Manuale d’uso / di manutenzione del prodotto F2225AA 40gs del fabbricante HP
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HP 4 0gs gr aphing calc ulator user's guide Ed i t io n 1 P ar t Number F2 2 25AA-90001 hp40g+.book Page i Friday, December 9, 2005 1:03 AM.
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iii Contents Preface Manual conventions ................ ................ ................. ............. P-1 Notice ...... ................ ................ ................. ................ .......... P-2 1 Getting started On/off, cancel operatio ns .
iv Function aplet intera ctive analysis .............. ................ ............. 3-9 Plotting a piecewise -defined function ........ ................ ........ 3-12 4 Parametric aplet About the Pa rametric aplet ....... ................ ..........
v About the Inference ap let ................ ................ ................... .. 11-1 Getting started with the Infe rence aplet ........................ ..... 11-1 Importing sample statistics from the S tatistics aplet ......... ..... 11-4 Hypothesis tests .
vi Symbolic calculations ........ ................ ................. ............... 13-20 Finding derivatives .............. ................ ................ ......... 13-21 Program constants and physical constants ......................... .. 13-24 Program constants .
vii Accessing CAS functio ns ............. ................. ................ ...... 15-12 Equation Writer variab les . ................ ................ ................ 1 5-16 Predefined CAS variables ................ ................ ............. 1 5-16 The keyboard in the Eq uation Writer .
viii Aplet naming conventio n ........................ ................ ...... 21-10 Example .................. ............. ................ ................ ...... 21-10 Programming commands ................ .................... ............... 21-13 Aplet commands .
ix Solve aplet variables ........... ................ ................. ........... R-11 Statistics aplet variables ............. ................ ................... .. R -12 MATH menu categ ories . ................. ................ ................
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P-1 Preface The HP 40gs is a feature-rich graphing calculator. It is also a powerful mathematics learning tool, with a built-in computer algebra system (CAS). The HP 40gs is designed so that you can use it to explore mathematical functions and their properties.
P-2 Notice This manual and any examples contained herein are provided as-is and are subject to change without notice. Except to the extent prohibit ed by law, Hewlett-Packard Company makes no express .
Getting started 1-1 1 Get ting star ted On/off, cancel operations To turn on Press to turn on the calculator. To cancel When the calculator is on, the key cancels the current operation. To turn off Press OFF to turn the calculator off. To save power, the calc ulator turns itself off after several minutes of inactivity.
1-2 Getting started The display To adjust the contrast Simultaneously press and (or ) to increase (or decrease) the contrast. To clear the display • Pres s CANCEL to clear the edit line . • Pres s CLEAR to cle ar the edit line and the display history .
Getting started 1-3 Annunciators . Annunciators are sy mbo ls that appear above the title bar and give you important status information. The keyboard Annunciator Description Shift in effect for next keystroke. To cancel, press again. α Alpha in effect for next keystroke.
1-4 Getting started Menu keys • On the calculato r ke yboar d , the top ro w of k ey s ar e called menu k ey s. T heir meanings depend on the conte xt—that’s w hy the y ar e blank. T he menu k e y s are so metimes called “ soft k ey s” . • The bo ttom line of the displa y sho w s the labels f or the menu k ey s ’ cur rent meanings .
Getting started 1-5 Entry/Edit keys The entry and edit keys are: K ey Meaning ( CANCEL ) Cancels the current operation if the calculator is on by pressing . Pressing , then OFF turns the calculator off. Accesses the function printed in blue above a key.
1-6 Getting started Shifted keystr okes There are two shift keys that you use to access the operations and characters printed above the keys: and . CHARS Displays a menu of all avai lable characters. To type one, use the arrow keys to highlight it, and press .
Getting started 1-7 HELPWITH The HP 40gs built-in help is available in HOME o nly. It provides syntax help for bu ilt-in math functions. Access the HELPWITH command by pressing SYNTAX and then the math key for which you require syntax help.
