | (“where”), RECURSE will ste p through the evaluation. RECURSE( sequencename , term-n, term1, term2) Example RECURSE(U,U(N-1)*N,1,2) 67 2?_ U1(N) Stores a factorial–cal culating function nam ed U1. When yo u enter U1(5) , for exa mple, the function calcul at es 5! ( 120 ). Σ Summation. Finds the sum of expression with respect to variabl e from initialvalue to finalvalu e. Σ ( variable= initialvalue, finalv alue , expression ) Example Σ (C=1,5,C 2 ) returns 55. Matrix functions These functio ns are for matrix data stored in matrix va riables. See “Mat ri x fu nc tio ns an d co m mands” on pa ge 12-9.
10-12 Using ma thematical functi ons Polynomial fu nct ions Polynomi als are products of constants ( c oefficients ) and variables raised to powers ( terms ). POLYCOE F Polynomial co effi cients. Returns the coeffici ent s of t he polyno mial with th e spe cified roots . POLYCOEF ([ ro ot s ]) Example T o f ind the polynom ial with roots 2, –3, 4, –5: POLYCOEF([2,-3,4,-5]) retur ns[1,2,-25, -26,120] , repr esenti ng x 4 2 x 3 –25 x 2 –26 x 120 . POLYEVA L Polynom ial evalu ation . Eva lu a te s a poly no mi al with the specified coefficients for the value of x . POLYEVAL([ coefficie nts ], value ) Example For x 4 2 x 3 –25 x 2 –26 x 120: POLYEVAL([1,2,-25,-26,120],8) retu rns 3432 . POLYFORM Polynomial form. Creates a polynom ial in variab le1 from expression. POLYFORM ( expression,varia ble1 ) Example POLYFORM((X 1)^2 1,X) returns X^2 2*X 2 . POLYROOT Polynomial ro ots. Returns the roots for the n th-order polyno mial with th e spe cified n 1 coefficients . POLYROOT ([ coefficie nts ]) Example For x 4 2 x 3 –25 x 2 –26 x 120: POLYROOT([1,2,-25,-26,120]) retu rns [2,-3,4,-5] .
Using m athematical functions 10-13 HINT The results of P OLYROOT will often not be easily seen in HOME due to the number of de cimal places, especial ly if they are complex n umbers. It is better to sto re the results of POLYROOT to a matrix. For example, POL YROOT([1,0,0,-8] 67 2?_ M1 will store the three com plex cu be ro ot s of 8 to m atrix M1 a s a co mp lex vector. T hen you can see them easi ly by going to the Ma trix Catalog. an d access them individually in calculation s by referring to M1(1), M 1(2) etc. Pro bability f unctions COMB Number of comb inations (without rega rd to order) of n things taken r at a t ime: n !/ (r !(n −r )). COMB ( n , r ) Example COMB(5,2) returns 10 . Tha t is, there are ten d if ferent ways that five t hings can be comb in ed two at a time. ! Factorial of a positive i nteger. Fo r non- integers, ! = Γ ( x 1). This calc ulates the gamma func tion. valu e ! PERM Number of permutations (with regard to order) of n thing s taken r at a tim e: n !/ (n -r )!. PERM ( n , r ) Example PERM(5,2) returns 20 . That is, there are 2 0 different permut ations of five thin gs take n two at a time. RANDOM Random nu mber (between ze ro and 1). Produc ed by a pseudo- random num b er sequen ce. The al go r ith m us e d in the RANDOM function uses a “see d” number to begin its sequence . To ensure that two cal culators must pro duce different results for the RANDOM function, u se the RANDSEED function to seed different starting values before using RANDOM to pro duc e the numbers. RANDOM
10-14 Using ma thematical functi ons HINT The setting of Time will b e different for ea ch calculator, so using RANDSEED(Time) is guarante ed to pro duce a set of numbers whi ch are as clos e to random as possi ble. You can set the seed using the comma nd RANDSEED. UTPC Upper-Tail Chi- Squared Prob a bil ity giv en degr e es of freedom, eva l uated at value . Returns the p rob abil ity that a χ 2 random variabl e is gr eater than value. UTPC ( degrees, val ue ) UTPF Upper-Tail Snedecor’s F Proba bility given numera tor degre es of freed om an d denominator degrees of freedom (of the F distr ibution), evalua ted at value . Returns the probability that a Snedeco r's F rando m vari a ble is greater than value. UTPF ( numerato r , denominat or , value) UTPN Upper-Tail Norm al Pr ob abili ty giv e n mean and varian ce , evaluated at val ue. Returns the pr obability tha t a normal random variabl e is gr eater than value for a normal distri bution. Note: The variance is the square of the standard deviat ion . UTPN ( mean, varia nce, val ue ) UTPT Upper-Tail Student’s t-Prob ability give n deg rees of free dom, evaluated at value. Returns the p robability that the Student's t - random variabl e is gr eater than value. UTPT ( degrees, val ue )
Using m athematical functions 10-15 Real-number fu nct ions Some real-number functions can a l so take complex arguments. CEILING Smallest inte ger greater tha n or equal to value . CEILING ( value) Exam ples CEILING(3.2) returns 4 CEILING(-3.2) returns -3 DEG → RAD D e gre e s to ra dia n s. Conv er ts value from Degrees angle format to Radian s angle format. DEG → RAD ( value) Example DEG →RAD( 180) returns 3.14159265359 , the value of π . FLOOR Greatest inte ger less than or equ al to value . FLOOR ( value) Example FLOOR(-3.2) ret urns -4 FNROOT Function root-finder (like the Solve aple t). Finds the valu e for the give n vari abl e at which expres sion most nearly e valuates to zero. Uses gu ess as in itial estimate. FNROOT ( expression, variabl e, guess) Example FNROOT(M*9.8/600-1,M,1) returns 61.2244897959 . FRAC Fractio nal part. FRAC ( value) Example FRAC (23.2) returns .2
10-16 Using ma thematical functi ons HMS → Hou r s-minutes-sec onds to decimal. Conv erts a number or expre ssion in H.MMSSs format (time or angle that can include fractions of a second ) to x. x forma t (n um b er of hours or degrees with a d ecimal fraction). HMS → ( H.MMSSs) Example HMS → (8.30) returns 8.5 → HMS Decima l to hou rs-minute s-seconds. Co nverts a number or expre ssion in x.x format (numb e r of hours or degree s with a decimal fractio n) to H.MMSSs format (ti me or an gle up to fractions of a second ). → HMS ( x.x) Example → HMS(8.5) returns 8.3 INT Integer part. INT ( value) Example INT(23.2) returns 23 MANT Ma ntissa (sign ificant dig its) of value . MANT ( value) Example MANT(21.2E34) returns 2.12 MAX Maximum . The gr ea t er of two values. MAX ( value1 , value2 ) Example MAX(210,25) returns 210 MIN Mini mum. The lesser of two values . MIN ( value1 , value2 ) Example MIN(210,25) returns 25
Using m athematical functions 10-17 MOD Modulo. The remainder of value1 / value2. valu e1 MOD val ue2 Example 9 MOD 4 returns 1 % x percent of y ; th at is, x / 100*y . % ( x, y) Example % (20,50) returns 10 %CHANGE Percent change from x to y , that is, 100( y–x )/ x . % CHANGE( x ,y) Example % CHANGE(20,50) returns 150 %TOTAL Percent total : (100) y/x . What per centage of x is y . % TOTAL( x ,y) Example % TOTAL(20,50) returns 250 RAD →DEG Radia ns to deg rees. C onverts value from radi ans to degrees . RAD → DEG ( valu e ) Example RAD →DEG( π) returns 180 ROUND Round s value to decimal places . Accep ts complex numbers. ROUND ( value , places) Round can also round to a n umber of signif icant digit s as show ed in e xamp le 2. Exam ples ROUND(7.8676,2) returns 7.68 ROUND (0.0036757,-3) returns 0.00368
10-18 Using ma thematical functi ons SIGN Sign of value . If positiv e, the result is 1 . If negative, – 1. If zero, re sult is zero. Fo r a complex numb er, this is the u nit vector i n the directi o n of the number . SIGN ( value) SIGN (( x,y)) Examples SIGN (–2) returns –1 SIGN((3,4)) returns (.6,.8) TRUNCATE Truncates value to de cimal places . Accepts c omplex number s. TRUNCATE ( valu e , places ) Example TRUNCATE(2.3678,2) returns 2.3 6 XPON Expone nt of value . XPON ( value) Example XPON(123.4) returns 2 Statist ics-Two These are func tio ns for use with two-variabl e st atistics. See “Two - var ia b l e” on pag e 8-14.
Using m athematical functions 10-19 Symbolic functions The symbo lic fu nc ti on s are used for sy m bo lic manipul at i on s of expre ssions. The var iables can b e formal or nume ric, but the result is usually in symbolic form (not a number). You will find th e symbols for th e symbol ic functions = and | ( where ) in the CHARS menu ( >6 ,)7@ CHARS ) as well as the MATH menu. = ( equals ) Sets an eq uality fo r an e quatio n. Th is is not a logical op erator and does no t store va lues. (See “Te st functions” o n page 10 - 20.) expression1 = expression2 ISOLATE Isol ates the first occurrenc e of var iable in expression= 0 an d returns a new expression , where variable= newexpression. The result is a general solution that repre sents mul tiple solutions by including the (formal) va riables s1 to repr esent any sign and n1 to represent any integer. ISOLATE( expre ssion , va riabl e ) Exam ples ISOLATE(2*X 8,X) returns -4 ISOLATE(A B*X/C,X) returns -(A*C/B) LINEAR? Tests whether express ion is linear for the specified varia ble . Returns 0 (fa lse) o r 1 (true). LINEAR?( expre ssion , var iable ) Example LINEAR?((X^2-1)/(X 1),X) returns 0 QUAD Solves quadratic ex pression= 0 for variable a nd returns a new expressi on, where variable=newexpr ession. The res u l t is a general solution tha t represents b oth positive a nd negativ e solutions by including th e formal variab le S1 to represent any sign: or – . QUAD( expression , variab le ) Example QUAD((X -1) 2 -7,X) returns (2 s1*5.29150262213)/2
10-20 Using ma thematical functi ons QUOTE Encloses an expre ssion that shoul d no t be evaluated numerica lly. QUOTE( expression ) Examples QUOTE(SIN(45)) 6 72?_ F1(X) stores t he expression SIN(45 ) rather tha n the valu e of SIN(45). Another me th od is to enclose the exp r essi on in single quotes. For example, X^3 2*X 672 ?_ F1(X) puts the expressi on X^3_2*X into F1(X) in the Fu nction aple t. | ( where ) Ev aluates expression where ea c h gi v en vari a bl e is set t o t he given va lue . De f in e s nu meric ev aluatio n of a sym bolic expr e s s ion . expression | ( variable 1=value1, varia ble2=value 2,... ) Example 3*(X 1)|(X=3) returns 12 . Test functions The test fu nctions a re logical operators that always return either a 1 ( true ) or a 0 ( false ). < Less than. Returns 1 if true, 0 if fa lse. value1 < valu e2 ≤ Less than or e qual to. Re turns 1 if true, 0 if false. value1 ≤ valu e2 = = Equals (log ical test). Returns 1 if true, 0 if fal se. value1 == value2 ≠ Not equal to. R eturns 1 if true , 0 if false. value1 ≠ valu e2 > Greater than. Return s 1 if true, 0 if false. value1 > value2 ≥ Greater than or e qual to. Return s 1 if true, 0 if false. value1 ≥ valu e2
Using m athematical functions 10-21 AND Comp ares value1 an d value2 . Returns 1 if they are both non- zero, otherwise returns 0. valu e1 AND value2 IFTE If expression is true, do the trueclause ; if not, do th e falseclause. IFTE( expression , truecla use , falseclause ) Example IFTE(X>0,X 2 ,X 3 ) NOT Returns 1 if value is zero, otherwise returns 0. NOT value OR Returns 1 if eit her value1 or value2 is non-zero, otherw ise returns 0. valu e1 OR va lue2 XOR Excl usive OR. Returns 1 if either val ue1 or va lue2 —but not both o f them—is non-zer o, other wise return s 0. valu e1 XOR val ue2 Trigonom etry functions The trigonom etry functions can also ta ke complex numbers as arguments. For SIN, COS, TAN, ASIN, ACOS, and ATAN, see the Keyboa rd category. ACOT Arc cotang ent. ACOT ( value ) ACSC Arc coseca nt. ACSC ( value) ASEC Arc secant. ASEC ( value) COT Cotangent: cos x /sinx . COT ( value) CSC Cosecant : 1/sin x CSC ( value) SEC Secant: 1/c os x . SEC ( value)
10-22 Using ma thematical functi ons Symbolic calculations The HP 39 G/40G has the ab ility to perform symbolic calculat i ons, for example, symb olic integration an d differentiation. You can perform symbolic calculations in HOME and in the Functio n aplet. In HOME When you perform calculat ions that contain n ormal variables, the calcu lator substitute s values for an y variables. Fo r example , if you ent er A B on the command line an d press  >(17(5@ , the calculator retriev es the values for A a nd B from memory and substitutes them i n the calculation. Using formal variabl es To perform symbolic calculations, for example symbolic diffe re nti ati ons and integra tio ns , you nee d to use for mal names. Th e HP 39G/40G has six for mal names available f or use in symbol i c calculations . Thes e are S0 to S5. When you perform a calcul at ion that contains a formal na me, the HP 39G/40G does not carry out any substitu tions. You can mix fo r mal names and real va riables. Ev aluating (A B S1) 2 will evaluate A B , but no t S1 . If you ne e d t o ev al uate an exp ressio n tha t co nt ains fo rm al names nume rically, yo u use the | ( where ) command, listed in the Math menu under the Symboli c category. For example t o ev aluate (S1*S2) 2 whe n S1=2 and S2=4 , you would en t er the cal culation as follows: (The | symbol is in the CHARS menu: press >6 ,)7@ CHARS . The = sig n is listed in the MATH menu under Symbo lic funct ions.) Symbolic calculations in the Function aplet You can p erform sy mbol ic op e ration s in th e Fu nc ti on a pl et’s Symbolic v iew. For ex ample, to find the deriva tive of a function in the Func tion aplet’s Sy mbolic view, y ou define two fu nctions and defi ne the second function as a de rivative of the first func tio n. You then evalua te the seco nd function. See “To find deri vat ives in the Functio n aplet’s Symbolic view” on page 10-24 for an example.
Using m athematical functions 10-23 Finding derivatives The HP 39 G/ 40G can perf orm symbolic differenti at ion on some func tions. The re are two w ays of using the HP 39G/4 0G to find der ivatives. • Y ou can p erform differen tiations i n HOME by usin g t he formal variables, S1 to S5. • Y ou can p erform different iations of funct ions of X in the Function ap le t. To find deriva tives in HOME To find the de rivativ e of the func tion in HOME, use a fo rmal variable in place of X. I f you use X, the different iation function su bstitutes the va lue that X holds, and returns a numeric result. For example , co nsi der the function: 1. Enter the dif fere ntiat ion fu nction o nto th e com mand l ine, substituting S1 in place of X. >GG[@>$/3 $@ S1 >@>6,1@>$/3 $@ S1  >[  @ >@>@ 2 >[@ >&26@>$/3 $@ S1 >@ >@ 2. Evaluate the fun ction. >(17(5@ 3. Show the re sult. *k, 6 2: _  dx x ( 2 ) sin ( 2 x () ) cos HP 39G HP 40G
10-24 Using ma thematical functi ons To find derivativ es in the Function aplet’s Symbolic view To find the derivat ive of the fu nction in the Functio n aplet’s Symbol ic view, you defi ne two fun ct ions and def i ne the second func tion as a derivative of the first funct i on. For example, to differentiate : 1. Access the Function aplet’ s Symbol ic view and de fine F1. >6<0%@>6,1@ ;_ >[  @>@ >@ 2 >;@ >&26@ ;_ >@ 2._ 2. Define F2(X) as the deriva tiv e of F(1 ). >GG[@ ;_ >@>$/3 $@ F1 >@ ;_  >@>@ 2._ 3. Select F2(X) and evaluate it. *k, (9$ /_ 4. Press 6 2: _ to display th e result. (Use the a rrow keys to view the entire functi on.) 6 2:_ Y o u could also ju st define . x 2 () sin 2 x cos HP 39G HP 40G F 1 x () xx 2 () 2 x () cos sin () d =
Using m athematical functions 10-25 To find the indefinite integral using formal varia bles For example , to find the indefinite i ntegral of use: 1. Enter the funct ion. >6 ,)7@>GG[@ 0 >@ >$/3 $@ S1 >@ 3 >[@ >$/3 $@ X >[ @>@ 5 > @ >$/3 $@ X >@ >(17(5@ HINT If the Decimal Mark setting in the Modes in put form ( >6 ,)7@ MODES )is set to Comma, use >@ inst ead of >@. 2. Show the result format. *k, 6 2 :_ 3. Press 2._ to close th e show window. 4. Copy the result a nd evalua te. &23 <_ >(17(5@ Thus, subst ituting X for S1, it can be see n that: This result de rives from substi tuting X = S1 and X = 0 into the origin al expre ssion fo und in step 1. H owever , substi tuting X = 0 will n ot always evaluate to zero and may re sult in an unwante d consta nt. To see this, consider: 3 x 2 5 – x d ∫ 0 S 13 X 2 , 5 X , – , () ∫ HP 39G HP 40G 3 x 2 5 – x 5 x –3 x 3 3 ---- - X ∂ ∂ X () ------- --------      = d ∫ x 2 – () 4 x x ( 2 ) 5 – 5 ------ ------ ------ - = d ∫
10-26 Using ma thematical functi ons The ‘ex tra’ consta nt of 6.4 results from the substitutio n of into ( x –2 ) 5 /5, and sho uld be disrega rded if an indefinite integral is required. x 0 =
Variab les and me mory manage ment 11-1 11 V ariable s and m emory m anagem ent Introduct ion The HP 39G/40G h as approx imately 232 K of user memory. The calculator uses this memory to store varia bles, perform comput at ion, and store hi story. A variable is an object tha t you create in memory to h old data. The HP 39G/40G ha s two ty pes of variables, ho me var i ables and aplet variab les. • Home v ariables are availa ble in al l aplets. For exam ple, you ca n sto re rea l numb ers i n vari ables A to Z and complex nu mbers in variables Z0 to Z9 . Th ese can be numbers yo u have enter ed , or the result s of calculations . These variables are availab le within all aplets a nd within any pr ograms. • Aplet variables a pply onl y to a si ngle aplet. Aplets have specific vari ables allocated to them which va ry from aplet to ap let. You use the calculator’s me mory to store the following objects: • copies of aplets with specific configura tion s • new aplet s that you dow nlo a d • aplet var i ables •h o m e v a r i a b l e s • variable s created through a catalog or edit or , for example a mat rix or a te xt note • progra ms t hat yo u create. You can use the Memory Manager ( >6 ,)7@ MEMORY ) to v iew the amoun t of m emory avail able. The ca talo g views , whic h are accessib le via the Memory Ma nag er, can be used to transfer variab les such as lists or matri ces be tween calculat ors.
11-2 Variabl es and memo ry manageme nt Storing and reca lling variables You can store num bers or e xpressions fr om a prev ious inpu t or result into variables. Numeric Precision A number store d i n a va riable is always stored as a 1 2-digit mantis sa with a 3-dig it ex ponent. Nu mer ic precision i n the displa y, however, de pends on the disp l ay mode (Stand ard, Fixed, Scientif i c, Engineer i ng, or Fracti on). A displ aye d numb er has only th e prec ision th at is d isplaye d. If yo u copy it from the HO ME view display hi st ory, you ob tain only th e precision displayed, not the full inte rnal precision . On the other hand, the varia ble Ans always contains the most recent resu lt to ful l precis ion. To store a value 1 . On th e com mand l ine, enter the valu e or the calculation for the result you wish to sto re. 2. Press 6 72a ?a  3. Enter a name for the varia ble. 4. Press >(17(5@ .