1-8 Getting started • Pr essing display s the list of Pr ogr am Cons tants. Y ou can use the se in pr ograms that you d eve l o p. • Pr essing displa ys a menu of ph y sical constants fr om the f ields o f chemistry , phys ics, and quantum mechani cs.
Getting started 1-9 To search a menu • Pres s or to scr oll through the list. If y ou pres s or , y ou’ll go all the w ay to the end or the beginning of the list .
1-10 Getting started Mode settings You use the Modes input form to set the modes for HOME. HINT Although the numeric setting in Modes affects only HOME, the angle setting controls HOME and the current aplet. The angle setting selected in Modes is the ang le setting used in both HOME and current aplet.
Getting started 1-11 Setting a mode This example demonstrates how to change the angle measure from the default mode, radians, to degrees for the current aplet. The procedure is the same for changing number format and decimal mark modes. 1. Pres s MODES t o o p e n t h e H O M E M O D ES i n p u t form.
1-12 Getting started The c ursor (hi ghlight) is in the firs t fie ld, A ngle Measure . 2 . Pres s to display a li st of choic es. 3. Pre s s to select Degrees , and press .
Getting started 1-13 symbolic views of the aplets in the following table. See “Aplet view configuration” on page 1-18 for further information. In addition to these aplets, wh ich can be used in a variety of applications, the HP 40 gs is supplied with two teaching aplets: Quad Explorer and Trig Explorer.
1-14 Getting started charge and transferred to the HP 40gs us ing the provided Connectivity Kit. Quad Explorer aplet The Quad Explorer aplet is used to investigate the behaviour of as the values of a .
Getting started 1-15 Trig Explorer aplet The Trig Explorer aplet is used to investigate the behaviour of the graph of as the values of a , b , c and d change, both by manipulating the equation and seeing the change in the graph, or by manipulating the graph and seeing the change in the equation.
1-16 Getting started Aplet library Aplets are stored in the Aplet library. To open an aplet Press to display the Aplet library menu. Select the aplet and press or .
Getting started 1-17 Numeric view Press to display the aplet’s Numeric view. In this view, the functions that you have defined are displayed in tabular format. See “About the numeric view” on page 2-16 f or further information. Plot-Table view The VIEWS menu contains the Plot-Table view.
1-18 Getting started Note view Press NOTE to display the aplet’s note view. This note is transferred with the aplet if it is sent to another calculator or to a PC. A note view contains text to supplement an aplet. See “Notes and sketche s” on page 20-1 for further information.
Getting started 1-19 To change views Each view is a separate environment. To change a view, select a different view by pressing , , keys or select a view from the VIEWS menu. To change to HOME, press . You do not explicitly close the current view, you just ente r another one—like passing from one room into another in a house.
1-20 Getting started Example Calculate : Long results If the result is too long to fit on the display line, or if you want to see an expression in textbook format, press to highlight it and then press . Negative numbers Type to start a negative number or to insert a negative sign.
Getting started 1-21 However, for clarity, it is better to include the multiplication sign where you expect multiplication in an expression. It is clearest to enter AB as A*B . HINT Implied multiplication will not always work as expected. For example, entering A(B+4) will not give A*(B+4) .
1-22 Getting started Algebraic precedence order of evaluation Functions within an expression are evaluated in the following order of precedence. Functions with the same precedence are evaluated in order from left to right. 1. Ex pressions within p arentheses.
Getting started 1-23 When you highlight a previous input or resu lt (by pressing ), the and menu labels appear. To copy a previous line Highlight the line (press ) and press . The number (or expression) is co pied into the ed it line. To reuse the last result Press ANS (last answer) to put the last result from the HOME display into an expression.
1-24 Getting started HINT When you retrieve a number from ANS , you obtain the result to its full precision. When you retrieve a number from the HOME’s display history, you obtain exactly what was displayed. Pressing evaluates (or re-evaluates) the last input, whereas pressing ANS copies the last result (as ANS ) into the edit line.
Getting started 1-25 Accessing the display history Pressing enables the highlight bar in the display history. While the highlight bar is active, the following menu and keyboard keys are very useful: Clearing the display history It’s a good habit to cl ear the display history ( CLEAR ) whenever you have finish ed working in HOME.
1-26 Getting started 2 . Select Number Format , press to displ ay the options , and highligh t Fraction or Mixed Fraction . 3 . Pres s to select the Number F ormat option, then mov e to the prec ision value field . 4. Enter the prec ision v alue that you w ant to use , and pre ss to set the pr ec ision .
Getting started 1-27 • Prec ision set to 1: • Prec ision set to 2 : • Prec ision set to 3: • Prec ision set to 4 Fraction calculations When entering fractions: • Y ou use the ke y to separate the numerator part and the denominator par t of the fr action .
1-28 Getting started 2. E n t e r t h e c a l c u l a t i o n . 32 3 45 7 8 Note: Ensur e y ou ar e in the HOME v ie w . 3 . Ev aluate the calc ulation. Note that if you had selected Mixed Fraction instead of Fraction as the Number format, the answer would have been expressed as 25+7/8.
Getting started 1-29 In this ex ample , the fr action pr ec ision is set to 6. Complex numbers Complex results The HP 40gs can return a complex number as a result for some math functions. A comp lex number appears as an ordered pair ( x, y ), where x is the real part and y is the imaginary part.
1-30 Getting started Catalogs and editors The HP 40gs has several catalogs and editors. You use them to create and manipulate objects. They access features and stored values (numbe rs or text or other items) that are independent of aplets. • A catalog lists items, w hich y ou can delete or tr ansmit , for e xam ple an aplet .
Aplets and their views 2-1 2 Aplets and th eir vie ws Aplet views This section examines the options and func tionality of the three main views for the Functio n, Polar, Parametric, and Sequence aplets: Symbolic, Plot, and Numeric views.
2-2 Aplets and their views – F or a Func tion definition , en ter an ex pre ssion t o def ine F(X) . The only independent variab le in th e exp re ss io n is X. – For a P arametric definition , en ter a pair of expr essi ons to def ine X(T) and Y(T) .
Aplets and their views 2-3 Evaluating expressions In aplets In the Symbolic view, a variable is a symbol only, and does not represent one specif ic value. To evaluate a function in Symbolic view, press . If a function calls another function, then resolves all references to other functions in terms of their independent vari able.
2-4 Aplets and their views In HOME You can also evaluate any expression in HOME by entering it into the edit line and pressing . For example, define F4 as below. In HOME, type F4(9) and press . This evaluates the expression, substituting 9 in place of X into F4 .
Aplets and their views 2-5 About the Plot view After entering and selecting (check marking) the expression in the Symbolic view, press . To adjust the appearance of the graph or the interval that is displayed, you can change the Plot view settings. You can plot up to ten expressions at the same time.
2-6 Aplets and their views Plot view settings The plot view settings are: Those items with space for a checkmark are settings you can turn on or off. Press to display the second page. Field Meaning XRNG, YRNG Specifies the minimum and maximum horizontal ( X ) and vertical ( Y ) values for the plotting window.
Aplets and their views 2-7 Reset plot settings To reset the default values for all plot settings, press CLEAR in the Plot Setup view. To reset the default value for a field, highlight the field, and press . Exploring the graph Pl ot v ie w gi v es y ou a s e le c ti on o f ke ys a nd m en u ke ys t o explore a graph further.
2-8 Aplets and their views Trace a graph You can trace along a function using the or key which moves the cursor along the graph. The display also shows the current coordinate position ( x, y ) of the cursor. Trace mode and the coordinate disp lay are automatically set when a plot is drawn.
Aplets and their views 2-9 To jump directly to a value To jump straight to a value rather than using the Trace function, use the menu key. Press , then enter a value. Press to jump to the value. To turn trace on/off If the menu labels are no t displayed, press first.