Variab les and me mory manage ment 11-3 To store the results of a calc ulati on If the value you want to store is in the HOME view di splay histo ry, for example t he results of a pr evious calcu lation, you need to copy it to th e command line, then store it. 1. Perform the calculati on for the result yo u want to store. 3 >;@>@8 >[@6 >@>[ 8 @ 3 >(17(5@ 2. Move the highlig ht to the result you wish to stor e. 3. Press &2 3<a  to copy th e result to the comma nd line. 4. Press 67 2?a . 5. Enter a nam e for th e varia ble. *k, & 23< a  67 2?a >$/3 $@ A 6. Press >(17(5@ to store the result. The results of a cal culation can also b e st ored directly to a variable. Fo r exa mple: 2 >[ 8 @>  @ 5 > j@ 3 >@ 672 ?a >$/3 $@ B >(17(5@ To reca ll a value To recall a variable’s v alue, type the name of th e variable an d press >(17(5@ . >$/3 $@ A >(17(5@
11-4 Variabl es and memo ry manageme nt To use variables in calculations You can use vari ab les in calculati ons. The calculat o r substitutes the variable ’s value in the calculation: 65 >@>$/ 3 $@ A > ( 17(5@ The VARS menu You use the VARS menu to acc ess all variables in the calculator. Th e VARS menu is organised by cat eg ory. For each variabl e category in the left column , th ere i s a list of variables in th e right column. You select a varia ble category and then select a variable in the category . 1. Open the V ARS menu. >9$56@ 2. Use the ar row key s or press the alph a key of the first letter in the categ ory to select a variable cat eg ory . For example, t o sel ec t the Matrix categ ory , press >@ . Note: In th is instance, there is no need to pr ess the ALPHA key. 3. Move the highligh t to the variab les column. *A, 4. Use the arrow keys to selec t the variable th at you want. For examp le, to select the M2 variable, p ress *e, . *e,
Variab les and me mory manage ment 11-5 5. Choose wheth er to place the variabl e nam e or the variable value on th e command line. – Press 9$ /8( a to indica t e th at you want the variable’s content s t o appear on the command li ne. – Press 1$0 (a to indic ate that yo u want the v ariable’ s name t o appear on the com mand line. 6. Press 2.a to place th e va lue or name on the co mmand line. The sele cted object appea r s on t he command line. 2.a Note: The V ARS men u ca n als o be use d to en te r the name s or va lues of v ariab les into p r ograms . Example This example de monstrates how t o use the VARS menu to add the contents o f two list variab les, and to store the result in another list variable. 1. Display t he List catalog. >6 ,)7@ LIST to select L1 (', 7a 2. Enter the data fo r L1. 88 2. a 90 2.a 89 2. a 65 2. a 70 2.a 3. Return to the List Cat alog to create L 2. >6 ,)7@ LIST *e, to select L2 (', 7a
11-6 Variabl es and memo ry manageme nt 4. Enter data for L2. 55 2. a 48 2.a 86 2. a 90 2 .a 77 2. a 5. Press > 20(@ to acce ss HOME . 6. Open the v a ri able menu and sele ct L1 . >9$56@ *e,*e,*e,*A, 7. Copy it to the c ommand l ine. Note: Because the 1$0 (a option is highlighte d, th e varia ble’ s name, rath er th an its contents, is c opied to th e command line . 2.a 8. Insert the oper ator a nd se lect th e L2 vari able fr om the List vari able s. >@>9$56@ *e,*e,*e,*A,*e, 2.a 9. Store the answer in the List cat alog L3 variable. 67 2? a >$/3 $@ L3 >(17(5@ Note: Y ou can also typ e list names dir ectly fr om the ke yboar d.
Variab les and me mory manage ment 11-7 Hom e variables It is not possible to st or e data of on e t ype in a variab le of anoth er type. For exa mple, you us e the Matri x catalog to create matr i ces. You can create up to ten matrices, and you can store the se in variables M0 to M9 . You cannot store matrices i n variables other than M0 to M9. Category A vai lable names Complex Z0 to Z9 For example, (1, 2) 6 72? a Z0 or 2 3 i 67 2? a  Z1. Y ou can enter a compl ex number by typin g ( r , i ), whe re r represents the real part, and i repr esen ts the imaginary part. Graphic G0 to G9 See “Gra phic comman ds” on page 15- 20 for more i nformatio n on s toring gr aphic obje cts via p rogra mming co mmands . See “T o stor e into a grap hics va ri a bl e” on pa g e 14-5 for more i nformatio n on s toring gr aphic obje ct via the sketch view. Library Aplet lib rary variables can store aplets that you have cr eated, eit her by saving a cop y o f a standard apl et, or downloading an aplet from anot he r source. Lis t L0 to L9 For example , {1,2,3} 6 72? a L1. Matrix M0 to M9 can store matrices or v ectors. For example, [[1,2],[3 ,4]] 6 72? a M0. Modes Modes variables store the modes settin gs that you can config ure usi ng >6 ,)7@ MODES . Notepad Notepad v ariables store note s. Program Program variab les store programs. Real A to Z and θ. For exam ple, 7.45 672 ?a A.
11-8 Variabl es and memo ry manageme nt Aplet variable s Aplet variables store values that are unique to a particu lar aplet. These incl ude symbolic expres sions and equations (see below), set tings for the Plot and Num eric views, an d the results of some calculation s such as roots and intersections. See the Reference Information chapter for more information about aplet vari abl e s. To access an aplet variable 1. Open th e aplet that c ontains the variable you want to recall. 2. Press >9$56@ to display the V A RS m enu. 3. Use the arrow keys to selec t a variable category in the left column, then press *A, to access the variab les in the right column. 4. Use the arr ow keys to select a v ariable in the right column. 5. T o copy the name of the va riable on to th e edit line, pre ss 2. a . ( 1 $ 0( a is the defau lt setting.) 6. T o copy the value of th e variable into the edit line, press  9$/ 8(a and pres s 2. a . Categor y A va ilable nam es Func tion F0 to F9 (Symbolic v iew). See “F unction aplet var i ables” on page R-9. Parametric X0, Y0 to X9, Y9 (Symbolic vie w). See “Parametric ap let variables” on pag e R-10. Polar R0 to R9 (Symboli c vie w ). Se e “Pol ar aplet var i ables” on page R-11. Sequenc e U0 to U9 (Symb olic view). See “S equence aplet var i ables” on page R-12. Solve E 0 t o E9 (Symboli c vi ew). See “Solve aplet var i ables” on page R-13. Statistics C0 to C9 (Num e ric view). Se e “Statistics aplet var i ables” on page R-14.
Variab les and me mory manage ment 11-9 Memory Manager You can use t he Memory Manag er to determine t he amount of availabl e memory on the calcu lator. You can also us e Memory Ma nager to organize memo ry. For example, if t he avail abl e memory is low, you can use the Memory Man ager to determ ine which aplets or va riables consume la rge amounts of memo ry . You ca n make deletio ns to free up memory. Example 1. Start th e Memory Manage r . A list of var iable categories is disp l ayed. >6 ,)7@ MEMORY Free me mory is displayed in the top right corn er an d the bo dy of the screen list s eac h category , the memory it uses, and the percentag e of the tota l memo r y it use s. 2. Select the category with which you wan t to work and press 9, (:a . Memo ry Mana ger di splays memory d etail s of variab les within the category . *e,*e,*e,  9, (:a 3. T o delete variabl es in a category: – Press >'(/@ to delete the selected variab le . –P r e s s >6 , )7@ CLEAR to delete all vari ables in the selected category .

Matri ces 12-1 12 Matrices Introduct ion You can pe rform matrix ca lculations in HOME and in programs. The matrix and each row of a mat r ix appear in bracket s, and the elements a nd rows are separated b y commas. For exampl e, the foll owing matrix: is disp l ayed in the hi st ory as: [[1,2,3],[4,5,6 ]] (If the Decimal Mark in MODES is set to Comma, then th e row separators are periods.) You can en ter matrices directly in the command line, or crea te them in the matrix editor. Vectors Vectors are one-d im ensional arrays. They are co mposed of just one row. A vector is re presented with single brackets; for example, [1,2,3]. A v ector can be a real numb er vector or a complex nu mber vector, for exampl e [(1,2), (7,3)]. Matr ices Matrices are t w o-d imensional ar ra ys. They are compos ed of more than one row and more than one column. T wo- dimens ional ma trices are r e pr esented wi th nested brac ket s; 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 te n matrix variables av ailable, na med M0 to M9. You can use the m in calculations in HOME or in a pr og ram. You can r etrieve the matri x names from the VARS menu, or just type their names from the keyboa rd. 123 456
12-2 Matri ces Creating and storin g matrices You can create, edit, delete, send, and rec eive matrices in the Matrix cat alog. To open the Mat r ix catalog, press > 6 ,)7@ MATRIX . You can also creat e an d store matrices—na med or unnamed— - in HOME. For examp le, the command: POLYR OOT([ 1,0,–1, 0]) & M1 stores th e root of the c omp lex vector of length 3 int o the M1 variable. M1 now co ntains the three roots of Matrix Catalog keys The tabl e below lists the operations of the menu ke ys in the Matrix Catalo g, as well as th e use of Delete ( >'( /@ ) and Clear ( >6 ,)7@ CLEAR ). x 3 x –0 = Key Meaning ( ',7_ Opens the hi ghlighted matrix for editin g. 1(: _ Prom pt s for a matri x type, then ope n s an empty matr ix with the hig hli ghted name. 6 (1'_ Tra n s mits t he high light e d matr ix to another HP 39G /40G or a disk dr ive. See “Send ing and receiv ing aplets” on page 16-5. 5 (&9_ Receives a matrix fro m ano ther HP 39G/40 G or a disk drive. See “Sendin g and receivin g aple ts” on page 16-5. >'(/@ Clears the h ig hli ghted matrix. >6 ,)7@ CLEAR Clears all matrices. >6 ,)7@ *e, or *k @ Moves to the end or the be ginning o f the catalo g.
Matri ces 12-3 To crea te a matrix in the matrix cata log 1. Press >6 ,)7@ MATRIX to open the Matrix cat alog. The Matrix cata log lists the 10 available matrix variable s, M0 to M9. 2. Highlight the matrix variable na me you want to use and press 1(: _ . 3. Select the typ e of matr ix to create . – For a vec tor (one-di mensional array ) , selec t Real vector or Complex vector . Certain op e r at ion s ( , - , CROS S ) d o not recogn ize a one-dim ensi onal matrix as a v ector , so this sele ction is impo rtant. – For a mat rix (two-dime nsional array), select Real matrix or Complex matrix. 4. For each elem ent in the matrix , typ e a number or an expre ssion, and pre ss >(17(5@ . (The expres sion may not contain symbolic va r iable names.) For co mp lex num b e r s , enter each number in complex form; that is, ( a, b ), where a is the real part and b is th e imaginary p art. Y o u must includ e the pare ntheses a nd the com ma. 5. Use th e cursor keys to mo ve to a different r ow or column. Y ou can chang e the dir ection of the hig hlight b ar by pressing *2 _ . The *2 _ menu key to ggles betwe en the follow in g thr ee option s: – *2 _ _ specifies that the curso r moves to the cell below th e curr ent cell w hen you press >(17 (5@ . – *2 # _ specifies that t he cursor moves to the cell to th e right of t he current cell when you press >(17(5@ . – *2 _ specifies that the curso r stays in the current cell when yo u pre ss >(17(5@ . 6. When do ne, press >6 ,)7@ MATRIX to see the Matrix catalog, or pre ss  > 20( @ to return to HOME. The matrix entries are au tomatically stored. A matrix is liste d with two dimens ions, even if it i s 3×1. A vector is lis ted with the number of elemen ts, such as 3.
12-4 Matri ces To trans mit a matrix You can send matrices between calculators ju st as you can send a plets, p rograms, lists, and notes. 1. Align the HP 39G calculators’ infra red ports. 2. Open th e Matrix catalog s on both calculators. 3. Highligh t the matrix to send. 4. Press 6 (1'_ . 5. Press 5 (&9 _ on the receiv ing calculator . Matrice s can also be trans mitted to o r from a computer a c able and Co nnectivi ty Kit. Working with matri ces To edit a matrix In the Matrix catalog , highligh t the name of the matrix you want to e dit and press ( ',7_ . Matrix e dit keys The follo wing table lists the matrix edit key operations . Key Meaning ( ',7_ Copies the hi g hlighted element to the edit line. ,16_ Inserts a row of zeros above, or a column of zeros to the left, o f the highli ghted cell. (You are pr ompted to choose row or co lumn.) *2_ A three-wa y toggle for cu rsor advance ment in the Matrix editor. *2# _ advance s to the right, *2_ ¸ advances downward, and *2_ does not ad va nc e at all. %, * _ Switches bet ween larger and smaller font sizes. >'(/@ Deletes the highlighted cells, row, or column (you are prompt ed to make a choice). >6 ,)7@ CLEAR Clears all elemen t s from the matrix. >6 ,)7@ *k, *e, *A,*>, Moves to the first ro w, last row, first column, or last co lumn respectively.
Matri ces 12-5 To display a matrix • In the M atrix catalo g ( >6 ,)7@ MATRIX ), highli ght the matri x name an d press (' ,7_ . • In HOME, enter the name of the matrix v ariable and press >(17(5@ . To display one element In HOME, enter matrixname ( row,c olum n ). F or example, if M2 is [[3,4],[5 ,6]], then M2(1,2) >( 17(5@ returns 4. To crea te a matrix in HOME 1. Enter the matrix in the edit lin e. Start a nd end the matrix and eac h r o w with squa re brackets (the shifted > @ and >@ keys). 2. Separate eac h element and eac h r ow wit h a comma. Example: [[1 ,2],[3,4]]. 3. Press >(17(5@ to enter and display the ma trix. The left screen below shows the matrix [[2.5,729],[16,2]] being store d into M5. The screen on the rig h t s ho w s the vector [66,33 ,11] bein g stored into M 6. Note that yo u can enter an expression (lik e 5/2) for an element of the matri x, and it will be ev aluated. To store one element In HOME, enter: value 67 2?_ matrix name ( row,column ) For exampl e, to change the elem ent in the first row a nd second column of M5 to 72 8, then displa y the resultin g matrix: 728 672 ?_  >$/3 $@ M5 >@ 1 >@2 >@ >(17(5@>$/3 $@ M5 >(17(5@ . An attempt to store an elemen t to a ro w or column beyond the size of the matrix results in an error message.
12-6 Matri ces Matrix arithmetic You can use the arithmeti c functions ( , – , ×, / ) with matrix arguments. Division le ft–multiplies by the inverse o f the divisor. You can enter th e matrices themselv es or enter the names of st ored matrix va riables. The mat rices can be rea l or complex . For the next four examples, store [[1,2],[3,4]] into M1 and [[5,6],[7,8] ] into M2. Example 1. Create the first matrix. >6 ,)7@ MATRIX 1(: _  2._ 1 >(17(5@ 2 > ( 1 7 ( 5 @ * e , 3 >(17(5@ 4 >(17(5@ 2. Create the secon d matrix. >6 ,)7@ MATRIX *e, 1(:_ 2._ 5 >(17(5@ 6 >(17(5@  *e, 7 >(17(5@ 8 >(17(5@ 3. Add t he matrices that you c reated. > 20(@>$/3 $@ M1 >@ >$/3 $@ M2 >(17(5@ To multiply and divide by a scalar For divisio n by a scalar, enter th e matrix first, then the operato r, then the sca lar. For multiplic ation, the o rder of the operands do es not matter. The matr ix and the scalar can be real or complex . For examp le, to divide the resul t of t he previo us ex ample by 2, us e the f ol l owin g key press e s : > j@ 2 >(17(5@
Matri ces 12-7 To multiply two matrices To multiply the two matric es M1 and M2 that you created for the previo us example, use the follo wing keystrokes: >$/3 $@ M1 >[@ >$/3 $@ M2 >(17(5@ To multiply a matrix by a v ector, enter t he matrix first, the n the vector . The number of elements in the v ector must equal the numbe r of columns in t he matrix. To divide by a squar e ma trix For d ivision of a mat rix or a vector by a squ are matr ix, the number of rows of the divid end (or the number o f elements, if it is a vector) must equ al the nu mber of rows in the divisor. This opera tion is not a m athematica l division: it is a left– multipli cation by th e inverse of the divisor. M1 /M2 is equiv alent to M2 –1 * M1. To divide th e two matrices M1 an d M2 that you c reated for the previo us example, use th e following ke ystrokes: >$/3 $@ M1 > j @>$/3 $@ M2 >(17(5@ To invert a matrix You can invert a s quare matrix in HOME by typ ing the matrix (or its variable name) a nd pressing >6 ,)7@ x –1 >(17(5@ . Or you can use the matrix INVERSE comm and. Enter INVERSE( matrixname ) in HOME and pre ss >(17(5@ . To negate each element You can chan ge the sign of each ele ment in a matrix by pressing >@ before the matr ix name.
12-8 Matri ces Solving systems of linear equations Example Solve the followin g linear system: 1. Open the M at rix catalog and cho ose to create a vector i n the M1 v ariable. >6 ,)7@ MATRIX  1( : _ *e, >(17(5@ 2. Create t he vector of the constant s in the li near system. 5 >(17(5@7 >(17( 5@ 1 >(17(5@ 3. Return to the Matrix catalog. Th e vector you created is list ed as M1. >6 ,)7@ MATRIX 4. Select the M 2 variable and create a ne w matrix. *e, 1(: _ Sele ct Real matrix 2._ 5. Create a new matr i x and enter the equat ion coefficients. 2 >(17(5@ 3 >(17(5@ 4 >(17(5@ *e, 1 >(17(5@ 1 > ( 17(5@ >@ 1 >(17(5@ 4 >(17(5@ >@ 1 >(17(5@ 2 >(17(5@ 2 x 3 y 4 z 5 xy z – 7 4 xy –2 z 1 = = =
Matri ces 12-9 6. Return to HOME and ent er the calculati on to left multip ly the consta nt s vector by the in verse of the coefficients ma tri x . > 20(@>$/3 $@ M2 >6 ,)7@ x –1 >[@ >$/3 $@ M1 7. Evaluate the calcu lation. >(17(5@ The result is a vector of the solutions: • • • An alter native method, is to use the RREF function. Se e “RR E F” on page 1 2-12. Matrix funct ions and comman ds About functions • Functions can be used in any a plet or in HOME. T hey are listed in the MA TH menu under th e Matrix cat egory . They can be us ed in mathemati ca l expressions—primarily in HOME—as well as in progr ams. • Funct i ons always produ ce and display a resu lt. They do not chang e any stored variables , such as a matrix varia ble. • Funct i ons have arguments tha t are encl os ed in parent heses an d s ep a r at ed by comma s ; for ex am p le, CROSS( vector1 , vecto r2 ). The matr i x input can be ei ther a matrix variab le na me (such a s M1) or the actu al matrix data i nside brackets. For example, CROSS(M1,[1,2]). x 2 = y 3 = z 2 – =
12-10 Matri ces About commands Matrix commands are li sted in the CMDS m enu ( >6 ,)7@ CMDS ), in the matrix catego ry. See “Matrix comm ands” on page 15-23 for detail s of the matrix c ommands availabl e for use in programming. Functions differ from commands in that a function can be used in an ex pr e ssion. Comman ds cannot be used i n an expr ession . Argument conventions •F o r ro w# or col u mn# , su pply th e num ber of the r ow (counting from the top , starting with 1) or the number of the colum n (counting from the left, sta rting with 1). • The argument matrix can refer to either a vec tor or a matrix. Matrix functions COLNORM Column Norm. Finds the maxim um valu e (over all colu mns) of the sums of the absolute va lues of all elem ents in a column. COLNORM( matrix ) COND Condit ion Number. F inds the 1-no rm (column n orm) of a square matrix . COND( ma trix ) CROSS Cross Prod uct of vector1 with ve ctor2 . CROSS( vector1 , ve ctor2 ) DET Determinan t of a square matrix . DET( matrix ) DOT Dot Product o f two arrays, matrix1 matrix2. DOT( matrix1, matrix 2 )
Matri ces 12-11 EIGENVA L Displa ys the eigenval ues in vecto r form for matrix . EIGENV AL( m atrix ) EIGENVV Ei genvectors an d Eigenvalues for a squar e matrix . Displ ays a list of t wo arra ys. The first co ntains the eigenv ectors a nd the second co ntains the eigenval u es. EIGENVV( matrix ) IDENMA T Identity m atrix. Creates a square matrix of d imension size × size whose d iagonal elements are 1 and off-diagonal elements are zero. IDENMA T( size ) INVERSE Inverts a square matrix (real or c omplex). INVERSE( matrix ) LQ LQ Factorization . Factors an m × n matrix into three matrices : {[[ m × n lowertrapez oidal ]],[[ n × n orth ogonal ]], [[ m × m permuta tio n ]]}. LQ( matr ix ) LSQ Least Squ ares. Displays the minimu m norm least squares matr ix (or vector). LSQ( matrix1, mat rix2 ) LU LU Decomposition. F actors a square matrix into th ree matrices: {[[ low ertri angul ar ]],[[ uppertriang ular ]],[[ permut ation ]]} The uppertriangu lar h a s on e s on its diag on al. LU( matr ix ) MAKEMAT Make Matrix. Cre ates a matrix o f dimension rows × column s , using expre ssion to calculate ea ch element. If expressi on contain s th e vari ab les I and J, then the calculat i on for each element sub stitutes the current row number fo r I and the current column number for J. MAKEMA T( expression , ro w s , columns) Example MAKEMA T(0,3, 3) returns a 3×3 zer o matrix, [[0,0,0],[0,0,0 ],[0,0,0]].
12-12 Matri ces QR QR Fac torization. Factors an m × n matrix into three matrices: {[[ m ×m orthogona l ]],[[m ×n uppertrapez oidal ]],[[n × n permut ation ]]}. QR( matrix ) RANK Rank of a rectangular matrix . RANK( ma trix ) ROWNORM Row Norm. Finds the maximum value (over all ro ws) for th e sums of the absol ute values of all elem ent s in a row. ROWNORM( matrix ) RREF Reduced Row E chelon Form. Change s a rectangular matrix to its red uc ed row-ec he lon form. RREF( matrix ) SCHUR Schu r Decompos ition. F actors a square matrix into two matrices. If matrix is real, then th e result is {[[ orth ogonal ]],[[ upper-qu asi triangula r ]]}. If matrix i s complex, then the result is {[[ unita ry ]],[[ upper- triangular ]]}. SCHUR( matrix ) SIZE Dim e ns io ns of matrix . Returned as a list: {rows, columns}. SIZE( matrix ) SPECNORM S pectral Norm of matrix . SPECNORM( matrix ) SPECRAD S pectral Ra dius of a square ma trix . SPECRAD( matrix ) SVD Singular Value Decompositio n. Facto rs an m × n matrix into two matrices and a vector: {[[ m × m square orthog onal ]],[[ n × n squ are orthogon al ]], [ real ]}. SVD( matrix ) SVL Sing ul ar Value s . Retu r ns a ve c tor co nt aining the sin g ular values of ma trix. SVL( matrix )
Matri ces 12-13 TRACE Finds the tra ce of a square matrix. The trace is equal to the sum of the diago nal elements. (It is also equal t o the sum of the ei ge nv a l ue s .) TRACE( matrix ) TRN Tr ansposes matrix . For a complex matrix, TRN find s the conjugat e transpose. TRN( matrix ) Examples Identity Mat rix You can cre ate an iden tity matrix with the IDEN MAT function. For example, IDENMAT(2) creates the 2×2 identit y matrix [[1,0],[0,1]]. You can also c reate an identi ty matrix u sing th e MAKEMA T ( make matrix) function. For exa mple, e ntering MAKEMAT(I ≠ J,4,4) creates a 4 × 4 matrix showing the numeral 1 for all elem ents except zeros on t he di a gonal. The logical op erator ≠ returns 0 when I (the row number) and J (the column nu mber) are equal, and returns 1 whe n they are not eq ual. Transposing a Matr ix The TRN function swaps the row-column and column-row elements o f a matrix. For instance, el eme nt 1,2 (row 1, column 2) i s sw app ed with element 2, 1 ; element 2,3 is swapped wi t h element 3,2; an d so on. For example, TRN([[1,2],[3,4]] ) cre ates the matrix [[1,3],[2,4]].