2-10 Aplets and their views Y-Zoom In Divides vertical scale only, using Y-factor. Y-Zoom Out Multiplies vertical scale only, using Y-factor. Square Changes the vertical scale to match the horizontal scale. (Use this after doing a Box Zoom, X- Zoom, or Y-Zoom.
Aplets and their views 2-11 ZOOM examples The following screens show the effects of zooming options on a plot of . Plot of Zoom In : In Un-zoom : Un-zoom Note: Press to move to the bottom of the Zoom list. Zoom Out : Out Now un- zoom. X-Zoom In : X-Zoom In Now un- zoom.
2-12 Aplets and their views Y-Zoom In: Y-Zoom In Now un-zoom. Y-Zoom Out: Y-Zoom Out Zoom Square: Square To box zoom The Box Zoom option lets you draw a box around the area you want to zoom in on by selecting the endpoints of one diagonal of the zoom rectangle.
Aplets and their views 2-13 To set zoom factors 1. In the P lot vi ew , press . 2. P r e s s . 3. Se l e c t Set Factors... and pr ess . 4. Enter the z oom f actors . Ther e is one z oom facto r for the horiz ontal scale ( XZOOM ) and one for the v ertical scal e ( YZOOM ).
2-14 Aplets and their views Split the screen The Plot-Detail view can give you two simultaneous views of the plot. 1. Pres s . Select P lot-Detail and press . The gr aph is plotted t wi ce. Y ou can now z oom in on the ri ght side . 2. P r e s s , select the z oom method and pres s or .
Aplets and their views 2-15 – mov es the leftmost cur sor to the scr een ’s left edge and mov es the ri ghtmost c urs or to the sc ree n’s r ight edge . – T he menu k e y copie s the ri ght plot to the le ft plot . 3 . T o un -split the sc reen , pr ess .
2-16 Aplets and their views About the numeric view After entering and selecting (check marking) the expression or expressions that you want to explore in the Symbolic view, press to view a table of data values for the independent variable ( X , T, θ , or N ) and dependent variables.
Aplets and their views 2-17 Reset numeric settings To reset the default values for all table settings, press CLEAR . Exploring the table of numbers NUM view menu keys The following table details the menu keys that you use to work with the table of numbers.
2-18 Aplets and their views Zoom within a table Zooming redraws the table of numbers in greater or lesser detail. ZOOM options The following table lists the zoom options: The display on the right is a Zoom In of the display on the left. The ZOOM factor is 4.
Aplets and their views 2-19 Automatic recalculation You can enter any new value in the X column. When you press , the values for the dependent variables are recalculated, and the entire table is regenerated with the same interval between X values.
2-20 Aplets and their views “Build Your Own” menu keys Example: plotting a circle Plot the circle, x 2 + y 2 = 9 . First rearrange it to read . To plot both the positive and negative y values, you need to define two equations as follows: and 1. In the F unctio n aplet, s pec ify the functi ons.
Aplets and their views 2-21 Select Function 9 9 2 . R eset the gr aph se tup to the def ault setting s. SETUP - PLOT CLEAR 3 . P lot the two f unctions and hide the men u so that yo u can see all the ci rcl e. 4. Re set the numer ic se tup to the default s ettings.
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Function aplet 3-1 3 Function aplet About the Function aplet The Function aplet enables you to explore up to 10 real-valued, rectangular functions y in terms of x .
3-2 Function aplet Define the expressions 2 . T here ar e 10 fu nction de finition f ields o n the F unction aplet’s S ymbolic v ie w scr een . The y ar e labeled F1(X) to F0(X). Highlight the f uncti on definiti on fi eld yo u w ant to us e , and ente r an ex pre ssi on.
Function aplet 3-3 Change the scale 6. Y ou c an change the sc ale to see more or less of your gra phs. In this e xam ple, c hoose Auto Scale . (See “VIEW S menu options ” on page 2-13 f or a descrip tio n of Auto Sc al e) . Select Auto Scale Trace a graph 7 .
3-4 Function aplet Analyse graph with FCN functions 9. Display the Plot view menu. From the Plot view menu, you can use the functions on the FCN menu to find roots, intersections, slopes, and areas for a function defined in the Function aplet (and any Function-based ap lets).
Function aplet 3-5 12 . Choose the linear f unctio n whos e inter secti on w ith the quadr atic func tion y ou w ish to f ind. The coo rdinat es of the intersec tion po int are display ed at the bottom of the screen .
3-6 Function aplet 16 . Pre ss to accept using F2(x) = (x + 3) 2 – 2 as the other boundar y for the integr al. 17 . Choose the e nd value for x . 1 Th e cu rso r jum ps to x = – 1 on the linear functi on. 18. Display the numerical value of the integral.
Function aplet 3-7 HINT The Root and Extremum functions return one value only even if the fun ction has more than one root or extremum. The function finds the value closest to the position of the cursor. You need to re-locate the cursor to find other roots or extrema that may exist.
3-8 Function aplet To navigate around a table 2 4. Move t o X = –5.9 . 6 times To go directly to a value 2 5 . Move dir ectl y to X = 10. 1 0 To access the zoom options 2 6. Z oom in on X = 10 by a f actor of 4. Note: NUMZOOM has a setting of 4 . In To change font size 2 7 .
Function aplet 3-9 Function aplet interactive analysis From the Plot view ( ), you can use the functions on the FCN menu to find roots, intersection s, slopes, and areas for a function defined in the Function aplet (and any Function-based aplets). See “FCN functions” on page 3- 10.
3-10 Function aplet FCN functions The FCN functions are: Function Description Root Se lect Root to find the root of the current function nearest the cursor. If no root is fo und, but only an extremum, then the result is labeled EXTR: instead of ROOT: .
Function aplet 3-11 Shading area You can shade a selected area between functions. This process also gives yo u an approximate measurement o f the area shaded. 1. Open the Function aplet . The F unction aplet opens in the S ymboli c vi ew . 2 . Se lect the e xpr essio ns who se c urves y ou w ant to study .
3-12 Function aplet Plotting a piecewise-defined function Suppose you wanted to plot the following piecewise- defined function. 1. Open the F unctio n aple t. Select Function 2 . Hi ghlight the line y ou wan t to use , and enter the expr ession . (Y ou can pre ss to delete an e xisting line , or CLEAR to clear all line s.
Parametric aplet 4-1 4 Pa r a m e t r i c a p l e t About the Parametric aplet The Parametric aplet allows you to explore parametric equations. These are equations in which both x and y are defined as functions of t .
4-2 Parametric aplet Set angle measure 3 . Set the ang le measu re to degr ees. MODES Select Degrees Set up the plot 4. Display the graphing options. PLOT The P lot S etup input f orm has tw o fi elds not inc luded in the Functi on aplet, TRNG and TSTEP .
Parametric aplet 4-3 Overlay plot 8. Plot a triangle graph over the existing circle graph. PLOT 120 Select Overlay Plot A tria ngle is display ed r ather than a cir cle (w ithout c hanging the equation) because the c hanged va lue of TSTEP ensur es that points being plotted are 120 ° apa rt instead of near ly continuous .
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Polar aplet 5-1 5 Po l a r a p l e t Getting started with the Polar aplet Open the Polar aplet 1. Open the P olar apl et . Se lect Polar L ike the F uncti on aplet , the P olar aplet opens in the S ymbo lic v ie w . Define the expression 2 . Def ine the polar equati on .
5-2 Polar aplet Explore the graph 5 . Displa y the Plot v ie w menu k e y labels. Th e Plo t view o p t io n s av ailable ar e the same as those fo und in the F unction aplet . See “Explor ing the gr aph ” on page 2 - 7 for f urther information . Display the numbers 6 .
Sequence aplet 6-1 6 Sequence aplet About the Sequence aplet The Sequence aplet allows you to explore s equences. You can define a sequence named, for example, U1: • in terms of n • in terms of U1 ( n –1) •i n ter ms of U1 ( n –2) • in terms o f another sequence , for e xample , U2 ( n ) • in an y combination o f the abov e .