12-14 Matri ces Reduced-Row Echelon Form The follo wing set of equ ations can be written as the au gmented matri x which can th en st ore d as a real ma trix in M1. You can use the RREF function to change this to reduced row ech el on form, storing it as M2 for convenien ce. The reduced row ech elon matrix gi ves the solutio n to the line ar equation in the forth column. An advanta ge of using t he RREF function is that it will also work with inconsiste nt matric es resulting from systems of equatio ns which have no solutio n or infi nite solu tio ns. For example , the following set of equations h as an infinite number of solutio ns: The final row of zeros in the reduced –row echelon for m of the augm ented matrix indicates a n inconsistenc y. 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 13-1 13 List s You can do list operation s in HOME and in programs. A list consists o f comma-separated rea l or complex numbers, expressi ons, or matrices, all enclosed in braces. A li st may, for example, con tain a sequence of real numb ers such as {1,2,3} . (If the Decimal Mark in MODES is set to Com ma, then the separato rs ar e peri ods.) Lists represent a conv eni ent way to gr oup related objects. There are te n list variab les available, named L0 t o L9. You can use them in calcu lations or expressions in H OME or in a program. Retri eve the list nam es from the VARS m enu, or just type their names from the keyboard. You can create, edit, delete, sen d, and receive named l ists in the List catal o g ( >6 ,)7@ LIST ). You can also cr eat e and store lists—nam ed o r unnnamed—in HOME. Creating lists List variab les are identical in behaviour to the columns C1 .C0 in the S tatistics aplet. You can store a statistic s column to a list (or vice versa) and use any of the list functions on the statistics columns, or t he statistics funct ions, on the list v ariables. Create a list in the List Cat alog 1. Open the List cat alog. >6 ,)7@ LIST . 2. Highlight the list n ame you want to use (L1, etc. ) and press ( ',7a  to display the List ed itor . (', 7a
13-2 Lists 3. Enter th e values yo u want in the li st, pressing >(17(5@ after each one. V alues c an be re al or complex numbers (o r an expression). If you enter a calculatio n, it is evaluated and the result is inserted in the list. 4. When done, p ress >6 ,)7@ LIST to see the List catalog, or press > 20(@ to return to HOME. List cat alog keys The list catalog keys are: Key Meaning ( ',7a Opens the hi ghlighted list for editing. 6 (1'a Transmits the highligh te d list to another HP 39G /40G or a P C . See “Sendin g and receivin g aple ts” on page 16-5 for further information. 5 (&9 a Receives a list from ano ther HP 39G/ 40G or a PC. See “Se nding and receiving apl et s ” on page 16-5 for further information. >'(/@ Clears the hi ghlighted list. >6 ,)7@ CLEAR Clears all lists. >6 ,)7@ *e, or *k, Moves to the end or the be ginning o f the catalo g.
Lists 13-3 List ed it keys When you press edit to creat e or change a list, the follo wing keys are av a ila bl e to you: Create a list in HOME 1. Enter the list in the edit line. S tart and e nd the list with braces (the shifted >@ and >@ keys) an d sep arate each element wit h a comma. 2. Press >(17(5@ to evalu ate and display the list. Immediatel y after typing in the list, you can store it in a variabl e by pre ssing 67 2?a listname >(17(5@ . Th e list varia b le na m e s are L0 thr o ug h L9. This examp l e st ores the list {25,147, 8} in L1. (Y ou can omit the final brace when en tering a list.) Key Meani ng (' ,7a Copies th e highlig hted list item into the edit line. ,16a Inserts a new value before the highlig hted item. >'(/@ Deletes the highlighted it em from the list. >6 ,)7@ CLEAR Clears all elem ents from the list. >6 ,)7@ *e, or *k, Moves to th e end or th e beginn ing of the list.
13-4 Lists Displaying and editing lists To displa y a list • In the L ist catalog, highlight t he list name and press  ( ' ,7a . • In HOME, e nter the name of th e list and pres s >(17(5@ . To display one element In HOME, enter listn ame ( element# ). For examp le, if L2 is {3,4,5, 6}, then L2(2) >(17(5@ returns 4 . To edit a list 1. Open the List catalo g. >6 ,)7@ LIST . 2. Press *k, or *e,  to highlight the nam e of the li st you want to edit (L1, etc. ) and press (' ,7a  to displa y the list conten ts. (' ,7a 3. Press *k, or *e, to highlig ht the eleme nt you want t o edit. In t his example, edit the third element so that it ha s a val u e of 5. *e, *e, ( ',7 a >'(/@ >'(/@ 5 4. Press 2. a .
Lists 13-5 To in sert an element in a lis t 1. Open the List cat alog. >6 ,)7@ LIST . 2. Press *k, or *e, to highligh t the name of the list you want to edit (L1, etc .) an d press (',7 a to display the list conten ts. (', 7a 3. Press *k, or *e, to the insertion po sition. New el ements are ins e r t e d ab ove th e hi g h light e d position. In this e xamp le, an elemen t, with the va lue o f 9, is inserted between the first and secon d elements in the list. *e, ,16a  9 4. Press 2.a . To store one element In HOME, enter value 6 72? a listname ( element ) . For example , to store the second elem e nt of L1 to 14 8, type 148 67 2? a L1(2) >(17(5@.
13-6 Lists Deleting lists To delete a list In the List catalog, hi ghlight the li st name and p ress >'( /@ . You are prom pted if you wan t to delete the co ntents of th e highli ghted list va riable. Press >(17( 5@ to delete the con tents. To delete all list s In the List catalog, press >6 ,)7@ CLEAR . Transmitting lists You can se nd lists to calculato rs or PCs ju st as you c an aplets, progra m s, matric e s, and not e s. 1. Align the HP 39G calculators’ infra red ports. 2. Open the L ist catalog s on both calc ulators. 3. Highligh t the list to send. 4. Press 6 (1'a . 5. Press 5 (&9 a on the receivi n g calculator . Lists can also be t ransmitted to o r from a compu ter a cable and Conne ctivity Ki t.
Lists 13-7 List functi ons Following a re details of list function s. You can use them in HOME, as well as in programs. You can ty pe in the name of the functio n, or you can co py the nam e of the func tion from the List category of the MATH menu. Press >0$7 @>@ (the alpha L character ke y). This display s the List categ ory . Press *A, , select a funct io n, and press 2.a . List fu nctions have the following syntax: • Functio ns ha ve ar guments that are encl ose d in parent heses an d s ep a r at ed by com mas . E xa m ple : CONCAT(L1,L2) . An argument can b e either a list variab le na m e (suc h as L1 ) or the actu al list. For example, REVERSE({1,2,3}) . • If Decimal Mark in MODES is set to Comma, use period s to separate argum ents. For exam pl e, CONCAT(L1.L2) . Common op erat ors like , –, ×, and / can ta ke l ists as arguments. If there are two argumen ts and both are li sts, then the lists must have the sa me length, since the calcula tion pairs up the element s. If there are two arguments and one is a real number, then the calcu lation pairs th e number with e ach element of th e list. Example 5 * {1,2,3} returns {5,10 ,15} . Besides the co mmo n operators that can t ake numbers, matrices, or list s as arguments, there are co mma nds that can only operate o n lists.
13-8 Lists CONCAT Concate nates two lists into a n ew list. CONCAT( list1 , list2 ) Example CONCAT({1,2,3},{4}) returns {1,2,3,4} . ∆ LIST Creates a new list co mposed of the differences b et w een th e sequential ele ments in list1. The n ew list has one fewer elements t han list1 . The first differences for { x 1 x 2 ... x n } are { x 2 – x 1 ... x n – x n– 1 }. ∆ LIST( list1) Example In HO ME, stor e {3,5,8,1 2,17,2 3} in L5 and fin d the first differences for the list. > 20(@>6 ,)7@ { 3,5,8,12, 17,23 >6 ,)7@} 672 ?a >$/3 $@ L 5 >(17(5@ >0$7 @ L *A, Sele ct 1 LIST 2.a >$/3 $@ L5>(17(5@ MAKELIST Calculates a sequ ence of elements for a new list . Evaluates expression with variabl e from be gin to end values, ta ken at increment step s. MAKELIST( expression , variable , begin , end , increment ) The MAKELIST fun ction generates a series by automatically producing a l ist from the repeated evalua tion of an expression . Example In HOME, generate a list of squares from 23 to 2 7. >0$7 @ L *A, Select MAKELIST 2.a  >$/3 $@ A >[  @ >@>$/3 $@ A >@ 23 > @ 27 >@ 1 >@ >(17(5@ HINT If the Dec imal Mark setting i n the Modes inp ut form ( >6 ,)7@ MODES )is set to Comma, use > @ instead of >@.
Lists 13-9 Π LIST Calculates the product of all elements in list. Π LIST( list) Example Π LIST({2,3,4}) returns 24 . POS Returns the position of an elem ent within a list. Th e element can be a value, a va riable, or an expressi on. If there is more than one insta nce of the el ement, the positio n of the first occurrence is returned. A value of 0 is return ed if there is no occurre nce of the specified element. POS( list, element ) Example POS ({3, 7, 12, 19},12) returns 3 REVERSE Creates a list by reversing the order o f the elements in a list. REVERSE( list ) SIZE Calculates t he n umber of elements in a list. SIZE( list ) Also works with matrices. Σ LIST Calcula tes the sum o f all elements in list. Σ LIST( list) Example Σ LIST({2,3,4}) ret u rns 9 . SORT Sorts element s i n ascending order. SORT( list )
13-10 Lists Finding statistical values fo r list elements To find values su ch as the mean, median, ma ximum, and minimum values of the elements in a list, use the Statistics aplet. Example In this exam ple, use the Statistics aplet to find the m ean, median, ma ximum and m inimum values o f the eleme nts in the list, L1. 1. Create L1 with v alues 88, 90, 89, 65 , 70, and 8 9. >6 ,)7@ { 88 >@ 90 >@ 89 >@65 >@ 70 >@ 89 >6 ,)7@ } 67 2? a >$/3 $@ L1 >(17(5@ HINT If the Dec imal Mark setting i n the Modes inp ut form ( >6 ,)7@ MODES )is set to Comma, use > @ instead of >@. 2. In HOME, store L1 into C1. Y ou will then be abl e to see the list da ta in the Nume ric view of the S tatistics ap let. >$/3 $@ L1 67 2? a >$/3 $@ C1 >(17(5@ 3. Start th e Statistics a plet, and select 1–v ariable mode (press 9$ 5a , if necessary , to disp l ay 9 $5 a ). >$3/(7@ Select Statistics 67 $5 7a Note : Y ou r list va lues are now in c olumn1 (C1).
Lists 13-11 4. In the Symbolic view , define H1 (for example) as C1 (sample) and 1 (frequency). Make sure that H1 is checkmarked . >6<0%@ 5. Go to the Numeri c vi ew to display calcula ted statisti cs. >180@ 6 7$7 6a See “One-v ariable” on page 8-13 for t he meaning of each computed statistic.

Notes and sketches 14-1 14 Notes and sketches Introduct ion The HP 39G/40G has text and pictu re editors for en tering notes and sk etch es . • Each aplet ha s its own independen t Note view and Sketch vi ew . Notes and sketches that you cr eat e in these views are associated w ith the aplet . When you sa ve the aplet, or send it to anoth er calculator , the notes and sketches are sav ed or sent as well. •T h e Note pad is a collec tio n of no tes ind e pe n dent of all aplets. Th ese no tes can also be sent t o another calculat or via the Notepad Catalog . Aplet note view You can att ach text to an aplet in its Note view. To write a note in Note view 1. In an aple t, pres s >6 ,)7@ NOTE for the Note view . 2. Use the note editin g keys sho wn in the ta ble in the followin g s ectio n . 3. Set Alph a lock ( $=_ ) for quick e ntry of letters. For lower case Alpha lock, press >6 ,)7@ $  = _ . 4. While Alpha lock i s on: – T o type a single letter of the op posite case, pre ss >6 ,)7@ letter . – T o type a single non -alpha character (such as 5 or [ ), press >$/3 $@ first. (This turns off Alpha lock for one char ac t e r .) Y our work is automat ically saved. Pre ss any view ke y ( >180@, >6<0%@,  >3/27@ , >9,(:6@ ) o r > 20( @ to exit the Notes view .
14-2 Notes and s ketches Note edit keys Key Mean ing 6 3$&( _ Spac e key f or te xt en tr y . 3 $*(_ Displays next page of a m ulti-page note. $  =_ >6 ,)7@ $  =_ Alpha-lock fo r le tte r entry. Lower-case Alph a-l ock . % .63_ Backspaces cu rsor and deletes character. >'(/@ Deletes current ch aracter. >(17(5@ Starts a new l ine. >6 ,)7@ CLEAR Erases the entire note. >9$56@  Menu for e ntering variable names, and content s of variables. >0$7 @ Menu for entering math operations, and const an ts. >6 ,)7@ CMDS Menu for entering program commands. >6 ,)7@ CHARS Disp lays special characte rs. To type one, hi gh light it an d press 2. _ . To copy a charac ter with out closing the CHARS screen, press ( & 2 _ .
Notes and sketches 14-3 Aplet sketch view You can atta ch pictures to an aplet i n its Sketch view ( >6 ,)7@ SKETCH ). Y our work is automat ically saved with t he aplet. P r ess any other view ke y or > 20(@ to exit th e Sketch view Sket ch ke ys To draw a line 1. In an aple t, pres s >6 ,)7@ SKETCH for the Sket ch view . 2. In Sket ch view , press ' 5$: _ and move the cu rsor to where you want to start the line 3. Press /,1(_ . This turns on l ine-drawing. 4. Move the cursor in any direction to the end p oint of the line by pressing the *k, , *e, , *A,, *>, k eys. 5. Press 2._ to finish the line. Key Mea ning 672 _ Stores the specifi ed portion of the current sket ch t o a graphics variable (G1 th rough G0 ). 1(:3 _ Adds a new, blan k page to the current sketch se t. 3$*(  _ Displa ys ne xt sketch in t he sk etch set. Anima tes if h e ld down. 7(; 7_ Opens the edit line t o type a text label. '5$ :_ Displa ys the menu-key labels for drawin g. >'(/@ De letes th e curr e nt sket ch. >6 ,)7@ CLEAR Erase s th e ent ire sketch set. >@ Toggles m enu key la bels on and off . If menu key labels are hidd en, >@ or any menu k ey, redispl ays the menu key labe ls.
14-4 Notes and s ketches To draw a box 1. In S ketch view , press '5$ :_ and mo ve the cursor to where you want any corner of t he box to be. 2. Press % 2;_ . Thi s turns on bo x-drawi ng. 3. Move the cursor to m ark the opposite corne r for the bo x. Y o u can adjust th e si ze of the box by moving th e cursor . 4. Press 2. _ to fi nish the bo x. To draw a circle 1. In Sketch vi ew , pres s '5$ :_ and mo ve the cursor to wher e yo u wan t the ce nte r of th e cir cle t o be. 2. Press & ,5&/ _ . Th is tu rns on circ le dr awing . 3. Move th e curso r the distance of the radius. 4. Press 2. _ to d raw t he ci rcle. DRAW keys Key Mean ing ' 27_ Dot on. Turns pi xels on as the cursor moves. ' 27_ Dot off. Turns pixels o ff as the cursor moves. / , 1( _ Draws a line from the cursor’s st art ing position to the cursor’s current positi on. Press 2. _ whe n you ha ve finis hed. Yo u can draw a line at an y angle by moving t he cursor. % 2;_ Draws a box from the curso r’s st arting position to the poin t at which yo u press 2. _ . & ,5&/ _ Draws a circle with the cursor’s start i ng position as the center. The radius is the distance between the c ursor’s starting and ending positio n. Press 2._ to draw the circle.
Notes and sketches 14-5 To label parts of a sketch 1. Press 7( ;7_ and type t he text in th e edit line. T o loc k the Alpha shift on, press $=_ (for up pe rcas e) or >6 ,)7@ $   =_ (for lowercase). T o make the label a smaller char act er si ze, turn off % , * _ before pressing $   =_ . ( %,*_ is a toggle be tween small and lar ge fo nt s ize). The s mall er ch aract er si ze ca nnot displ ay lowercase l etters. 2. Press 2._ . 3. Position the label where you want it by pressing t he *k, , *e, , *A, , *>, keys. 4. Press 2._ again to affix the l abe l. 5. Press '5 $:_ to contin ue drawin g, or pre ss > 20(@ to exit Sketch view . To create a set of sketche s You can create a set of u p to ten sketches. This all ows for simple anim ation. • After maki ng a s ket ch , press 1(: 3_ to add a new , blank page. Y ou can now make a new sket ch , which become s part of the curr ent se t of sk etch es. • T o view the next sketch in an existing set, press 3$ *( _ . Hold 3 $*(_ down for an imation. • T o remove the current pag e in the current sketch series, press >'(/@ . To store into a graphi cs variab le You can defi ne a portion of a sket ch inside a box , and then store that grap hic into a graphics vari able. 1. In the Sket ch view , dis play the sketch you wa nt to cop y (store into a variable). 2. Press 67 2?_ . 3. Highlight the var ia bl e name you w an t to us e an d pres s 2._ . 4. Draw a bo x arou nd the portion yo u want to copy : move the cu r s or to on e co rner , press 2. _ , then move the cursor to the opp osite corner an d pr e ss 2. _ .
14-6 Notes and s ketches To import a grap hics variab le You can copy th e con tents of a graph i cs variable into the Sketch view of an aplet . 1. Open t he Sk etch view of th e aple t ( >6 ,)7@ SKETCH ). Th e graphic will b e copied he re. 2. Press >9$56@ , 2 0(_ . Highl ight Graphic , then press *A, and high light the name of the variabl e ( G1 , et c.). 3. Press 9 $/8 (_ 2._ to recall the conten ts of the graphic s varia ble. 4. Move the bo x to where you woul d like to copy t he graphic , then press 2._ . The notep ad Subject to availabl e memory, you can store as ma ny notes a s you want in t he Notepad ( >6 ,)7@ NOTEPAD ). The se no tes ar e indepe ndent of an y aplet. The No tepad cata log lists the existing e ntries by name. It does not incl ude notes that were created in a plets’ Note view s , but these c an be impor ted. S ee “To imp ort a note” on pa ge 14-8 . To creat e a note in the Notepad 1. .Display the Notepad catalog. >6 ,)7@ NOTEPAD 2. Create a new note . 1(: _ 3. Enter a na me for your note. $=_ MYNOTE 2._ Note: In th is example, the name of the note is ‘M YNOTE’.
Notes and sketches 14-7 4. Write your not e. See “Note edi t keys” on page 14-2 for m ore informatio n on the entry and edi ting of notes. 5. When yo u are finished, press > 20(@ or a n ap le t key to e xit Note p ad. Yo u r w o r k is automatically sa ved. Notepad Catalog keys Key M eaning (', 7_ Opens the select ed n ote for editin g. 1(:_ Begins a ne w note, and ask s for a name. 6(1' _ Transmits the selected note to anothe r HP 39G/40G o r PC. 5(& 9_ Receives a no t e being transmitted fr om another HP 39G/40G or PC. >'(/@ Deletes the selected note. >6 ,)7@ CLEAR Deletes all notes in the c atalog.
14-8 Notes and s ketches To import a note You can import a no te from th e Notepad int o an aplet’s Note view , an d vice-vers a. Suppos e you want to copy a not e na med “Assignments” from the Notepa d into the F unction Note view: 1. In th e Func tio n aple t, disp lay the Note view ( >6 ,)7@ NOTE ). 2. Pres s  >9$56 @ 2 0(_ , highlig ht Notepad in the left-hand list, then h ighlight th e name “Assig nments” in the right- hand list. 3. Press 9 $/8 (_ 2._ to co py the co ntents of “As signme nts” to the Fu nction Note v iew . Note: T o recall the name instea d of the contents, press 1$0 (_ inst ead of 9$/ 8(_ . Suppose you want to copy the Note view from the cur r ent aplet in to the not e “Assignments” i n the Notepa d. 1. In the Not epad ( >6 ,)7@ NOTEPA D ), open the no te “Assignme nts”. 2. Press >9$56@ $3/ (7_ , high l ight Note in the l eft co l umn, then press *A, an d highligh t NoteText in the right column. 3. Press 9 $/8 (_ 2._ to re call the conten ts of the Note v iew into the note “Assign ments”.