6-2 Sequence aplet Open the Sequence aplet 1. Open the Sequence apl et. Select Sequence The Sequence apl et starts in the S ymbo lic view . Define the expression 2 . Def ine the F ibonacc i sequence, in w hich eac h term (after the fir st two) is the sum of the pr eceding two terms: , , for .
Sequence aplet 6-3 Plot the sequence 4. Plot the F ibonacci seque nce. 5. In Plot Setup, set the SEQPLOT option to Cobweb . SETUP - PLOT Select Cobweb Display the table 6.
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Solve aplet 7-1 7 Solve aplet About the Solve aplet The Solve aplet solves an equation or an expression for its unknown variable . You define an equation or expression in the symbolic view, then supply values for all the variables except one in the numeric view.
7-2 Solve apl et Getting started with the Solve aplet Suppose you want to find th e acceleration needed to increase the speed of a car from 1 6.67 m/sec (60 kph) to 27.78 m/sec (100 kp h) in a distance of 100 m. The equation to solve is: Open the Solve aplet 1.
Solve aplet 7-3 4. Enter the value s for the kno w n vari ables . 2 7 7 8 1 6 6 7 1 0 0 HINT If the Decimal Mark setting in the Modes input form ( MODES ) is set to Comma, use instead of . Solve the unknown variable 5. Solv e fo r the unknow n var iable ( A ).
7-4 Solve apl et 6. P lot the equation f or var iable A . Sele ct Auto Scale 7 . T r ace along the graph repr es enting the left side o f the equation until the c ursor near s the inter sectio n. 20 times Note the v alue of A displa yed near the bottom left corner of the scr een.
Solve aplet 7-5 Use an initial guess You can usually obtain a fa ster and more accurate solution if you supply an estimated value for the unknown variable before pressing . Solve starts looking for a solution at the initial guess. Bef ore plo tting, mak e sur e the unknow n va riable is highlig hted in the numer ic v ie w .
7-6 Solve apl et Interpreting results After Solve has returned a solution, press in the Numeric view for more information. You will see one of the following three messages.
Solve aplet 7-7 If Solve could not find a solution, you will see one of the following two messages. HINT It is important to check the information relating to the solve process. For example, the solution that the Solve aplet finds is not a solution, but the closest that the function gets to zero.
7-8 Solve apl et where X is distance, V 0 is initial velocity, T is time, and A is acceleration. This is actually two equations, Y = X and Y = V 0 T + (AT 2 ) / 2 . Since this equation is quadratic for T , there can be both a positive and a negative solution.
Solve aplet 7-9 5. Move the cursor near the positive (right-side) intersection. This cursor value will be an initial guess for T . Pres s until the c ursor is at the intersec tion. The t wo po in ts o f inters ection sh ow that ther e are tw o soluti ons for this eq uation.
7-10 Solve apl et Using variables in equations You can use any of the real variable names, A to Z and θ . Do not use variable nam es defined for other types, such as M 1 (a matrix variable).
Linear Solver a plet 8-1 8 Li n e a r S ol ve r a p l e t About the Linear Solver aplet The Linear Solver aplet allows you to solve a set of linear equations. The set can contain two or three linear equations. In a two-equation set, each equation must be in the form .
8-2 Linear Solver aplet ex ample in the pr ev io us step). T o sol ve a thr ee - equation s et , pre ss . No w the input f orm displa ys thr ee eq uations . If the three-equation input fo rm is displayed and you want to solve a two-equation set, press .
Linear Solver a plet 8-3 As you enter each of the re maining know n value s, the soluti on change s. T he e x ample at the ri ght sho ws the final s olution once all th e co - efficient s a nd constants ar e enter ed f or the set of equati ons w e set out to solve.
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Triangle S olve aplet 9-1 9 T riangle Solv e aplet About the Triangle Solver aplet The Triangle Solver aplet a llows you to determine the length of a side of a triangle, or the angle at the vertex of a triangle, from information you supply about the other lengths and/or other angles.