Progr amming 15-1 15 Programming Introduct ion This chapt e r describes ho w to pr og ram using the HP 39G/ 40G. In this c hapter you’ll learn about: • using the P rogram c atalog to c reate and ed it programs • progr ammi ng comm ands • storing and retrieving v ariables in prog rams • progr amming variable s. HINT More informati on on programming , in cl uding examples and special too ls , can be found at HP’s calculators web si te: www.hp.com/calculators The Contents of a Program An HP 39G/40 G pr og ram contains a se que nce of numbers, mathema tical expressi ons, and co mmands that execute aut omatic ally to perfo r m a task. These items are sepa rated by a colon ( : ). Commands that take multiple ar g um e nt s have tho s e ar gu ments sepa r a te d by a semicolon ( ; ). For exampl e, PIXON xposition ; ypos ition : Structur ed Programming Insi de a prog ram yo u can us e branc hing str ucture s to con trol the exec ution flow. You can ta ke advantage of structured progra mming by cre a t ing building -block pro grams. Eac h buildin g- b l oc k prog ram stan ds alon e— a n d it ca n be ca lle d from other programs. Note: If a program ha s a space in its name the n you have to pu t quotes arou nd it when you want to run it . Example RUN GETVALU E: RUN CALCULATE: RUN " SHOW ANSWER" : This program i s separated into th ree main tasks, each an individu al program. With in each program, the task can b e simpl e— or it can be di vided furthe r into othe r programs that perform smaller tasks.
15-2 Progra mming Program catalog The Progra m cat al og is where you create, edit , delete, send, receive, o r run progra ms. This sect ion describes ho w to • open th e Pr og r a m catalo g • cre ate a new pr og ram • ent er com mands fr om the program comm ands me nu • ente r functio ns from t he MA TH menu • edi t a progra m • run an d debug a pr og r am • stop a pr o gr a m • cop y a pro g r am • send and recei ve a program • del ete a progr am or its co ntent s • customi ze an aple t. Open Program catalog 1. Press >6 ,)7@ PROGR M . The Prog ram catalog displays a li st of prog ram names. If you haven 't create d any programs , the only n a me y ou'll see is Editline . Editline contain s the last expression that yo u en tere d from the edit line in HOM E, or the last d ata you ente red in an input form. (If y ou press >(17(5@ from HOME without e ntering a ny data, th e HP 39 G/40G ru ns the content s of Editlin e. ) Before starting to work with prog rams, you should take a few minut es t o become fami li ar with the Pr og ram catalo g menu keys. You ca n use any of the follow ing keys (both menu and keyboa rd), to perform tasks in the Program cata log. Editline is a built-in function. Program catalog menu
Progr amming 15-3 Program catalog keys The prog ram cat alog keys are: Key Meanin g (' ,7a Opens the highli gh ted pro gra m for editing . 1(: a Prompt s f or a new program nam e, then op ens an empty pro gram. 6( 1 ' a Transmi ts the highli ghted program to another HP 39G/40G or to a disk drive . 5( &9a Receives the hig hli gh ted pro gra m from another HP 39 G/40G or from a disk drive. 58 1 a Runs th e highlig hted prog ram. >6 ,)7@ *k, or *e, Moves to th e beginn ing or en d of the Program cat al o g. >'(/@ De le tes the hi gh lighted pr ogram. >6 ,)7@ CLEAR Deletes all programs in the program catalog.
15-4 Progra mming Creating and editing program s Create a new program 1. Press >6 ,)7@ PROGRM to open the Prog ram catalog. 2. Press 1( :a . The HP 39G /40G prompts y ou for a name. A program nam e can contain special characters, such as a space. Howe ver , if you use spe ci al characters and then run the p rogr am by ty ping it in HOM E, you m us t enc los e the progr am name in dou ble quote s ( " " ). Don’ t use the " symb ol with in yo ur pro gram name . 3. T ype your progra m name, then pr ess 2. a . When yo u pre s s 2.a , the Progra m Editor ope ns. 4. Enter your progr a m . When done, st art any ot her activ ity . Y our wor k is sav ed automatic ally .
Progr amming 15-5 Enter commands Until yo u be com e fa milia r with th e HP 3 9G/40 G c omma nd s, the easiest way to enter co mmands is to use the Commands menu from the Program editor. You can always type i n comm ands us in g alph a ch a racte r s . 1. From the Program edito r , press >6 ,)7@ CMDS to open th e Progr am C ommands menu. >6 ,)7@ CMDS  2. On the left, us e *e, or *k, to highlight a com mand category , then press * A, t o acce ss the commands in the catego ry . Select th e com mand that you wan t . *e,*e,*A,*e, 3. Press 2.a to paste t he command in to the program editor . 2.a T o enter functions (more to come) Edit a program 1 . Press >6 ,)7@ PROGRM to open the Progra m catalog. 2. Use the arr ow keys to highlig ht the pr ogram yo u want to edit, an d pr e ss ( ',7 a . The HP 39G/40G opens the Progr am Editor . The nam e of your pro gram appears i n the title b ar of the disp lay . Y ou can use the following keys to ed it yo ur pr o gr a m .
15-6 Progra mming Editing keys The edi tin g keys are: Key Meaning 6 72? a Inserts the 672 ?a character at th e editing point. 6 3$& (a Inserts space into text. A3$ *(a Disp lays pre vious page of the progra m. 3 $*(a Disp lays next page of t he prog ram. *k,*e, Moves up o r down one line. *A,*>, Mo ves right or left one characte r. $  = a Alpha-lock for letter e ntry. Press >6 ,)7@ A...Z to lock lower case. % .63a Backspaces cu rsor and deletes character. >'(/@ Deletes cu rrent character. >(17(5@ Starts a new line . >6 ,)7@ CLEAR Erases the enti re program. >9$56@ >0$7 @ Menus for entering variable names, contents o f variables, math func tions, and progr a m co nstants. >6 ,)7@ CMDS Menu s fo r enter ing prog ram conmmand s. >6 ,)7@ CHARS Displays all characters. To type o ne, highlig ht it an d press 2.a . To enter several characters in a row, use the ( & 2 a menu key while in the CHARS menu.
Progr amming 15-7 Using prog rams Run a program From HOME, type RUN pr ogram_ name. or From the Program cata log, highlight the program you want to run and pr ess 58 1 a . Regardless of whe re you start the program, all pro grams run in HOME. What you see will differ slightly de pending on where you st arted the prog ram. If you start t he program from HOME, th e HP 39G/40G disp lays the cont ents of Ans (Home variable c ontaining th e last result ), when the pr ogram has finished. If you start the program from the P rogram catalog, the HP 39 G/40G returns you to the Program catalog wh en the prog ram ends . Debug a program If you run a program that c ontains errors, the program will stop and you will see an error message. To deb ug the pr ogram: 1. Choose < (6a to edit th e program. The insert curso r app ears i n the program at the point where the error occurred. 2. Edit the prog ram to fi x the erro r . 3. Re-start the program. 4. Repeat the process un til you find and correct all errors. Stop a program You c an stop the exe cution of a pro gram at a ny tim e by pressing CANCEL (the >21@ key). No te: You may hav e to press it a coup le of times.
15-8 Progra mming Working with programs Copy a program You can use t he following pro cedure if you want t o make a copy of your work bef ore edi ting—or if you wan t to us e one program as a tem plate for another. 1. Press >6 ,)7@ PROGR M to open t he Program catalo g. 2. Press 1( :a . 3. T y p e a ne w fil e na m e, then choo s e 2.a . The Prog r a m E ditor opens with a n ew pr ogram. 4. Press >9$56@ to open the V ariable me nu. 5. Press >@ t o quickly sc roll to Prog ram. 6. Press *A, , then highlight the pr o gra m you want to co py . 7. Press 9 $/8 (a , then pre ss 2.a . The c ontents of the h ighlight ed progr am ar e copied into the current program at t he cursor lo cation. HINT If yo u use a progra mming rou tine ofte n, save t he rout ine under a different program n ame, then use the abo ve method t o copy it into your p rograms. Transm i t a program You can sen d programs to, and receive p rograms from, other calculat ors j ust as yo u can send and receiv e aplets, matrices , li sts, a nd n otes . After aligning the ca lculators’ infrared ports, o pen the Prog ra m ca ta lo gs on bot h ca lc u lat ors. High lig ht the prog r a m to send, then press 6 (1'a on the sending cal culator and 5( &9 a on the receiv in g calculator. You c an al so sen d prog rams to, and re ceive progra ms fro m, a remote sto rage device ( a pl et disk drive or computer). Th is takes p lace via a cable conn ection and re quires an aplet dis k driv e or spe cialized softw are run ning on a PC (suc h as a connectiv ity kit). Delete a program You can delete any p rogram exce pt Editline. 1. Press >6 ,)7@ PROGR M to open t he Program catalo g. 2. Highli ght a program to delete, t hen press >'(/@ .
Progr amming 15-9 Delete all programs You can d elete all prog rams at onc e. 1. In the Program ca ta lo g, press >6 ,)7@ CLEAR . 2. Press <( 6a . Delete the contents of a program You can clear the co ntents of a p rogram withou t deleting t he progra m name. 1. Press >6 ,)7@ PROGRM to open the P rogram catalo g. 2. Highlight a program , then p ress ( ',7 a . 3. Press >6 ,)7@ CLEAR , then press <( 6a . 4. The contents of the program ar e deleted, but the prog ram name r emains. About cu stomizing an aplet You can con figure an apl et and develo p a set of program s to work with the aplet. Use the SETVIEWS com mand to create a custom VIEWS menu which l inks specially wri tten programs to th e ne w aplet. A useful metho d for customizing a n aplet is illustrat ed below: 1. De cide on the apl et type that you want to use, for example th e Function aplet or the Statistics a plet. The copied aplet in h eri ts all t he properties o f th e paren t a ple t. Save the stand ard aplet under a new name . 2. Configure the new aplet if you need to, for example by presettin g axe s or ang le meas ures . 3. De ve lop the prog rams to work with your aplet. When you develop the aplet’ s programs, use the standard aple t naming c onvention. This allows yo u to keep track of the progra ms in the Program catalo g that belong to each aplet. See “A plet naming co nv ention” on pag e 15-10. 4. Develo p a pro gram that uses the SETVIEW S comma nd to modify the aplet’ s VIEWS menu. T he menu o ptions provide l inks to associated pro gram s. Y ou can sp ecify any ot her prog rams tha t you wa nt tran sferred with the aplet. See “SETVI EWS” o n page 15-1 4 for info rmation on the comma nd. 5. Ensure that the new a plet is selected, t hen run the m enu configura tion program to configure the aplet’ s VIEWS menu . 6. T est the aplet and debu g the associated pro grams.(Refer to “De bug a p rogram” on pa ge 15-7).
15-10 Prog ramming Aplet naming convention To assist user s in keep ing track of aplets and as sociated programs, use the following naming conventio n when setting up a n aple t’s p rogram s: • Sta rt all p r ogra m na m es with an ab bre v iation o f the a plet name. W e will use APL in this example. • Name pro grams called by menu entries in the VIEWS menu number, after the entry , for exampl e: – APL.ME1 fo r the prog ram called by menu o ption 1 – APL.ME2 fo r the prog ram called by menu o ption 2 • Name the p rogram that conf igures the new VIEWS menu option A PL.SV where SV stands for SE TVIEWS. For example, a cus tomized aplet call ed “Differentiation” might cal l programs called DIFF.ME1, DIFF .ME2, and DIFF.SV. Customizing an aplet example This example aplet is design ed to de m onstra te the pro cess of configuri ng an aplet. The new aple t is based on the Functio n aplet. Note : This aplet is not intended to serve a serious use, merely to illustrate the proces s. Save t he aplet 1. Open the Func tion aplet and save it as “E XPERIMENT”. The new ap let appears in the Aplet library . >$3/(7@ Sele ct  Function 6$9 (a >$/3 $@ EXP ERIMEN T 2. a 2. Create a progra m cal led EXP .ME1 with conte nts as shown. This pr o gram configur es t he plot ranges, then ru ns a program that a llows yo u to configur e th e an gle format.
Progr amming 15 -11 3. Create a progr a m calle d EXP .ME2 with con tents as s hown. Th is prog ram sets the num eric view options for the aple t, and runs the p rogram that you can us e to configure th e angle mode. 4. Create a progr a m calle d EXP .ANG wh ich the previo us two program s call . 5. Create a progr a m calle d EXP .S which runs wh en you start the aplet, as shown. This progr am sets the ang le mode to degree s, and sets up the initial functio n that the aplet plot s. Configuring the Se tviews menu option programs In this section we will begin by configu rin g the VIEWS menu by using the SET VIEWS com mand. W e will th en crea t e t h e “h elpe r” prog r am s c alle d b y the V I EW S menu which will do the actual wo rk. 6. Open the Program cata log and creat e a pr og ram named “EXP .SV”. Inc lude the followin g code i n the p rogram. (T ext shown in italics below are co mme nts only .) Each entry line after the command SETVIE WS is a trio that c onsists of a VIEWS menu te xt line (a space in dicates none), a prog ra m name, and a number th at defines the view to go to after the program has run its c ourse. All programs list ed here will transfer with an aplet wh en the aplet is transfe rred.
15-12 Prog ramming SETVIEWS ’ ’ ’ ’ ; ;’ ’ ’ ’ ; 18; Sets the first men u op tio n to b e "Au to scale". This is the fo urth standard Fu nction aplet view m enu option and the 18 "Auto scale", specifies th at it is to be included in th e new menu. The e mpty quotes will en sure that the old nam e of "Auto scale" appears on the new menu. S ee “S ETVIEWS ” on page 15-14 . ’ ’ My Entry1’ ’ ;’ ’ EXP.ME1’ ’ ;1; Sets t he second me nu option . This op tion runs program EXP .ME1, then returns to view 1, Plot view . ’ ’ My Entry2’ ’ ;’ ’ EXP.ME2’ ’ ;3; Sets the th ird menu optio n. This option runs the progr am EXP .ME2, then returns to view 3, the NUM view ’ ’ ’ ’ ;’ ’ EXP.SV’ ’ ;0; This line specifie s that th e pr ogram to set the V iew menu (this program) is transferred with the aplet. The space character b etween the first set of quotes in the trio specifies that n o menu op tion app ears for the entry . Y ou do no t need to transfer t his program with th e aplet, but it allows users to modify th e aplet’ s menu if th ey want to. ’ ’ ’ ’ ;’ ’ EXP.ANG’ ’ ;0; The program EXP .ANG is a small routine that is calle d by oth e r progr ams th at th e ap let uses. This ent r y sp ecifies that the program.EXP .ANG is transferred when the aplet is tran sferred, but the space i n the first quotes e nsu res that no ent ry appears on the menu. ’ ’ START’ ’ ;’ ’ EXP.S’ ’ ;7: This specifies the Start me nu option. The program that is associated with th is entry , .EXP.S, runs automatically when you start the aplet. Because this m enu option specifies view 7, the VIEWS m enu opens when yo u start the aplet .
Progr amming 15 -13 Y ou o nly need t o run this program once to c onfigure your aplet’ s VIEWS menu. Once the aplet’ s VIEWS men u is configure d, it remains that way until you run SE TVIEWS agai n. Y ou do no t n eed to inc lu de th is pr og ram fo r y our aple t to work, but it is useful to specify that the progr am is attached t o the aplet, and tr ansmitted whe n the aplet is transmitted. 7. Return to the pr ogram catalog. Th e programs that y ou created sh ould appear as fol l ows: 8. Y ou must now RUN the program EXP .SV to execute t he S ETVIEWS command and creat e the modified VIEWS menu . Check that the name of the new aplet is highligh te d in th e APLET view . 9. Y ou can now re turn to the AP LET library a nd press ST AR T to run yo ur new a plet.
15-14 Prog ramming Programmin g commands This section d escribes the comman ds for programming with HP 39G/4 0G. You can ent er these com mands in yo ur program by typing them or by accessing th em from the Commands menu. Aplet commands These comm and s control aplets. CHECK Checks (selec ts) the corresponding func tion in the current aplet. For exa mple, Check 3 woul d check F3 if the current aplet is Fun ction. Then a ch eckmark would appear n ext to F3 in Symb olic view, F3 woul d be plotted in Plot view , and eval uate d in Nu meric view. CHECK n SELECT Selects the n amed aplet an d makes it th e current aplet. Note: Quotes are need ed if the name cont ai ns spaces or other special characters. SELECT apletna me SETVIE WS The SETVIEWS c ommand is used to define en tries in the VIEWS menu for aplets th at you custo mize. See “About customizi n g an aplet” on page 15-9 for an ex amp le of using the SETVIEWS co mma nd. When yo u use the SETVI EWS comman d, the aplet’ s standar d VIEWS m enu is deleted an d the cu stomized m enu is used in its pl ace. You only need to a pply the co mmand to an aplet once. The Vi ew men u changes remain un less you apply the command ag ain. Typica ll y, you develo p a program tha t uses the SETV IEW S command on ly. The command co ntains a trio of argum ents for each menu op tion to create, or prog ram to attach. Keep the following poin ts in mind when usin g thi s comma nd: • The SETVIEWS command dele tes an aplet’ s standard V i ews menu op ti ons. If you wa nt to use any of the stand ard optio ns on yo ur reco nfigured VIEWS m enu, you must include the m in the conf iguration. • When yo u invoke the SETVI E WS co m ma n d, the changes to a n aplet’ s VIEWS menu remain with the aplet. Y ou n eed to invoke the co mma nd on the aplet again to ch ang e the VIEWS menu.
Progr amming 15 -15 • All the program s th at are cal led from the VIEWS menu are tran sferred when the aplet is transferred , for example to anoth er cal cu lator or to a PC. • As par t of the VIEWS me nu config uration , you can specify p rograms that you want tran sferred with th e aplet, bu t are not calle d as menu op tions. For e xample, these can be su b-programs that menu op tions use, or the program tha t defines the aplet’ s VIEWS menu. • Y ou can i nclude a “Star t ” option in t he VIEWS menu t o specify a program that y ou want to run automatica lly when the aplet starts. This program typicall y sets up the aplet’ s in itial config uration. Th e Start option on th e menu is also useful for resetting th e aplet. Command syntax The syntax for th e co mmand is as follows: SETVIEWS " Pr ompt1 " ;" Pr ogramName1 " ; V iewNumber1 ; " Pr ompt2 " ;" Pr ogramName2 " ; V iewNumber2 : (Y ou can repeat as man y Prompt/Progr amName/ ViewNumber trios of argumen ts as you like.) Within eac h Prompt/ProgramName/ViewNumber trio, you separate each item with a semi-colon. Prompt Prom pt is the text th at is displayed for th e corresponding entry in the Views menu. Enclo se the pro mpt text in double quote s. Associa ting progr am s with your aple t If Prompt consis ts of a single sp ace, then no entry appea rs in the view menu. Th e pro gram specified in the Pr ogramName item is ass ociated with the aplet and transferred whene ver the aplet is tra nsmitted. Typic ally, you do this if you want to transfer the Se tviews program wi th the aplet, o r you want to transfe r a sub- progra m that ot her me nu progr ams use .
15-16 Prog ramming Auto-run programs If the Prompt item is “Start” , th en the ProgramName program runs whenever yo u start the aplet. Th is is useful for setting u p a program to configure the aplet. Use rs can select the Start item from th e Views menu to reset the aplet if they change config uration s. You can also define a menu it em called “Re set” which is autorun if the user choo ses the RESET bu tto n in the APLET view. ProgramName ProgramName is the name of the program th at runs when the correspond ing menu en try is sel ected. All prog rams that a re identified in the apl et’s SETVIEWS command are tran sferred when the aplet is transmitted. ViewN umber V iewNumber is the numbe r of a view to sta rt after the program finishe s running. For example, if yo u want the menu op tion to display the P lot view when the associ ated program finish es, you woul d spe cify 1 as the ViewNumber valu e . Including s tandard menu optio ns To include one of an aplet’s standard View me nu options in your cust omized menu, se t up the argu ments trio as follo ws: • The first argument spe cifies the menu item na me: – Leav e the argument e mpty to use t he standard V iews menu na me for the item, or – Ent er a menu item name to rep lace the standard name. • The secon d argument specifies t he p rogram to r un: – Leav e the argument empty to ru n t he standard menu opti on. – I ns ert a progra m nam e to run the prog ram before the standard menu option is selected . • The thir d argument specifi es the view and t he menu number for the item. Determ ine the men u number from the V iew numbers tab l e below . Note: SETVIE WS with no ar guments r esets the views t o defaul t of the base ap let.
Progr amming 15 -17 View numbers The views are numb ered as follows: UNCHECK Un checks (unsele cts) the corres po nding functi on i n the current apl et. For example, Unchec k 3 would uncheck F3 if the current aplet is Func tio n. UNCHECK n Branch commands Branch commands let a program make a decision base d on th e result of one or more tests. Unlike the other programm in g commands, th e branch comm ands work in logi cal groups. Therefore, t he co mmands are described to get her rather than each ind ependently. IF...THEN...E ND Executes a sequ ence of commands in t he t r ue–clause only if the test–clause e valuates to true. Its syntax is: IF test–claus e THEN true–c lause END Example 1 &A : IF A==1 THEN MSGBOX A " EQUALS 1" : END 0 1 2 3 4 5 6 7 8 9 10 HOME Plot Symbol ic Numeric Plot- Setup Symbol ic-Se tup Numeric-Setup Views Note Sket ch vi ew Aplet Catalo g 11 12 13 14 15 16 17 18 19 20 21 Lis t Cata log Matrix Catalo g Notepad C atalog Programs Cata log Plot-Detai l Plot-Table Overlay Plot Auto scale Decimal Integer Trig
15-18 Prog ramming IF... THEN... ELSE... E ND Executes t he true-clause sequence of comma nds if the test- clause is tr ue, or the false-clause sequence of commands if th e test-clause is f alse. IF test–cla use THEN true-claus e ELSE false-clause END Example 1 &A : IF A==1 THEN MSGBOX A " EQUALS 1" : ELSE MSGBOX A " IS NOT EQUAL TO 1" : END CASE...END Executes a series o f test-clause comma nd s that execute the appropri at e true-cla use sequence of commands. Its synt ax is: CASE IF test-clause 1 THEN true-cl ause 1 END IF test-clause 2 THEN true-cl ause 2 END . . . IF test-clause n THEN true-cl ause n END END When CASE i s executed, te st-claus e 1 is evalua ted. If th e te st is true, true-c lause 1 is exec uted, and e xecution skips to END. If test-cl ause 1 if false, execut i on proceeds to te st-cl ause 2 . Execution with the CASE structu re continues un til a true- clause is executed (or until all the test-cl aus es evalua te to false). IFERR... THEN... END... Many con ditions are auto matically recog nized by the HP 39G/40G as error conditio ns and are automatic ally treated as errors in programs. IFERR...THEN.. .END allows a progra m to intercept er ror conditio ns that oth erwise would cause the progra m to abort. Its synta x is: IFERR trap-c lause THEN err or-clause END
Progr amming 15 -19 RUN Runs th e named p rogram . If your progra m name c ontains special ch aracters, such as a space, then you must enclose the file nam e in doubl e quotes ( " " ). RUN " pr ogram na m e " or RUN pr ogramn ame STOP Sto ps the current program. STOP Drawing commands The Drawin g com mands act on the displa y. Th e scale of th e display depends on th e current aplet’ s Xmin, Xmax, Ymin , and Ymax va lues. The following exa mples assume the HP 39G/40G de fault setting s with the Func tion aplet a s the current ap le t. ARC Draws a circular a rc, of given rad ians, whose centre is at ( x ,y ) The arc i s drawn from st art_an gle_m easurem ent , and end_an gle_measureme nt . ARC x; y; radius ; st art_an gle_me asurme nt ; end_an gle_measurment : Example ARC 0;0;2;0;360: FREEZE: Draw s a ci r cle ce n t er ed at (0,0) of radius 2. The FREEZE comma nd causes the circle to remai n di splayed on th e screen until yo u press a key . BOX Dra w s a bo x w ith op po s ite cor ne r s ( x1,y1 ) and ( x2,y2 ). BOX x1; y1; x2; y2: Example BOX -1;-1;1;1: FREEZE: Draws a bo x, lowe r corn er at (–1,– 1), u pper  corn er at (1,1) ERASE Clears th e display ERASE:
15-20 Prog ramming FREEZE Halts the program, fre ezing the current display. Ex ecution resumes when an y key is pressed. LINE Draws a l ine from ( x1 , y1 ) to ( x2, y2 ). LINE  x1 ; y1; x2 ; y2  PIXOFF T urns off the pixel at the specified coord inates ( x,y ). PIXOFF x ; y  PIXON Turns on the pi xel at the sp ecified coord inates ( x,y ). PIXON x ;y  TLINE Toggles the pi xels along the lin e from ( x1, y1 ) to ( x2, y2 ) on and off. Any pixel that wa s turned off, i s turned on; a ny pixel that was turne d on, is turned off. T LINE can be used to erase a line. TLINE x1 ; y1; x2; y2  Example TLINE 0;0;3;3  Erases previou sl y drawn 45 degree line from (0,0) to (3,3), or d raws that line if it doesn’t already exist. Graphic commands The Graphic com mands use the graphics variab les G0 through G9—or the Page variable from Sk etch—as grap hicname arguments. The position ar gument ta kes the fo rm ( x,y ). Position coord inates depend on t he cu rrent aplet's scale, which is specifi ed by Xmin, Xmax, Ymin, and Ymax . The upper left corner of t he target graphic ( graphi c2 ) is at (Xmin,Ymax). You can capt ure the c urrent display a nd st ore it in G 0 by simultaneously pressing >2 1@ >3 /27@ . DISPLAY → Stores the cu rrent display in graph icname . DISPLAY → gr aphicnam e → DISPL AY Displays grap hic from gr ap hicname in the display. → DISPLAY gr aphicnam e
Progr amming 15 -21 → GROB Crea tes a graphic from expression , us ing fo nt_si ze , and stor es the resulting g raphic in graphic name . Font si zes are 1, 2, o r 3. If the fontsize argument is 0, t he HP 39G/40G creates a graphi c displ ay like that create d by the SHOW operation. → GROB graphicn ame ; expre ssion ; fontsize GROBNOT Replaces g raphic in gra phicname with bitwise-inverted graphic . GROBNOT grap hicname GROBOR Using th e logical OR, sup erimposes grap hicn ame2 onto graphi cname1 . The upper left corner of graphicname 2 is placed a t position . GROBOR grap hicnam e1 ; position ; graphi cname2 GROBXOR Usi n g the logical XOR, su perimposes graphi cname2 onto graphi cname1 . The upper left corner of graphicname 2 is placed a t position . GROBXOR grap hicname1 ; position ; grap hicnam e2 MAKEGROB Crea tes graphic wi th given width, height, and hexadecimal data, and store s it in graphicname . MAKEGROB grap hicnam e ; width ; heig ht;hexda ta PLOT → Stores th e Plot v iew disp lay as a graphic in gr aphicn ame . PLOT → grap hicnam e PLOT → and DISPLAY → can be used to tr ansfe r a copy of the current PLOT view int o t he sk et ch view of the aplet for later use an d editing. Example 1 & P ageNum: PLOT →Page: FREEZE: This program st ores the c urrent PLOT view to the first p age in the ske tch view of th e current aplet and then display s the sketch as a graphic obj ect un til any ke y is pressed. → PLOT P uts graph fro m graphicname into the Plot view displ ay. → PLOT grap hicnam e:
15-22 Prog ramming REPLACE Repla ces portion of g raphic in graphicname 1 with grap hicname2 , s tarting at positio n . REPLACE also works for lists and matrices. REPLACE graphicn ame1 ;( positio n) ; graphicna me2: SUB Extrac ts a portion of the na med graphic ( or list or matrix) , a nd stores it in a new vari abl e, name . The por tion is spec ified by positi o n and positions. SUB name ; g raphi cname ; ( posi tion); ( positions ): ZEROGROB Create s a blan k grap hic with given width and height , and stores it in graphi cname . ZEROGROB gr aphicnam e ; width ; height: Loop comm ands Loop structure s allow a program to execu t e a rout ine repeatedl y. The HP 39G/40 G has t hree loop struct ures. The example prog rams below illustra t e each of these structures incremen ting the vari able A from 1 to 12. DO…UNTIL …END Do ... Until ... End is a loop structur e that executes the loop- clause repeatedly un til te st-cl ause returns a true (nonzero) result. Because t he t est i s executed after the lo op-clause, the loop-claus e i s al ways executed at least on ce. Its syntax is: DO loop-cl ause UNTIL test-clause END 1 & A: DO A 1 & A UNTIL A = = 12 END WHILE … REPEAT… END While ... Repeat ... End is a loop structu re that repeated ly evaluates test-clau se and executes loop-clause sequence if the test is tru e. Because the t est-clause is executed before the loop-cla use, the loop-clause is not execut ed if the test is initially fa lse. Its syntax is: WHILE test-clause RE PEAT loop-clause END 1 &A: WHILE A < 12 REPEAT A 1 & A END
Progr amming 15 -23 FOR…TO…STEP ...END FOR name= start-expression TO end-expression [STEP increment ]; loop-c lause END FOR A=1 TO 12 STEP 1; DISP 3;A: END Note that t he STEP pa rameter is optio nal. If it is o mitted, a step valu e of 1 is assumed. BREAK Terminates loo p. BREAK Matrix commands The matrix com mands take variab les M0–M9 as argument s. ADDCOL Ad d Column. In serts values into a column before column_n umber in the specif ied matrix . You enter the val u es as a vec tor. The values mu st be separate d by commas and the number of valu es must be the same as the number of rows i n the matrix name . ADDCOL name;[ value1,... ,value n ]; column_nu mber ADDROW Ad d Row. Inserts values into a row before row_nu mber in the specified matrix. You en ter the values as a vector. The values must b e s epar ate d by com mas and the n umb er of va lue s mu st be t he sam e as t he num ber of colu mns in the matri x name . ADDROW name;[ valu e 1 ,..., value n ]; r ow_nu mber DELCOL Del ete C olumn . Dele tes the sp ecifie d co lumn f rom th e specified m atrix . DELCOL name; column _number DELROW Delete Row. Deletes t he specified row from the specifi ed matrix . DELROW name ; row_number EDITM AT Starts the Matrix Edit or and displays the specifi ed matrix . If used in p rogramming, returns to the program when use r presses 2.a . EDITMAT name
15-24 Prog ramming RANDMAT Crea tes random ma trix with a specified n umber of rows and column s and stores the re sult in nam e ( name must b e M0...M9 ). The entries will be integers ranging from –9 to 9. RANDMAT nam e ; ro ws ; co lumns REDIM Redim ensi ons the specif i ed matrix or vec tor to size . For a matrix, size is a list of two in tegers { n1 , n2 }. For a vector, size is a list co ntaining one i nteger { n }. REDIM name; si ze REPLACE Replaces po rtion of a matrix or vecto r stored in na me with a n object start ing at position start . start for a matrix is a list containi ng two numbe r s; for a vector, i t is a single numbe r. Replace also wo rks with lists and graph ics. REPLACE nam e ; start ; obje ct SCALE Multipli es the specifi ed row_numbe r of the specifi ed matrix by va lue . SCALE name; va lue ; ro w n um b e r SCALEADD Mult iplies the row of the matrix name by valu e , then adds this result to th e second specified ro w. SCALEADD nam e ; valu e ; ro w1 ; ro w 2 SUB Extracts a sub- ob ject— a porti on of a list, matri x, or graphic from object —and stores it in to name . start and end are each specified usi ng a list with two numb ers for a matrix, a n umber for vect or or lists, or an ordered pa ir, (X,Y), f o r graphics. SUB name ; object; start; end SWAPCOL Swaps Colu mns. Exchanges col umn 1 an d column2 of the specified matrix . SWAPCOL name ; colu mn1; col umn2 SWAPROW Sw ap Rows . Exchanges row1 and row2 in t he sp ecified matrix . SWAPROW nam e ; ro w1 ; row 2
Progr amming 15 -25 Print command s These comma nds print to an HP infrare d printe r, for exam ple the HP 82 24 0B printer. N ot e: The HP 40G does not ha ve an infrared po rt and will not p rint to an infra red printer. PRDISPLAY Prints the conte nts of the displ ay. PRDISPLAY PRHISTORY Prints all ob jects in the histo ry. PRHISTORY PRVAR Prints name and c ontents of vari ablename . PRVAR vari ablena me You can also use t he PRVAR command to print th e contents of a prog ram or a note. PRVAR pr ogr amname ;PROG PRVAR note name;NOTE Prompt comm ands You can use t he following comm ands to prom pt users for input du ring your program or to provide inf ormation to us ers. BEEP Bee ps at the frequency and for the time y ou speci fy . BEEP fr equenc y ; seconds CHOOSE Create s a Choose Box, wh i ch is a box contai ning a list of options from wh ich the u ser cho oses one . Each optio n is number ed, 1 thro ugh n . The result of the choose command is to stor e the num b er of the opt ion chos e n in a va r ia bl e. The syntax is CHOOSE default_ option_numb er ; title ; option 1 ; option 2 ; ... option n where defau lt_option_n umber is the num ber of the o p ti on that will be h ighlighted b y default whe never the Cho ose Box is disp layed, ti tle is the tex t displayed in th e title bar of the Choos e Box, and option 1 ...optio n n are the options liste d in the Choos e Box.
15-26 Prog ramming Example 3 & A:CHOOSE A; "COMIC STRIPS"; "DILBERT"; "CALVIN&HOBBES"; "BLONDIE"; DISP Displays textitem i n a row of the disp lay at the line_number . A tex t item con sists of any n umber o f exp ressi ons an d quote d strings of t ext. The expressi ons are evaluated and turned into strings. Lines are numbered from the top o f the screen, 1 being the to p and 7 be ing the b ottom. DISP line_ number;textitem Example DISP 3;" A is" 2 2 Result: A is 4 (displaye d on line 3) DISPTIME Displays t he current date and tim e. DISP TIME To set the d ate and time, sim ply store the correc t settings in the date an d time variab les. Use the following fo rmats: M.DDYYYY for the date and H.MMSS for the time. Examples 5.152000 & DATE( sets the date to Ma y 15, 20 00). 10.1500 & TIME (sets the time to 10:15 am). EDITM A T Mat rix Edi tor. Open s the Matrix editor for the specifi ed matrix. Returns to the pro gram when user presses 2. a EDITMAT matrixname The EDITMAT command can also be use d to create matrices. 1. Press >6 ,)7@ CMDS >@ *A, >6,1@ 2.a 2. Press >$/3 $@ M 1, and then press >(17(5@. 3. The Matri x catalog opens with M 1 av ailable for editin g. EDITMAT matrixname is a shortcut to op en in g the matrix editor wit h matrixname .
Progr amming 15 -27 FREEZE Thi s command pre vents the displa y from bein g updated af ter the pr ogram ru ns. Thi s allows you to vie w the gra phics create d by the progr am. Cancel FREEZE by press ing an y key. FREEZE GETKEY Waits f or a key, the n stores th e keycode rc .p in name, whe re r is row number, c is col umn numb er, an d p is ke y-plane number. Th e key-planes nu mbe rs are: 1 for unshi fted; 2 for shifted; 4 for alpha-shi fte d; and 5 for bo th al ph a-sh ifted and shifted. GETKEY name INPUT Creates an input form with a title bar and on e field. The fie ld has a la bel and a d efault value . There is text help at the bottom of the form. The user enters a value and pre sses the 2.a menu key. The va lue that the user ente rs is store d in the variable name . The title , label , a nd help items are text strings and need to be e nclose d in doub le quote s. Use >6 ,)7 @ CHARS to type the quote marks " ". INPUT name ; title, label; he lp ; defaul t Example INPUT R; "Circular Area"; "Radius"; "Enter Number";1:
15-28 Prog ramming MSGBOX Display s a messa ge box contain ing textitem. A text ite m cons ists of any numb er of ex pressio ns and quoted s trings o f text. The expressions are ev aluated and turned into strings of text. Fo r example, "AREA IS:" 2 2 become s AREA IS: 4 . Use >6 ,)7@ CHARS to type the quote m arks " ". MSGBOX textitem : Example 1 & 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 b reaks. For exam ple, pres s >6 ,)7@ NOTE and type AREA IS >(17(5@ . The positi on line MSGBOX NoteText " " π*A^2: will displa y the same m essage box as the previous examp le. PROMP T Displays an input box with name as the title , a n d pro m pts for a value for name . name can only be one cha ra cter in len g th. PROMPT nam e WAIT Halts progra m executio n for the sp ecified nu mber of seconds. WAIT secon ds
Progr amming 15 -29 Stat-One and Stat-Two commands The following comm ands are used for analysis of on e- variable a nd two-variable statistical data. Stat-One commands DO1VSTATS Calcul ates STATS using datasetname and stores t he results in the corre sp onding variab les: N Σ , Tot Σ , Mean Σ , PVarΣ , SVar Σ , PSDe v, SSDev, M in Σ , Q1 , Median, Q 3, and Ma x Σ . Datasetname can be H1, H2, ..., or H5 . Datasetname must define a t least two dat a points. DO1VSTATS datasetname SETFREQ Defines datasetname freque ncy accord ing to col umn or val ue. Datasetname can be H1, H2,..., o r H5, column can b e C0–C9 and val ue can be any positiv e integer. SETFREQ dataset name ; column or SETFREQ definition; value SETSAMPLE Defines datasetname sample accord ing to column. Datasetname ca n be H1–H5, and col umn can be CO–C9. SETSAMPLE datasetname ; column Stat-Two comm ands DO2VSTATS Calcul ates STATS using datasetname and stores t he results in correspondi ng variables: Mean X, Σ X, Σ X2, Mea nY, Σ Y, Σ Y2, Σ XY, Corr, PCov, SCov, and RELERR. Data setname can be SI, S 2,..., or S5 . Data setname must define at least four pairs of da ta points. DO2VSTATS datasetname SETDEPE ND Defines da tasetname dependent col umn . Datase tname can be S1, S2, …, or S5 an d colum n can be C0–C9 . SETDEPEND datasetname ; column SETINDEP Defines datasetna me independen t column . Datasetname can be S1, S2,…, or S5 and column c an be C0 –C9. SETINDEP datasetname ; column
15-30 Prog ramming Storing and r etrieving variables in programs The HP 39G/40G ha s both Ho me var iables and Aple t variables. Home variables are used for real numbers, complex numbers, g raphics, lists, and mat r ices. Home variables keep the same va lues in HOME and in aplets. Aplet variab les are those whos e values depend o n the current aplet. The a plet variables are used in programming to e mulate the definiti ons and settings y ou make when worki ng with aplets int erac tiv ely. You use the Variable menu ( >9$56@ ) to retrieve either Ho me variables or apl et variab les. See “The VARS menu” on page 11-4. Not al l vari ables are availabl e i n every aplet. S1fit–S5fit, for example , ar e only ava ila bl e in the Sta tistics aplet. Under each v ariable name is a list o f the aplets whe re the variable ca n be used. Plot-view variabl es The follo wing aplet va riables cont rol the Plot v iew. Area )XQFWLRQ Contains the last val ue found by the Area func tion in Plot - FCN menu . Axes $OO$SOHWV Turns axes on or o ff. From Plot Setu p, check (or unc heck) AXES . or In a program, type: 1 & Axes —to tu rn axes on (d efault). 0 & Axes —to turn axes off. Connect )XQFWLRQ 3DUDPHWULF 3RODU 6ROYH 6WDWLVWLFV Draws lines between successively plott ed points. From Plot Setu p, check (or unc heck) CONNECT . or In a program, type 1 & Connect —to c onnect plotte d points (defa ult, except in S tatistics where th e default is of f). 0 & Connect —n ot to con nect plot ted points.
Progr amming 15 -31 Coord )XQFWLRQ 3DUDPHWULF 3RODU 6HT XHQF H 6ROYH 6WDWLVWLFV Turns th e coordinat e-display mo de i n Plot view on or off. From Plo t view, use the Menu mean key to toggle coord inate disp la y on an off . In a program, type 1 &Coord —to turn co ordinate disp lay on (defa ult). 0 &Coord —to turn coor dinate disp l ay off. Extremum )XQFWLRQ Contai ns the last v alue found by the Extremum operatio n in the P lot-FC N menu. FastRes )XQFWLRQ 6ROYH Toggles re solution betwe en plotting i n every oth er column (faster ), or plott i ng in every co lumn (mor e detail). From P l ot Setup, cho ose Faste r or More Deta il. or In a program, type 1 &FastRes —for faster (default). 0 &FastRes —for mo re detail. Grid $OO$SOHWV Turn s th e backgrou nd grid in Plot vie w on or off. From P lot setup, che ck (or uncheck) GRID . or In a program, type 1 &Grid to tu rn the g rid on. 0 & Grid to tu rn the grid of f (defau lt). Hmin/Hmax 6WDWLVWLFV Defines mi nimum and maximum value s for histogram bars. From Plot S etup for one-variab le statistics, set valu es for HRNG . or In a program, type & Hmin  & Hmax where n 1 n 2 n 2 n 1 >
15-32 Prog ramming Hwidth 6WDWLVWLFV Sets th e width of histogr am bars. From P lot Setup i n 1VAR s tats set a v alue for Hwid th or In a program, type n & Hwidth Indep $OO$SOHWV Defines the value of the ind epe nd ent vari able use d in tracin g mode. In a program, type n & Indep InvCross $OO$SOHWV Toggles be tween solid cr osshairs or inv er ted crosshairs . (Invert ed is useful if the b ackground is so lid). From Plot Setu p, check (or unc heck) InvCross or In a program, type: 1 & InvCross —t o inv ert th e cro sshair s. 0 & InvCross —for solid crosshairs (def ault). Isect )XQFWLRQ Cont ains the la st value fo und by th e Interse ction fun ction in the Plot - FCN menu. Labels $OO$SOHWV Draws labels in Plot view showing X and Y ranges. From Plot Setu p, check (or unc heck) Labels or In a program, type 1 & Labels —to tu rn labels on. 0 & Labels —to turn labels off (default).
Progr amming 15 -33 Nmin / Nmax 6HT XHQF H Defines the min imum and maximum indep endent variable values. Appears as th e NRNG fields in the Plot Setup inp u t form. From P l ot Setup, enter values for NRNG . or In a program, type & Nmin & Nmax where Recenter $OO$SOHWV Recenters at the crosshairs locations when zooming. From Pl ot-Zoom-Se t Factors, ch eck (or unchec k) Recenter or In a program, type 1 & Recenter — to turn recenter on (defa ult). 0 & Recenter —to turn recenter off. Root )XQFWLRQ Contai ns the last val ue found by th e Root function in the Plot- FC N me nu. S1mar k–S5m ark 6WDWLVWLFV Defines the m ark to use for stat istics 2-variable sca tter plots. From Plot S etup for two-variab le statistics, S1mark- S5mark , then c hoose a mark. or In a program, type n & S1mark where n is 1,2,3,...5 SeqPlot 6HT XHQF H Toggle s type of s equence plot: Stairs tep or Cob web. From Pl ot Setup, select SeqPlot , the n choose Stairstep or Cobweb . or In a program, type 1 &SeqPlot —fo r stai rste p. 2 & SeqPl ot — for cobw eb. n 1 n 2 n 2 n 1 >
15-34 Prog ramming Simult )XQFWLRQ 3DUDPHWULF 3RODU 6HTXHQFH Toggles be tween simul taneous and seque ntial graphi ng of all selected expressio ns. From Plot Setu p, check (or unc heck) _ SIMULT or In a program, type 1 & Simult —for simultan eo us graphing. 0 & Simult —f or sequ ential gra phing. Slope )XQFWLRQ Cont ains the la st value fo und by th e Slope f unction in the Plot –FCN menu . Stat Plot 6WDWLVWLFV Toggles type of 1– varia b le statistics pl ot b et ween Histogr am or Box–an d–Whiske r . From Plot Se tu p, s elec t StatPlot , then choose Histogram or BoxWhisker . or In a program, type 1  & StatPlot —for Histogra m. 2 &StatPlot —fo r BoxW hisker. Umin/Umax 3RODU Defines the mi ni mum and maximum ind ependent val ues. Appears as the URNG field in the Plot Setup inpu t form. From th e Plot Setup input form, e nter values for URNG . or In a program, type & Umin & Umax where Ustep 3RODU Defines th e st ep size for an indepen dent variabl e. From th e Plot Setup input form, e nter values for USTEP . or In a program, type n & Ustep where n 1 n 2 n 2 n 1 > n 0 >
Progr amming 15 -35 Tmin / Tmax 3DUDPHWULF Defines the min imum and maximum indep endent variable values. Appears as th e TRNG field in th e Plot Setup input form. From P l ot Setup, enter values for TRNG . or In a program, type &Tmin &Tmax where Tracing $OO$SOHWV Turns t racing mode on or off in Plot vie w. In a program, type 1 & Tracing —to turn Tracing mod e on (default). 0 & Tracing —to t urn Tracing mod e off. Tstep 3DUDPHWULF Defines the step siz e for an independent varia bl e. From the Plot Setup in put form, enter values for TS TEP . or In a program, type n & Tstep where Xcro ss $OO$SOHWV Define s the hor iz o nta l co or d in ate of cro ss ha i rs . On ly works with TRACE off. In a program, type n & Xcross Ycro ss $OO$SOHWV Define s the verti cal coordi nate of cro sshairs . Only works wit h TRACE off. In a program, type n & Ycross n 1 n 2 n 2 n 1 > n 0 >
15-36 Prog ramming Xtick $OO$SOHWV Defines th e di stance between t ick marks for the hori zontal axis. From th e Plot Setup input form, en ter a value fo r Xtick . or In a program, type n & Xtick where Ytick $OO$SOHWV Defines the dist ance between tick ma rks for the vertical axis. From th e Plot Setup input form, en ter a value fo r Ytick . or In a program, type n & Ytick where Xmin / Xmax $OO$SOHWV Defines the mi nimum and maximum ho rizontal values of the plot screen . Appears as the XRNG fields (horiz ontal range) in the Plot Setup inpu t form. From P lot Setu p, enter v alues fo r XRNG . or In a program, type & Xmin & Xmax where Ymin / Ymax $OO$SOHWV Defines the mini mum and maximum vert ical values of the plot screen. Appears as t he YRNG fields (vert ical range) in the Plot Setu p inp ut form . From P lot Setup, enter the valu es for YRNG . or In a program, type & Ymin & Ymax where n 0 > n 0 > n 1 n 2 n 2 n 1 > n 1 n 2 n 2 n 1 >
Progr amming 15 -37 Xzoom $OO$SOHWV Sets the hori zon tal zoom factor. From Plot-ZOOM-Set F actors, enter the value for XZOOM . or In a program, type n & XZOOM where Yzoom $OO$SOHWV Sets the verti cal zoom factor. From Plot-ZOOM-Set F actors, enter the value for YZOOM . or In a program, type n & YZOOM Sym bol ic- vi ew v ar iab l e s The followin g a pl et v ariab le s availa b le in t he Symbolic vie w. Angle $OO$SOHWV Sets the an gle mode. From Symb olic Setu p, choose Degree s , Radians , or Grads for angle measure. or In a program, type 1  & Angle —for Degrees. 2 & Angle —for Radians. 3 & Angle —fo r Grads. F1...F9, F0 )XQFWLRQ Can co ntain an y expres sion. Ind epende nt variabl e is X . Example ’SIN( X )’ & F1( X ) In the above examp le, you mu st put sing le quot es around t he expres sion to keep it from be ing evalu ated befor e it is st ored. Use >6 ,)7@ CHARS to type the single quot e mark. n 0 >
15-38 Prog ramming X1, Y1...X 9,Y9 X0,Y0 3DUDPHWULF Can cont ai n any expre ssion. Indep endent var ia ble is T. Example ’SIN(4*T)’ & Y1( T):’2*SIN(6*T)’ STO & X1(T) R1...R9, R0 3RODU Can contai n any expre ssi on. Indepe nd ent variabl e is θ . Example ’2*SIN(2* θ)’ & R1( θ) U1...U9, U0 6HTXHQFH Can contai n any expressi on. Independ ent variabl e i s N. Example RECURSE (U,U(N-1)*N,1,2) & U1(N) E1...E9, E0 6ROYH Can contai n any equatio n or expression . In depend ent varia ble is selecte d by highlig hting it in Numeric View. Example ’X Y*X-2=Y’ & E1 S1fit...S5 fit 6WDWLVWLFV Defines the ty pe of fit to be used by th e FIT oper ation in drawi ng the re gression li ne. From S ymbolic Setup view, specify the fit in the field fo r S1FIT , S2FIT , etc. or In a program , store one of the f ollowing const ant names or numbers 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 & S2fit or 6 & S2fit
Progr amming 15 -39 Numeric-view var iables The follo wing aplet va riables control the Numeric view. The value of the varia bl e appl ie s to the cu rrent ap le t only. C1...C9, C0 6WDWLVWLFV C0 throug h C9 , for columns of d ata. Can contain lists. Enter data in the Num eric view or In a program, type LIST & C n where n = 0, 1, 2, 3 ... 9 Digits $OO$SOHWV Number of decima l 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 & Digits where Except in Solve , the value of Digits ta kes effect only after the current aplet is saved with a new name. Until then, HDigit is in e ffect. 0 n 11 <<
15-40 Prog ramming Format $OO$SOHWV Defines the nu mber display format. From Solve’ s Numeric Setu p view, choose Standard , Fixed , Scientific , or Engineering in the Number Format field. or In a program, store the constant name (or its number) into the variabl e Format . 1. Standard 2. Fixed 3. Scientific 4. Engineering Note: Fract ion is not a v alid mode i n aplets. Except in Solve, t he value of Format takes effect only after the current aplet is saved with a new name. Until the n, HFormat is in effect. Example Scientific & Format or 3 & Format NumCol $OO$SOHWVH[FHSW 6WDWLVWLFVDSOHW Defines th e hi ghlighted col u mn in Numeric view. In a program, type n & NumCol where n can be 0, 1, 2, 3, 4, 5, 6, 7, 8 , 9. NumFont )XQFWLRQ 3DUDPHWULF 3RODU 6HTXHQFH 6WDWLVWLFV Toggles th e font size in Num eric view. Does not appear in the Num Setu p input form. Corresponds to the BIG k ey in Numeric view. In a program, type 0 & NumFont for small (default). 1 & NumFont for big. NumIndep )XQFWLRQ 3DUDPHWULF 3RODU 6HTXHQFH List of indepe ndent valu es used by Build Yo ur Own Ta ble. In a program, type LIST & NumIndep
Progr amming 15 -41 NumRow $OO$SOHWVH[FHSW 6WDWLVWLFVDSOHW Define s the high lighted ro w in Nume ric view. In a program, type n & NumRow where NumStart )XQFWLRQ 3DUDPHWULF 3RODU 6HT XHQF H Defines the sta rting value for a table in Numeric view. From Num Se tu p, enter a value for NUMSTART . or In a program, type n & NumStart NumStep )XQFWLRQ 3DUDPHWULF 3RODU 6HT XHQF H Defines the step size (increment value) for an independent variable in Nu meri c vi ew. From Num Se tu p, enter a value for NUMSTEP . or In a program, type n & NumStep where NumType )XQFWLRQ 3DUDPHWULF 3RODU 6HT XHQF H Choose a ta bl e format. From Nu m Se tup, choos e Automatic or Build Your Own . or In a program, type 0 & NumType for Build Y our Own. 1 & NumType for Au tomatic (default). NumZoom )XQFWLRQ 3DUDPHWULF 3RODU 6HT XHQF H Defines the Zoom factor i n the Numeric v iew. From Num Setu p, type in a v alue for NUMZOOM . or In a program, type n & NumZoom where n 0 > n 0 > n 0 >
15-42 Prog ramming Stat Mode 6WDWLVWLFV Toggles be tween 1–va riable and 2– var i able statis t ics in the Statistics a plet . Do e s n ot app ear in th e P lot Se tu p in pu t f orm . Corresp onds to th e 9 $5 a and  9$5 a menu ke ys in Numeric View. In a program, store the constant name (or its number) into the variable StatMode. 1VAR = 1 , 2VAR = 2. Example 1VAR & StatMode or 1 & StatMode Note variables The follo wing aplet va riable is availab le in Note vie w. NoteText $OO$SOHWV Use NoteText t o recall text pr eviously entered in Note view. Sketch va riables The following ap let variables are ava ilab le in Sketch view. Page $OO$SOHWV Defines a p age in a sket c h s e t . A s k et ch s et can co nt ain u p to 10 grap hics. The graphics c an be viewed one at a time us ing the A3$*( a and 3 $*(  a keys . The Page variable refers to the currently displayed page of a sket ch s et. In a program, type grap hicname & Page PageNum $OO$SOHWV Index for referring to a p articular page of the sketch set (in Sketch vi ew). In a progra m, type the page that is shown when >6 ,)7@ SKETCH is pressed. n & PageNum
Extend ing apl e ts 16-1 16 Extending apl et s Aplets ar e th e ap plication enviro nments where you exp lore different classe s of mathematical operat ions. You can exten d the capability of th e HP 3 9G/ 40 G in the follow ing wa ys: • Create new aplets, b ased on e xisting aple ts, wit h specifi c config urations suc h as angle measure, graphical o r tabular settin gs, and annotatio ns. • T ransmi t aplets between HP 39G calcu lators via an infra red l ink. • Downlo ad e-lessons (teachin g aplets) from the Hewlett - Packard’ s Calculat or web site. • Prog ram new aplets. See chapter 15 , Programmi ng , for further details. Creating new ap lets based on existin g aplets You can create a ne w aplet based on an ex isting aplet. To create a ne w aplet, save an existin g aplet under a new name, then modify the aplet t o add the co nfiguration s and the functiona lity th at yo u wa nt . You c an se nd yo ur a p let to o th er calculat o rs so that other peopl e can use it. Informatio n that defines a n aplet is save d automatically as it is entered in to the calc ulator. To keep as much memo ry available for storage as p ossible, delete a ny aplets yo u no longe r need.
16-2 Extend ing a pl ets Aplet Keys Example: To create a new aplet from an existing Sol ve aplet A simple examp l e of a customized aplet is th e T RIANGLES aplet. Thi s aplet is a copy of the So lve aplet contain ing the formulas c ommonly us ed in calculatio ns involving right– angled tria ng les. 1. In APLE T , hig hlight Solve and SA VE it un der the n ew name. >$3/(7@ Select Solve 6$ 9(_ >$/3 $@ T R I A N G L E S >(17(5@ 6 7$5 7_ 2. Enter the four formul as: >6,1@ >$/3 $@ θ >@ _ >$/3 $@ O > j @ >$/3 $@ H >(17(5@ >&26@ >$/3 $@ θ >@ _ >$/3 $@ A > j@ >$/3 $@ H >(17(5@ >7$1@ >$/3 $@ θ >@ _ >$/3 $@ O > j @ >$/3 $@ A >(17(5@ >$/3 $@ A >; @ >@ >$/3 $@ B >;  @ _ >$/3 $@ C >;  @ >(17(5@ Key Meani ng 6 $9(_ Saves the hig hlighted a plet with a name. 5 (6(7 _ Resets the default v alues a nd settings in the highli gh ted ap le t. This erase s any stored da ta or functio ns. 6 257_ Alphabetica lly or chronolo gically sorts the items in the Aplet Library men u list. 6 (1'_ Transmits the h ighlighted a plet to another HP 39 G/40G or a storag e devic e. 5 (&9_ (receive) Receives the aplet sent from anoth er HP 39G/ 40 G or stora g e de v ice. 6 7$57 _ (or >(17(5@ ) Opens the sel ected aplet.
Extend ing apl e ts 16-3 3. Decide wh ether you want the aplet to operate in Degre es, Radians, or Grad s. >6 ,)7@ MODES & 2 26_ Select Degrees 2._ 4. Ensure the TRIANGLES aplet is saved in the Aplet Library . >$3/(7@ The Solv e apl et can now be reset and used for other probl em s . Example: To u se the customiz ed aplet To use the aple t, si mp ly select the appropriat e form ula, change to th e Numeric view and solve fo r the missing variab le. Find the length of a ladd er leaning a gainst a vertical wal l if it forms an an gle of 35 o with the ho rizontal and ex tends 5 metres up the wa ll. 1. Select the aplet. >$3/(7@ Select TRIANGLES 67$ 57_ 2. Choose the sine form ula in E1. *k, *k, *k, *k,  _ & ._ 3. Change to the Numeri c view an d enter the known values. >180@ 35 >(17( 5@ 5 >(17(5@
16-4 Extend ing a pl ets 4. Solve for the missing valu e. 62 /9( _ The leng th of the lad der is approximat ely 8.72 metres Resetting an aple t Resetting an aplet c lears all data and resets all default setting s. To reset an aplet, open t he Library, select the aple t and press 5 (6(7 _ . You can only reset an aplet that is based on a built-in aplet if the programmer wh o created it has provided a Re set option. Annotating an aplet wi th notes The Note view ( >6 ,)7@ NOTE ) attach es a no te to th e cu rrent aplet. See Chap ter 14, “Notes and Sk et ches.” Annotating an aplet wi th sketches The Sketch vi ew ( >6 ,)7@ SKETCH ) attaches a picture to th e current aplet . See chapter 14, “Notes and sketches”. HINT Notes an d sketches that you attach to an aplet beco me part of the aplet. When you tran sfer the aplet to a nother calcula tor , the associated note and sketch are tran sferred as well. Download ing e-lessons from the web In addition to the standard aplet s that com e with the calculator, y ou can download ap lets from the worl d wide web. For example, Hewle tt-Packard’s Calculators web site contains ap lets that demonst rate certain mathema tical concepts . Not e th at you need the Graphin g Calculator Connect ivity Kit in orde r to load aplets fro m a PC. Hewlett-Pa ckard’s Calcu lators web site can be f ound at: www.hp.com/calculato rs
Extend ing apl e ts 16-5 Sending and receivin g aplets A convenie nt way to distribu te or share problems i n class and to turn in ho mework is to transmit (c opy) ap lets direc tly from one HP 39G to anoth er. This takes pla ce via t he infrar ed port. You can also sen d aplets to, and receiv e aplets from, a remote stor age devi ce (aplet d isk drive or computer) . This t akes pla ce via a cable co nnection and require s an aplet disk drive or speci al softw are runn ing on a P C (such as the PC Co nnecti vity Kit). No te: The HP 40 G does not have an IR port. A P C adapt er and unit–t o–unit cabl e is supplied i nstead. To transmit an aplet 1. Connect th e storage device to the calculator by ca ble or alig n t he two calcul ators’ infr ared port s by matching up the triang le marks on the rims of the c alculators. Place the calcu la tors no more than 2 inches (5 cm) apart. 2. Sending calcul ator: Open the Library , highlig ht the aplet to se nd, and press 6 (1'_ . – Y ou hav e t wo options: anot her HP 39 G or a di sk drive on a PC . H igh lig ht yo ur selec tion a nd p res s 2. _ . – If transmittin g to a disk drive , you h ave the o ptions of send ing to the c ur rent (defaul t) direc tory or to anot her dir ectory . 3. Receivin g cal culator: Open the aple t library and press 5(& 9_ . – Y ou hav e t wo options: anot her HP 39 G or a di sk drive (or comp ute r) . H igh lig ht yo ur sel ec tio n a nd press 2._ . The Transmit annu nciator— —is displ ayed until transmission is complete. If you ar e using the PC Connectiv ity Kit to do wnload aple ts from a PC, yo u will see a list of ap lets in the PC’s current directory . Check as many items as you wou ld like to receive.
16-6 Extend ing a pl ets Sorting items in the aplet library menu list Once yo u have enter ed information into an aplet, you have define d a n ew version of an aplet. The in formatio n is automatical ly saved under the cu rrent aplet name, suc h as “Functi on .” To cr ea te ad d itio nal a pl et s of th e sam e typ e , y ou must give the current aplet a new name. The adva ntage of storin g an aple t is to allow you to keep a copy of a work ing envir onment fo r later use. The aplet l ibrary is where you go t o manage your aple ts. Press >$3/(7@ . Hig hlight (u sing t he arrow keys) th e name of the aplet y ou want to act on. To so rt the aplet list In the aplet library, pre ss 6 257 _ . Select t he sorting sch eme and press >(17(5@ . • Chronologically produces a chro nological or der based on the date an aplet was last used. (The last-used aplet appe ars firs t, and so on.) • Alphabetically produces an alphabeti cal order by aplet n ame. To delete an aplet You cann ot dele te a bu ilt-in a plet. Yo u can only cl ear its d ata and reset it s default se ttings. To delete a customized aple t, open the aplet library, hig hlight the aplet to be de leted, andess >'(/@ . To de lete a ll custom aplets, pre ss >6 ,)7@ CLEA R .
Reference inform ation R-1 R Reference information Regulatory in formation This section conta ins information tha t shows how the HP 39G/40G graphing calculator c omplies with regulatio ns in certai n regi ons. Any modifi cations to the c alculator not expressl y approved by Hewlet t -Packard coul d void the authori ty to operat e the HP 39G/40G in the se regio ns. USA This calcul ator generates, uses, and can radiate radio frequency en ergy and may in terfere with radio and television reception. The c alc ulat or co mplies with th e lim its for a Cl ass B digi tal device, pu rsuant to P art 15 of the FCC Rules. T hese limits are d esigned to p rovide reaso nable protection against harmful interfe rence in a resident ial installation. However, the re is no guarantee that inte rference will not occu r in a parti cular installatio n. In the u nlikely even t that there is interf erence to radio or tele vision r eceptio n (which c an be determined b y turning t he calculator off a nd on), the user is encourag ed to try to c orrect the interference b y one or more of the following me as ure s: • Reorient or rel o cate the receiving antenna. • Relocate t he calculator, with respect to the receiver. Connections to peripheral device s To maintain compliance with FCC Rules and Regula tions, use only the cable ac cessories provided. Cana da This Class B digita l appara tu s complie s with Ca na di an EMC Class B requirements. Cet apparei l numérique de la classe B est com forme à la classe B des normes canadiennes de compatibi lité électromag nétiques (CEM ) .
R-2 Reference infor mation LED safety The infra red port located on the top of t he calculator is classified as a Class 1 LED (light emitting dio de) device accordi ng to Inter national S tandard IEC 8 25-1 (EN 60 825-1. This devic e is not conside red harmful , but the follo wing precaution s are recommended: • Do not att empt to make a ny adjustments to the unit. • A void direct eye exposure to the infrared LED beam. Be aware that t he beam is invisible l ight and cannot be seen. • Do not att empt to view the infrared LED beam with any type of optical device. Warranty HP 39G/40G Graphical Calcu lator Warr anty peri od: 12 months 1. HP warra nts to you, the end -user custom er , that HP hardware, accessories and supplies will be free from defects in materi al s and workmanship af te r the dat e of purchase, fo r the pe riod specified abov e. If HP receive s notice of suc h defects durin g the warranty per i od, HP will, at its option , e ith er repa ir o r repla c e prod uc ts whi ch prove to b e defective. Replacement pr od ucts may be either ne w or like-ne w . 2. HP warrants to you that HP software will not fail to execute its programming instructions after t he date of purchase, for the period specified above, due to defects in mater ial and workma nship whe n proper ly insta lled and used. If HP receives no tice of such defects durin g the warranty per iod, HP will replac e software media wh ich does not exec ute its progr ammi ng instructio ns due to such defects. CLASS 1 LED PRODUCT LEDSCHÜTZKLASSE 1 PRODUKT
Reference inform ation R-3 3. HP does no t warrant th at the operation of HP product s will be uninterrupte d or error free. If HP is unable , within a rea sonable t ime, to repair o r replace any pr oduct to a condition a s warran ted, y ou will b e en titled to a re fund o f the purc hase price up on prompt ret ur n of the product . 4. HP prod uct s may contain r e man ufactured par t s equiv alent to new in performanc e or may have bee n subject to incidental use. 5. W arranty does not apply to defects resulting from (a) improp er or in ad equate maintenan ce o r calibration, (b) software, interfacing, parts or supplies n ot sup plied b y HP , (c) unauthorized modification or misuse, (d) operat ion outsid e of th e publi shed en vironmen tal specificati o ns for the product, or (e) improp er site prepar ation or mainte nance. 6. HP MAKES NO OTHER EXPRESS W ARRAN TY OR CONDITION WHETHER WRITTEN OR ORAL. TO THE EXTENT ALLOWED BY LOCAL LA W , ANY IMPLIED W ARRANTY OR CONDITION OF MERCHANT ABILITY , SA TIS F ACTOR Y QUALITY , OR FITNESS FOR A P AR TICULAR PURPOSE IS LIMITED T O THE DURA TION OF THE EXPRES S W ARRANTY SET FOR TH ABOVE. Some countries, states or pro vinces do not a llow limitation s on the duration o f an implied warranty , so the above li mitation or ex clusion migh t not ap ply to you . This war ranty gives you s pecific le gal rights and yo u might a lso have o ther rights that vary from country to country , state to state, or provin ce t o province. 7. TO THE EXTENT ALLOWED BY LOCAL LA W , THE REMEDIES IN THIS W ARRANTY ST A TEMENT ARE YOUR SOLE AND EXCLUSIVE REMEDIES . EXCEP T AS INDICA TED ABOVE, IN NO EVENT WILL HP OR ITS SUPPLIERS B E LIABLE FOR LOSS OF DA T A OR FOR DIRECT , SPECIAL , INCIDENT AL, CONSEQUENTIAL (INCLUDING LOST PROFIT OR DA T A), OR OTHER DAMAGE, WHETHER BASED IN CONTRACT , TOR T , OR OTHER WISE. Some countries, S tates or pr ovinces do not a llow the exclu sion or limitatio n of incid ental or cons equential dam ages, so the above limitatio n or exclusi on may not apply to you.
R-4 Reference infor mation 8. FOR CONSUMER TRANSACTIONS IN A USTRALIA AND NEW ZEALAND: THE W ARRANTY TERMS CONT AINED IN THIS ST A TEMENT , EXCEP T TO THE EXTENT LA WFULL Y PERMITTED, DO NOT EXCLUDE, RESTRICT OR MODIF Y AND ARE IN ADDITION TO THE MANDA TOR Y ST A TUTOR Y RIGHTS APPLICABLE T O THE SALE OF THIS PRODUCT TO YOU. CAS The HP 40G is pack aged with a computeri zed algebra system (CAS). Refer to the CAS User M anual for further information. Resetting the HP 39G/40G If the calculator “l ock s up” and seems to be stuck , you must reset it. This is much lik e resetting a PC . It cancels cer tain operation s , resto r es certain conditions , and clears tempo ra ry memory lo cations. However, it does not clear stored data (variables, apl et databases, prog rams) unless you use th e procedure be low, “To erase all memory and rese t defaults”. To reset using the keybo ard Press an d ho ld the >2 1@ key and the third me nu key simultane ously, then r elease them. If the c alculator do es not resp ond to the ab ove key seque nce, then: 1. Tu rn the cal cu lator over and locate the small hole in the back of t he calcula tor . 2. Insert th e end of a straightened metal paper clip i nto the hole as far a s it will go. Ho ld it there fo r 1 second, the n remove it. 3. Press >21@ . If necessary , press >21@ and the first and last menu keys simu ltaneously .
Reference inform ation R-5 To erase all memory and reset de faults If the calculat or does not respond to the abo ve resetting procedu res, you mi ght need to restart it by e rasing all of memory. You will lose every thing you h ave stored. All factory-defa ult settings are restored. 1. Press and ho ld the >21@ key , the fi rs t menu key , and t he last menu k ey simultaneousl y . 2. Release all key s. Note: T o c ancel this p r ocess, r elease only the top-r ow keys, then pr ess the third menu key . If the calculator does not turn on If the HP 39 G/40G does not turn on follow th e steps below until the calc ulator tu rns on. You ma y find tha t the calcu lator turns on bef o r e you ha ve co m ple te d the pro ce d ure . I f the calculat or still doe s not turn on , please cont act Customer Support for further i nformation. 1. Press and ho ld the >21@ key for 10 s econ ds. 2. Press and ho ld the >21@ key and th e third menu k ey simultaneou sly . Rel ease the thir d menu key , then re lease the >21@ key . 3. Press and ho ld the >21@ key , the fi rs t menu key , and t he sixth m enu key simultane ously . Relea se the six th menu key , then release the first menu k ey , and then rele ase t he >21@ key . 4. Locate the small hole in the back of the calc ulator . Insert the end of a stra ig hten ed m e tal p ape r c lip in to th e h ole a s far as it will g o. Hold it there f or 1 second, then remove it. Press the >2 1@ ke y . 5. Remove the b atteries (see “Batterie s” on p age R-7), press and hold the >21@ key for 10 seconds, and the n put the batteries b ack in. Press the >21@ key .
R-6 Reference infor mation Glossary aplet A small applic ation, limite d to one topic. The built-in apl et types are Function , Parametric , Polar, Sequ ence, Solve, and Statistics . An aplet can be filled with th e data and solutions for a specific problem. It is reusab le (like a prog ram, but easi er to use) and it r ecord s all your settin gs and defin itions. comman d An ope ration f or use in prog r ams. Commands can store resu lts in variables, b ut do not disp lay results. Argum ents are separa ted by se mi- colons, such as DISP expression ; line#. expressio n A numb er, v ari abl e, or algebraic expres sion (numbers pl us functio ns) that produc e s a va l u e. functio n An operation , po s s ibly with argu ments, that returns a result. It does not store results in variable s. The arguments must be encl os e d in pa r e nth e ses and separated with commas (or periods in Comma mode), suc h as CROSS ( matrix1,matrix2 ). HOME The basic st arting po int of th e calculator. Go to HOME to do calcul ations. Libr ary F or aple t manage ment: to start, save, reset, send and rece ive aplets. list A set of va lues separated by commas (periods if the Decima l Mark is Comma) and enclose d in braces. Lists are commonly used to ente r statisti cal data and to e valuate a funct ion with multipl e values. C reated and mani pu lated by th e List e ditor and catalo g. matrix A t w o- dimensio nal array of values separated by commas (periods if the Decim a l M ark is C om ma) an d en c lose d in nested b r ack ets. Created and manipu lated by the Mat rix catalog and editor. Vect ors are al so handled by the Matrix catal o g and editor.
Reference inform ation R-7 Operating det ails Operating temperature: 0 ° to 45 ° C (32 ° to 1 13 ° F). Storage temperature: –20 ° to 65 ° C (–4° to 149 ° F). Operat i ng and storag e humidity: 90% relative hu midity at 40 ° C (104° F) maximu m. Avoi d ge tting the ca lculator w et. Batter y operates at 4. 5V dc , 60mA maximu m. Batteries When batte ry power is low, th e ( ( •) ) annunci ator stays on, even when the calculator is off. There i s also a w arning menu A choi ce of options gi ven in the displ ay. It can appear as a list or as a set of menu- key labels across the botto m of t he display. menu key s The top row of keys . Thei r operation s depend on the curren t context. The labels along the bottom of the displ ay show th e current mean ings. note Text that yo u wri te in th e Note p ad o r in the Note vi ew for a speci fic aplet. program A reusable se t of instruction s that you record using t he Program editor. sketch A drawing that you mak e in the Sketch view for a sp ecific aplet. variable The name of a numbe r, list, matrix, note , or graph ic that is stored in memory. Use 672? _ to s tore and use >9$56@ to retrieve. vector A one-d imensiona l arra y of values sepa rated by com m as ( periods if the Decimal M ark is Comma) and encl osed in single b rackets. Created and manipula ted by th e Matrix cat alog and editor. views The po ssible co ntext s for an ap let: Plot , Plot Setup, Numeric, Nu meric Setu p, Symboli c, Symbolic Setup, Ske tch, Note, and special views l ike split screens.
R-8 Reference infor mation message th at appears when the ca lc ulator is on: Warning: Low Bat . The HP 39 G/40G uses three AAA batter i es. Be sure all three are of the same bran d and type. Recharge able batteries are not recommende d be cause of their lower capacit y and more sudden dem ise. To replace batt eri es: 1. Tu rn the cal cu lator off and place the slide cov er ov er the keyboar d to prevent key s from being p ressed. CAUTION Your calcu lator can lose me mory if it is turn ed on while the batte ri e s ar e be in g rem oved. Under no circ umstances shou ld the batte r ies be delib erately inserted bac kward s and the calculator turne d on . This may cause har dwar e d amage and will vo id the warranty. 2. Remove th e bat t ery compartment door from the rear of the calcul at or by pressing down on the d imple and pushin g t he door off. 3. Replace the batteries wit hin 2 minutes to a void memory loss. Position the fr esh batteries according to the diagram inside the ba ttery compartment. The Netherlands This regulation applie s only to The Nethe rlands. Batteries a re delivered with this produc t. When e mpty do not thro w them away b ut col lect as small chemical wast e. Bij dit p rodukt zijn batterijen geleverd. Wan neer deze leeg zijn, moet u ze niet weggoolen maar inlevern a ls KCA. Menu map s of the VA RS menu Home variable s The home variabl es are: Categor y A v ailable na me Complex Z1 ... Z9, Z0
Reference inform ation R-9 Funct ion apl et var iables The function aplet variable s are: 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 Category A vailable name (Con tinued) Category A vaila ble n ame Plot Axes Connect Coord FastRes Grid Indep InvCross Labels Recenter Simult Tracing Xcross Ycross Xtick Ytick Xmin Xmax Ymin Ymax Xzoom Yxoom
R-10 Reference infor mation Parametric aplet variab les The parame tric aplet variab les are: Plo t-FCN Area Extremum Isect Root Slope Symbolic Angle F1 F2 F3 F4 F5 F6 F7 F8 F9 F0 Numeric Digits Format NumCol NumFont NumIndep NumRow NumStart NumStep NumType NumZoom Note NoteText Sketch Page PageNum Category A vailable name (Continued) Categor y A v ailable na me Plot Axes Connect Coord Grid Indep InvCross Labels Recenter Simult Tmin Tmax Tracing Tstep Xcross Ycross Xtick Ytick Xmin Xmax Ymin Ymax Xzoom Yzoom
Reference inform ation R-11 Polar aplet variable s The polar aplet variables are: 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 Category A vailable name (Con tinued) Category A vailable n ames Axes Connect Coord Grid Indep InvCross Labels Recenter Simult Umin Umax θ step Tracing Xcross Ycross Xtick Ytick Xmin Xmax Ymin Ymax Xzoom Yxoom Symbolic Angle R1 R2 R3 R4 R5 R6 R7 R8 R9 R0
R-12 Reference infor mation Sequence aplet variables The sequence apl et variables are: Numeric Digits Format NumCol NumFont NumIndep NumRow NumStart NumStep NumType NumZoom Note NoteText Sketch Page PageNum Category A vailable names (Continued) Categor y A v ailable na me 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 inform ation R-13 Solve aplet variab les The solve aplet variables are: Category A vaila ble n ame Plot Axes Connect Coord FastRes Grid Indep InvCross Labels Recenter Tracing Xcross Ycross Xtick Ytick Xmin Xmax Ymin Ymax Xzoom Yxoom Symbolic Angle E1 E2 E3 E4 E5 E6 E7 E8 E9 E0 Numeric Digits Format NumCol NumRow Note NoteText Sketch Page PageNum
R-14 Reference infor mation Statistics aplet variables The statistics ap let variables are: Categor y A v ailable na me 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 Sta t-One Max Σ Mean Σ Median Min Σ N Σ Q1 Q3 PSDev SSDev PVar Σ SVar Σ Tot Σ Sta t-T wo Corr Cov Fit MeanX MeanY RelErr Σ X Σ X2 Σ XY Σ Y Σ Y2 Note NoteText Sketch Page PageNum
Reference inform ation R-15 Menu maps of t he MATH menu Math functions The math function s are: Category A vaila ble n ame Calculus % ) TAYLOR Complex ARG CONJ IM RE Constant e i MAXREAL MINREAL π Hyperb. 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 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
R-16 Reference infor mation Polyn om. 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 Sta t-Two PREDX PREDY Symbolic = ISOLATE LINEAR? QUAD QUOTE | Tests < ≤ = = ≠ > ≥ AND IFTE NOT OR XOR Trig ACOT ACSC ASEC COT CSC SEC Category A vailable name (Continued)
Reference inform ation R-17 Progr am cons tants The p rogram const ants are: Category A vaila ble n ame Angle Degrees Grads Radians Format Standard Fixed Sci Eng Fraction SeqPlot Cobweb Stairstep S1...5fit Linear LogFit ExpFit Power QuadFit Cubic Logist User StatMode Stat1Var Stat2Var StatPlot Hist BoxW
R-18 Reference infor mation Progra m co m man d s The program comm and s are: Categor y Comma nd Aplet CHECK SELECT SETVIEWS UNCHECK Branch IF THEN ELSE END CASE IFERR RUN STOP Drawing ARC BOX ERASE FREEZE LINE PIXOFF PIXON TLINE Graphic DISPLAYR RDISPLAY RGROB GROBNOT GROBOR GROBXOR MAKEGROB PLOTR RPLOT REPLACE SUB ZEROGROB Loop FOR = TO STEP END DO UNTIL END WHILE REPEAT END BREAK Matr ix ADDCOL ADDROW DELCOL DELROW EDITMAT RANDMAT REDIM REPLACE SCALE SCALEADD SUB SWAPCOL SWAPROW Prin t PRDISPLAY PRHISTORY PRVAR Prom pt BEEP CHOOSE DISP DISPTIME EDITMAT FREEZE GETKEY INPUT MSGBOX PROMPT WAIT Sta t-One DO1VSTATS RANDSEED SETFREQ SETSAMPLE Sta t-Two DO2VSTATS SETDEPEND SETINDEP
Reference inform ation R-19 Selected status messages The status messages are: Message Meaning Bad Argument Type Incorrect input for t his operation. Bad Argum ent Value The value is out of range for this operation . Infinit e Result Mat h exce p tio n, such as 1/0. Insufficient Memory You must recove r some memory to continue o p eratio n . Dele te one or more ma trices, lists, n otes, or programs (using catalogs), or custom (no t built-in) apl ets (using >6 ,)7@ MEMORY ). Insufficient Statistics Data Not enou gh data poin ts for the calculation . For two-variable statistics ther e must be two columns o f data, an d each column must have at least fo ur numbers. Invali d Di mension Array arg ument had wron g dimension s. Inva l id Sta tistic s Data Need two colu mns with equal number s of data values. Invalid Syntax Th e functio n or com mand you entered do es no t include the proper arg uments or ord er of arguments. The delimite rs (parentheses, com mas, periods, and semi-colon s) must also b e correc t. Look u p the fu nction name in th e index to fin d its proper sy nt ax. Name Conflict The | (where) function attempted to assign a value to the va riable of integra tion or summation index. No Equations Checked You must ente r and check an equatio n (Symb olic view ) before evalua ting this fun ction.
R-20 Reference infor mation (OFF SCREEN) Function v alue, root, extremum, or intersect ion is not visibl e in the current sc reen. Receive Error Problem with dat a reception from another calcu l ator. Re-send the data. Too Few Arguments The com man d requires more argu ments than you su pplied. Undefined Name The gl ob al variable nam ed does not exis t. Undefined Resul t T he calculation ha s a mathematica lly undefined result (such as 0/0). Out of Memo ry Y ou mu st recover a lot of memory to c ontinue operati on. Delete one or mo re matrices, lists, notes, or pro grams ( using catalo gs), or cus tom (not built -in) aplets (using >6 ,)7@ MEMORY ). Messa ge Meaning (Co ntinued)
Index I-1 Index A absolute value 10-6 add 10-4 algebraic en try 1-18 alpha cha r act ers typing 1-6 alphabetic al sorting 16-6 angle meas ure 1-9 in statistics 8-10 setting 1-11 animat ion 14-5 creating 14-5 annu nciators 1-3 Ans (last answer) 1-22 antiloga rithm 10-4, 10-10 aplet attachin g n otes 16-4 clearing 16-4 copyin g 16 -5 definit ion of R-6 deleti ng 16-6 Func tion 10-22 Inference 9-2 key 1-4 library 16 -6 Note view 14-1 openin g 1-15 Parametric 4- 1 Pola r 5-1 receiving 16-5 resetting 16-4 sending 16-5 Sketch v iew 14-1 Solv e 7-1 sorting 16-6 statistics 8-1 aplet comm ands CHECK 15-14 SELECT 15- 14 SETVIEWS 15-1 7 UNCHECK 15-17 aplet vari ables defi nition 11-1, 11 -8 in Plot view 15-30 new 11-1 aplet v iews cance li n g operation s in 1-1 changi ng 1-17 note 1-16 Numeric view 1-15 Plot vi ew 1- 15 sketch 1-17 split-screen 1-16 Symbolic view 1-15 arc cosecant 10-21 arc cosine 10-5 arc cotangen t 10- 21 arc secant 10-21 arc sine 10-5 arc tangent 10-5 area grap hical 3-10 interactive 3-10 variab le 15-30 arguments with matrices 12-10 attaching a note to an ap let 14-1 a sketch to an apl et 14- 3 auto scale 2-14 axes plott ing 2-6 variab le 15-30 B bad argu ment R-19 bad guesses error message 7-7 batte ries changi ng R-8 low-battery wa rning R-8 box-an d- wh isker plot 8-16 bran c h comma n ds CASE...E ND 15-18 IF...THE N...ELSE...END 15-18 IFERR...THEN... ELSE 15-18 RUN 15-1 9 STOP 15-1 9 branch s t ructures 15-17 build yo ur own table 2-19
I-2 Index C calculus operatio ns 10-8 catalogs 1-2 8 chronolog i cal sorting 16-6 circle dr awing 14-4 clearing aplet 16 -4 characters 1- 21 disp lay 1-21 disp lay hi story 1-24 edit line 1-21 lists 13-6 plot 2-6 cobweb grap h 6-2 coefficients polyno mial 10- 12 columns changing po sitio n 15-24 combinatio ns 10-13 comma mode with matrices 13-7 commands aplet 15-14 Branch 15-17 definiti on of R-6 Drawing 15-1 9 Graphic 15-20 Loop 15-2 2 Print 15-25 Program 15-5 , R-18 Prompt 15-25 Stat-One 15-29 Stat-Two 15-29 with matrices 12-10 comple x functions 10 -6 , 10-18 comple x number fun ctions conju gate 10 -8 imaginary p art 10-8 real part 10-8 complex numbers 1-27 entering 1-27 maths f unction s 10-8 storing 1-28 confidence intervals 9-16 conjug ate 10-8 connect ing data po ints 8-18 variab le 15-30 connectiv ity kit 16-5 cons ta nt? error me ssag e 7-7 cons tants 10-9 e 10-9 i 10-9 maximu m real number 10-9 minim u m real nu mb er 10-9 progra m R-17 contr ast decreasing display 1-2 increas ing display 1-2 coord inate displ ay 2-8 copyi ng display 1-2 1 graphic s 14- 6 notes 14-8 progra ms 15-8 correlation coefficient 8-17 CORR 8-1 7 statistical 8-14 cose cant 10-2 1 cosi ne 10-4 invers e hy perboli c 10-9 cota ngent 10-21 cova riance statistical 8-1 4 crea ting aple t 16-1 notes in Note pad 14-6 progra ms 15-4 sketches 14-3 critical value(s) disp layed 9-4 cros s prod uct vector 12-1 0 curve fitting 8-11 , 8-1 7 D data set d efinition 8-7 date, setti ng 15-26 debugg ing progra ms 15-7 decima l changing marker format 1-10 scaling 2-14 , 2-1 6 decreasing display contrast 1-2 definite in tegral 10-7
Index I-3 deleting aple t 16-6 lists 13-6 matrices 12-4 progra ms 15- 9 statistical da ta 8-10 delimiters, pro gram ming 15-1 deriv atives definitio n of 10-7 in Function ap le t 10-2 4 in Home 10-23 determina nt square matrix 12-1 0 differentia tion 10-7 display 15-20 adjusting contrast 1-2 annuncia tor line 1-2 capt ure 15-20 clearing 1-2 date and ti me 15-26 elemen t 12-5 engi neering 1-10 fixed 1-10 fraction 1-10 history 1-21 line 1-21 list elements 13- 4 matrices 12-5 parts of 1-2 printing cont ents 15-25 rescaling 2-14 scientific 1-10 scrolling throu gh history 1-23 soft k ey labe ls 1-2 stan dard 1-10 divi de 10-4 drawin g cir cles 14- 4 keys 14-4 lines and boxes 14- 3 Drawi ng co mmands ARC 15-19 BOX 15-19 ERASE 15-19 FREEZE 15 -20 LINE 15-20 PIXOFF 15-20 PIXON 15-20 TLINE 15-20 E e 10-9 edit li ne 1-2 editing matrices 12-4 note s 14-2 programs 15-5 Editline Progra m catalo g 15-2 editors 1-28 eig enval ues 12-1 1 eigenvectors 12-1 1 element storing 12-5 E-les sons 1-1 1 enginee ring numb er format 1-10 equals for equations 10-19 logical test 10- 20 equatio ns solving 7-1 erasing a line in Sket ch view 15-20 error messages bad guesses 7-7 consta nt? 7-7 excl usiv e O R 10-21 executi ng programs 15- 7 exiting vie w s 1-17 expo nent minus 1 10-10 of valu e 10-1 8 raising to 10-6 expr ession def ining 2-1 , R-6 entering in HOME 1-18 evalua tin g in aple ts 2-3 literal 10-20 plot 3-3 extremum interactive 3-9 F factorial 10-13 FastRes variable 15- 31 fit a curve to 2VAR data 8-17 choo sing 8-11 defi ning you r own 8- 12 regressi on curve 1-29
I-4 Index fixed nu mber format 1-1 0 font size change 3-8, 14-5 forecasting 8-21 fraction number format 1-10 full-precision disp la y 1-10 function analyse grap h with FCN tools 3-3 definiti on 2-2 definiti on of R-6 entering 1-18 gamma 10- 13 intersectio n po in t 3-4 math menu R-15 quadratic 3-4 slope 3-5 syntax 10-3 tracing 2-8 Functi on aplet 2-21, 3-1 functio n va r ia bl es Area 15-3 0 Axes 15- 30 Conne ct 15-30 FastRes 15-31 Grid 15-31 in menu map R-9 Indep 15-32 Isect 15-32 Labels 15-33 Recenter 15-33 Root 15-33 Ycross 15-3 6 G glossary R-6 graph analyzing statistic al data in 8-2 0 auto scale 2- 14 box-a nd-whiske r 8-16 capture current display 15-20 cobweb 6-2 comparing 2-5 connected points 8-16 defi ning the ind ependent var iable 15-35 drawin g axes 2-6 expres sions 3-3 grid po int s 2-6 in Solve aplet 7-8 index valu es 2-6 one-varia bl e stat istic s 8-18 overl aying 2-16 scatter 8-15 , 8-16 split-screen view 2-15 splitting in to plot a nd close-up 2-14 splitting in to plot a nd table 2-14 stairsteps 6-2 statistical data 8-15 t values 2-5 tickmar ks 2-6 tracing 2-8 Graphic co mmands DISPLAY 15-20 GROB 15-21 GROBNOT 15-21 GROBOR 15-21 GROBXOR 15-21 MAKEGROB 15-21 PLOT 15-21 REPLACE 15-22 SUB 15-22 ZEROGROB 15-22 graphic s copyi ng 14-6 copying into Ske tc h vie w 14-6 stori ng an d recalling 14-6, 15 -20 guaran tee R-2 H histog ram 8-15 adjusting 8-15 range 8- 18 setting min /max value s for bars 15-31 width 8-18 histor y 1-2 , 15-25 Home 1-1 calculating in 1-18 display 1-2 evaluat ing expressions 2-3 reusin g lines 1-21 home va ri a bl es 11-1, R-8 definition 11-7 horizont al zoom 15- 37 hyperb olic maths functio ns 10-10
Index I-5 hyperb oli c trigonom e try ACOS H 10-9 ALO G 10-10 ASI NH 10-9 ATANH 10-9 COSH 10 -9 EXP 10-10 EXPM1 10-10 LNP1 10-10 SINH 10 -9 TANH 10-9 hypoth esis alternative 9-3 inference tests 9-9 null 9-3 tests 9-3 I i 10- 9 implied m ultiplicati on 1-19 importing graphi cs 14-6 notes 14-8 increasi n g display contr ast 1-2 indefini te integral using sym bolic variables 10-25 indep endent val ues adding to tabl e 2-19 indep endent var iable defined for Tracing mode 15-32 inference confiden ce intervals 9-16 hypothe sis tests 9-9 One-Proportio n Z-In te rval 9-18 One-Sample Z-Interval 9-16 One -Sam ple Z -Te st 9-9 Two-Pr oportion Z-Interv al 9-19 Two-Pr oportion Z-Test 9-12 Two-Sample T-Interval 9-21 Two-Sample Z-Interval 9-17 infinite result R-19 infrared transmission of aplets betwe en ma- chines 16-5 initial g uess 7-5 input forms resetting defau lt values 1-9 setting Mo des 1-11 insufficient memory R-19 insufficient stati stic s data R-19 integer rank matrix 12-12 integer scaling 2-14, 2-1 6 inte gral definite 10-7 indefinite 10-25 integr ation 10-7 interpreting intermediate g uesses 7-7 int ersec tion interactive 3-10 inva lid dimension R-19 statistics data R-19 syntax R-19 inver se hyperbol i c cosine 10-9 inve r se hyperboli c functions 10-10 inver se hyperboli c sine 10-9 inver se hyperbol i c tangent 10-9 inverting matrices 12-7 isect variabl e 15-32 K keyb oard editin g keys 1-5 entry ke ys 1-5 inact ive keys 1-7 list ke ys 13-2 math func tio ns 1-7 menu keys 1-4 Notepa d keys 14-8 shifte d ke y st r ok es 1-6 L labeling axes 2-6 parts of a sketch 14-5 letters, ty ping 1-6 libra ry, mana ging apl ets in 16-6 linear fit 8-12
I-6 Index list arithmetic wi th 13-7 calculat e sequence o f elements 13-8 calc ulating p roduct of 13-9 composed fro m differences 13-8 concat enating 13-8 count in g el ements in 13-9 creating 13-1 , 13-3 , 13-4, 13-5 deleting 13 -6 deleting list items 13-3 disp laying 13-4 display ing list eleme nts 13-4 editing 13-3 finding statistic al values in list ele- ment s 13-10 gener ate a seri e s 13-8 gener ating ser ies 13-8 list functi on syntax 13-7 list variables 13-1 returning position o f element in 13-9 reversing order in 13-9 sending an d receiving 13-6 sorting eleme nts 13-9 storing el eme nts 13-1, 13 -4 , 13-5 storing on e element 13-7 logarithm 10-4 logarithm ic fit 8-12 functio ns 10-4 logical op erators AND 10- 21 equals (log ical test) 10-20 greater th an 10- 20 greate r than or equal t o 10-20 IFTE 10-2 1 less than 10- 20 less than or equa l to 10-2 0 NOT 10-21 not equa l to 10-20 OR 10-2 1 XOR 10-2 1 logistic fit 8-12 loop c ommands BREAK 15-23 DO...UNTIL...END 15-2 2 FOR I= 15-23 WHILE...R EPEAT...END 15-22 loop fu nctions ITERATE 10-1 1 RECURSE 10-1 1 summatio n 10-11 low battery 1-1 lowercase letters 1-6 M mantissa 10-16 math functio ns compl ex number 10-8 hyperb olic 10-10 in menu map R-15 keybo ard 10-4 logical op erators 10-20 menu 1-7 polyno minal 10-12 probability 10-1 3 real- number 10-15 symbolic 10-19 trigonome try 10-21 math opera tions 1-18 enclo sing argument s 1-20 in scientific notation 1-19 negati ve numb ers in 1-18 matri ces addi ng row s 15-23 addi tion and subtrac tion 12-6 argum ents 12-10 arithmetic operations i n 12-6 assembly from v ectors 12-1 changi ng row position 15-24 colu mn nor m 12-10 com ma 13-7 comma nds 12-10 conditi on num ber 12-10 create i den tity 12-13 creating 12-3 creating in Hom e 12-5 deleting 12- 4 deleting co lu mns 15-23 deleting rows 15-23 determina nt 12-1 0 display eig enval ue s 12-1 1 displayin g 12-5 displaying matrix elem ents 12-5 divi di ng by a squa r e matrix 12-7 dot pr oduct 12-10 editing 12 -4 extracting a portion 15-24 finding the t race of a square matrix 12-13 inverting 12-7 matrix calc ulations 12-1
Index I-7 multiplying and dividin g by scalar 12-6 multiplying by vector 12-7 multiplying row by valu e and ad ding result to sec ond row 15-24 multiplying ro w number by va lue 15-24 negat ing elements 12-7 opening M atrix Editor 15-26 redimension 15-24 repl acing port ion of m atrix o r vector 15-24 send ing or r eceivin g 12-4 singular v alue dec omposition 12-12 sing ular valu es 12-12 size 12-12 spect ral norm 12-1 2 spect ral radiu s 12- 12 start Matrix Ed itor 15-23 storin g eleme nt s 12-3 , 12- 5 storing matrix elements 12- 5 swap co l umn 15-24 swap row 15-24 transposing 12- 13 varia bles 12-1 matrix fun ctions 12-10 COLNORM 12-10 COND 12-10 CROSS 12-10 DET 12-10 DOT 12-10 EIGENVAL 12-11 EIGENVV 12-11 IDENMAT 12-11 INVERSE 12-11 LQ 12-11 LSQ 12-11 LU 12 -11 MAKEMAT 12-11 QR 12-12 RANK 12-12 ROWNORM 12-12 RREF 12-12 SCHUR 12-1 2 SIZE 12-12 SPECNORM 12-1 2 SPECRAD 12-1 2 SVD 12-12 SVL 12-12 TRACE 12-13 TRN 12-13 maximum real numb er 1-20, 10-9 memory R-19 clearing all R-5 organizi ng 11-9 out o f R-20 savi ng 1-24, 16-1 viewing 11 -1 menu lists searching 1-8 minimum real nu mber 10-9 Modes angle meas ure 1-9 decimal mark 1-10 number format 1-10 multiple solutions plottin g to find 7-8 multiplic ation 10-4 implied 1-19 N name con flict R-1 9 naming programs 15-4 natura l expone ntial 10-4, 10-10 natura l log pl us 1 10-10 natural log arith m 10-4 negatio n 10-5 negativ e numbe rs 1-18 no equa tions checked R-19 Normal Z -distribu tion, conf idence in ter- vals 9-16 note copyin g 14-8 editing 14-2 importing 14-8 printing 15-25 viewing 14-1 writing 14-1 Notepad 14-1 catalog key s 14-7 creating no tes 14-6 writing in 14-6 nrng 2-5 n th root 10-6 null hy pothesis 9-3 number format enginee ring 1-10 fixed 1-10 fraction 1-10
I-8 Index in Solve aplet 7-5 scientific 1-10 Standard 1-1 0 numeric pr eci sion 11-9 Numeric view adding X valu es 2-19 automatic 2-17 buil d yo ur own tabl e 2-19 disp lay defin in g func ti on for co lumn 2-18 recalculatin g 2-19 setup 2-17 , 2-1 9 O off automatic 1-1 powe r 1-1 On/Cancel 1-1 One-P roporti on Z-Inte rval 9-18 One-Sample T-Interval 9-20 One-Sample T-Te st 9-13 One-Sample Z-Interval 9-1 6 One-Sample Z-Te st 9-9 order of pr ecedence 1-20 overla ying plots 2-1 6, 4-3 P π 10-9 paire d columns 8- 11 Parametric aplet 4-1 parametric v ariables Axes 15-30 Conne ct 15-30 Grid 15-31 in menu map R-10 Indep 15-32 Labels 15-33 Recenter 15-33 Ycross 15-3 6 parent heses to close argu ments 1-20 to specify o rder of operation 1-20 pause 15-28 permut ations 10-13 pictur es attachin g in Sk etch view 14-3 plot analyzing statistic al data in 8-20 auto scale 2-14 box-a nd-whiske r 8-16 cobweb 6-2 com parin g 2-5 conn ected point s 8-16, 8-18 decimal sc aling 2-1 4 defining the inde pendent v ariable 15-35 drawing axes 2-6 expr essio ns 3-3 goto functio n 1-29 grid points 2-6 in Solve aple t 7-8 index val ues 2-6 inte ger sca ling 2-14 one-varia bl e stat istic s 8-18 overl a y plot 2-14 overl aying 2-16 , 4- 3 scaling 2-14 scatter 8-15, 8-16 sequenc e 2-6 setting up 2-5, 3-2 split-screen view 2-15 splitting 2-1 5 splitting in to plot a nd close-up 2-14 splitting in to plot a nd table 2-14 stairsteps 6-2 statistical data 8-15 statistics parameters 8-18 t values 2-5 tickmar ks 2-6 to capture cu r re nt dis p la y 15-20 tracing 2-8 trigonome tric scaling 2-14 plotting resolution and tra cing 2-8 plot-vie w variable s Area 15-30 Connect 15- 30 FastRes 15-31 Function 15-30 Grid 15-31 Hmin/Hmax 15-31 Hwidth 15-32 Isect 15-32 Labels 15-33 Recenter 15-33 RNG 15-34 Root 15-33 S1mark-S5mark 15- 33 StatPlot 15-34 Tracing 15-32 Ustep 15-3 4
Index I-9 polar variables Axe s 15-30 Connect 15-3 0 Gri d 15-31 in menu map R- 11 Indep 15-32 Labels 15-3 3 Recenter 15-3 3 Ycro ss 15-36 polyno mial coefficient s 10-12 evaluatio n 10-12 form 10-12 roots 10-12 Taylor 10-7 polyno mial fun c tio ns POLYCOEF 10-12 POLYEVAL 10-12 POLYFORM 10-12 POLYROOT 10-12 position arg ume nt 15-20 power (x raised to y) 10- 6 preceden ce 1-20 predic ted values statistical 8-2 1 print cont ents o f dis play 15-25 name and contents of vari able 15-25 object in hi story 15-25 varia bles 15-25 probability functions ! 10-13 COMB 10-13 permuta tions 10-13 RANDOM 10-13 UTP C 10-14 UTP F 10-14 UTP N 10-14 UTP T 10-14 progra m comma nds 15-5 copyi ng 15-8 creating 15-4 debugg ing 15-7 deleting 15-8 delimiters 15-1 editing 15-5 naming 15-4 pausing 15-28 printing 15-25 running 15-7 send in g an d r ec e iv ing 15-8 stopping 15-7 structured 15-1 prompt com mands beep 15-2 5 create choose bo x 15-25 create input form 15-27 displa y item 15-26 displa y message box 15-28 halt prog ram execution 15 -28 insert line b reaks 15-28 prevent scre en display being upd ated 15-27 set date and time 15-2 6 store keyco de 15-27 Q θ<∆εφαυλτ φοντ παρα>στεπ 2-5 θ rng 2-5 quadratic extremum 3-6 fit 8-1 2 functi on 3-4 quittin g vie ws 1-17 quotes in prog ram nam es 15-4 R random n umb ers 10-1 4 real number maximum 10 -9 minimum 10-9 real part 10-8 real-number functions 10-1 5 % 10-1 7 %CHANGE 10-1 7 %TOTAL 10-17 CEILING 10-15 DEGtoRAD 10-15 FNROO T 10- 15 HMSto 10-16 INT 10-16 MANT 10-16 MAX 10-16 MIN 10- 16 MOD 10-17 RADtoDEG 10-17 ROUND 10-17 SIGN 10- 18
I-10 Index TRUNCATE 10-18 XPON 10-18 recalculatio n for table 2- 19 receive error R-20 receiving aplet 16-5 lists 13-6 matrice s 12-4 prog rams 15-8 redrawing table of num bers 2-18 reduced row ech el on 12-12 regression analysis 8-1 7 fit models 8-12 formula 8-12 user-defined fit 8-12 regulatory information Canada R-1 USA R-1 relative error statistical 8-17 resetting aplet 16-4 calcul ator R-4 If calculator do es no t turn on R-5 memory R-5 result copying to edit line 1-21 reusing 1-21 root interactive 3-9 n th 10-6 variab le 15-33 root-finding disp laying 7-7 interactive 3-8 operatio ns 3-9 variab les 3-9 runnin g a program 15-7 S S1mar k- S5mark var iables 15-33 scaling automatic 2-14 decima l 2-9, 2-10 , 2-14 intege r 2-11 , 2-14 , 2-16 options 2-14 resetting 2-14 trigonome tric 2- 14 scatter plot 8-15, 8-16 conn ected 8-16, 8-18 SCHUR decompositio n 12-12 scie nt ific number f ormat 1-10, 1-1 9 scrolling in Tr ace mode 2-8 searching menu lists 1-8 speed search es 1-8 secant 10-21 sending aplets 16 -5 lists 13-6 progra ms 15 -8 sequence definition 2-2 sequence variables Axes 15-30 Grid 15-31 in menu map R-12 Indep 15-32 Labels 15-33 Recenter 15-33 Ycross 15-36 setting date 15-2 6 time 15-26 sign reversal 7-6 sine 10-4 invers e hy perboli c 10-9 singul ar value de c om p os iti on matri x 12-12 singul ar valu es matri x 12-12
Index I-11 sketches creating 14-5 creatin g a bla n k graphic 15-2 2 creating a set of 14-5 erasing a line 15-20 labeling 14-5 openin g view 14-3 sets 14-5 storin g in gra p hics varia ble 14-5 slope interactive 3-9 soft key la bels 1-2 solve error messages 7-7 initial guesses 7-5 interpreting intermediate g uesses 7-7 interpreting re sults 7-6 plotting to find guesses 7-8 setting number form at 7- 5 solve variables Axe s 15-30 Connect 15-3 0 FastRes 15-31 Gri d 15-31 in menu map R-13 Indep 15-32 Labels 15-33 Recenter 15-33 Ycro ss 15-36 sorting 16 -6 aplets in alp habetic order 16-6 aplets in chron ological ord er 16-6 elements in a list 13-9 spectral norm 12-1 2 spectral radius 12-12 squar e ro ot 10-5 stack hist ory printing 15-25 stairste ps graph 6-2 standard number format 1-10 statistics anal ysis 8-1 analyz in g plo ts 8-20 angl e mo de 8-10 calc u l at e one- va r i a bl e 15-29 calc u l at e two-v aria bl e 15-29 computing 2VAR 8-11 data set vari ables 15-39 data st ructure 15-39 define on e-variable samp l e 15-29 define t wo-variable d ata set’s depen - dent col u mn 15-29 define two-variab le data se t’s inde - pendent column 15-29 defi ning a f it 8-11 defi ning a r egress ion mode l 8-11 deleti ng data 8-10 editing d ata 8-10 frequency 15-2 9 inserting d ata 8-11 plot typ e 8-18 plottin g data 8-15 predicte d values 8-21 regression curve (fit) models 8-1 1 savi ng data 8-10 sorting da ta 8-11 spec ifyi n g angl e se t t ing 8-1 0 toggli ng between one-variab le and two-variab le 8-11 tracin g plo ts 8- 20 troubl eshooting wi th plots 8-19 zoom ing in plo ts 8-20 statistics v ariables Axes 15-30 Connect 15-30 Grid 15-31 Hmin/Hmax 15-3 1 Hwidth 15-32 in menu map R-14 Indep 15-32 Label s 15-33 Recenter 15-33 S1mark-S5mark 15-33 Ycross 15- 36 step size of in dep endent variable 15-35 storing list element s 13-1 , 13-4 , 13-5 , 13 -7 matrix elem ents 12- 3 , 12-5 results of calculation 11-3 value 11-2 strings literal in symbolic operatio ns 10-20 structure d programming 15-1 subtract 10-4 summation fun c tion 10-11 symbolic calcula ti on s in Fu nctio n ap le t 10-22 defining ex pressions 2- 1 differentiation 10-2 3
I-12 Index disp laying d efiniti ons 3-8 evalua ting varia bl es in view 2-3 setup view for statistics 8-10 symbol ic functi ons | (where) 10-20 equals 10-19 ISOLATE 10-1 9 LINEAR? 10-19 QUAD 10-19 QUOTE 10-20 Symbolic view defini ng expressi ons 3-2 syntax 10-3 syntax errors 15-7 T table navig ate around 3-7 numer ic value s 3-7 numer ic view s etup 2-17 tangent 10-4 invers e hyperbol ic 10-9 Taylo r polynom ial 10-7 tickmark s for plotti ng 2-6 time 10-1 6 setting 15-26 time, convert i ng 10-16 times sign 1-19 tmax 15-35 tmin 15-35 too fe w arguments R-20 tracing functio ns 2-8 more th a n on e curv e 2-8 not ma tching p lot 2-8 plots 2-8 transmitting lists 13-6 matrice s 12-4 prog rams 15-8 trans posing a ma tr ix 12-13 trigon ometric functio ns 10-21 scaling 2-11, 2-14, 2-16 trigon ometry cosine 10-9 trigon ometry fun c t ions ACOT 10-21 ACSC 10-21 ASEC 10-21 COT 10-2 1 CSC 10-21 SEC 10-21 sine, co s ine , ta ng en t 10-4 trng 2-5 troubl eshooting R-1 truncat ing values to d ecimal places 10-18 tstep 2-5, 15-3 5 Two-Prop ortion Z -Interval 9-19 Two-Prop ortion Z -Test 9-12 Two-Sample T-Interval 9-21 Two-Sample T-t est 9-14 Two-Sample Z-Interval 9-17 typing letters 1-6 U undef ined name R-20 result R-20 un-z oom 2-11 upper-tail chi-squared probability 10-14 upper-tail normal pr obabilit y 10-14 upper-tail snedecor’s f 10-1 4 upper-tail student’s t-prob ability 10-14 user d efined regression fit 8-1 2 user p rompts 15-25
Index I-13 V value go dir ectly t o 3-7 recall 11-3 stori ng 11-2 varia bles aple t 11-1 cate gorie s 11-7 definition 11-1, 11 -7, R-7 in equation s 7-10 in Symboli c vie w 2-3 indepe ndent 15-35 local 11-1 previous result (Ans) 1-22 printing 15-25 root 15-3 3 root-finding 3-9 step size of i nd ependent 15-35 types 11-1, 11 -7 use in ca lculations 11-4 VARS menu 11-4, 11 -5 map R-8 vector s colu mn 12-1 cros s prod uct 12-10 definitio n of R-7 views 1-17 configura tion 1-17 definitio n of R-7 W warning symbol 1-7 warranty R-2 whe r e co mman d ( | ) 10-20 X xrng 2-5 Y Ycross variable 15-3 6 yrng 2-5 Z Z-Interval 9-16 zoom 2-18 axes 2-12 box 2-8 center 2-8 examples of 2-11 factors 2-13 in 2-9 , 2-1 0 optio ns 2-8, 3- 7 options with in a table 2-18 out 2-9 , 2-1 0 redra wing tabl e of number s options 2-18 square 2-9, 2-10 un-zoo m 2-11 within Numeric view 2-18 X-zoom 2-9 , 2-10 Y-zoom 2-9, 2-10