9-2 Triangle So lve aplet Open the Triangle Solver aplet 1. Open the T riangle Sol ver a plet. Select Triangle Solver The T riangle Solv er aplet opens. Note : if y ou hav e alr eady u sed the T r iangle Sol ver , the entries and results fr om th e pre vi ous use will still be displayed .
Triangle S olve aplet 9-3 lengths as B and C, w e wo uld need to spec ify the angle as α . The illus trati on on the displa y will help yo u determine wher e to enter the k now n values. Note: if you need to c hange the angle neasure mode , pres s MODES , change the mode , and then pres s to r eturn to t he aplet.
Not enough data If you are using the general input form, you need to specify at least three values for the Triangle Solver to be able to calculate the remaining attributes of the triangle. If you specify less than three, No t enough data appears on the screen.
Statistics aplet 10-1 10 Statist ic s ap let About the Statistics aplet The Statistics aplet can store up to ten data sets at one time. It can perform one- variable or two-vari able statistical analysis of one or more sets of data. The Statistics aplet starts with the Numeric view which is used to enter data.
10-2 Statistics aplet Open the Statistics aplet 1. Open the St atistic s aplet and clear e x isting data b y pres sing . Select Statistics Th e St a ti st ic s ap l et starts in the Numer ical view .
Statistics aplet 10-3 Choose fit and data columns 4. Select a f it in the S ymboli c setup vi ew . SETUP - SYMB Select Linear Y o u c a n cre a t e up t o five exp l o rat i on s o f t wo - va ria b le data, named S1 to S5 . I n t h i s exa m pl e, we wil l cre a te just o ne : S1 .
10-4 Statistics aplet Setup plot 8. Change the plotting range to ensur e all the data points ar e plotted (and select a differ ent point mark , if yo u wi s h ) . SETUP - PLOT 7 100 400 0 Plot the graph 9 . P lot the gr aph. Draw the regression curve 10.
Statistics aplet 10-5 Predict values 13 . T o find the pr edic ted sales f igur e if ad vertising w er e to go up to 6 minute s: S ( to highlight Stat-Two ) (to highli ght PREDY ) 6 14. Retur n to the P lot vi ew . 15 . Jump to the indi cated point on the r egr essi on line.
10-6 Statistics aplet Entering and editing statistical data The Numeric view ( ) is used to enter data into the Statistics aplet. Each column represents a variable named C0 to C9 . After entering the data, you must define the data set in the Symbolic view ( ).
Statistics aplet 10-7 Example You are measurin g the height of students in a classroom to find the mean height. The first five students have the following measurements 160cm, 165cm, 170c m, 175cm, 180cm. 1. Open the Statistics apl et . Select Statistics 2 .
10-8 Statistics aplet 3 . F ind the mean of the sample. Ensur e the / menu k ey label reads . Pr ess to see the statistic s calculated fr om the sample data in C1 . Note that the title o f the colu mn of s tatis tics is H1 . Ther e are 5 data set de finitions av ailable for one- var iable stat ist ics: H1–H5 .
Statistics aplet 10-9 To continue our example, supp ose that the heights of the rest of the students in the class are measured, but each one is rounded to the nearest of the five values first recorded. Instead of entering all the new data in C1 , we shall simply add another column, C2 , that holds the frequencies of our five data points in C1 .
10-10 Statistics aplet 5 . Mov e the highli ght bar into the r ight column of the H1 def inition and replace the frequency value o f 1 w ith the name C2 . 2 6 . Retur n to the numer ic v ie w . 7 . Enter the f req uency data sho w n in the abov e table .
Statistics aplet 10-11 Edit a data set In the Numeric view of the Statistics aplet , highlight the data value to change. Type a new va lue and press , or press to copy the value to the edit line for modification. Press after modifying the value on the edit line.
10-12 Statistics aplet Defining a regression model The Symbolic view includes an expression (Fit1 through Fit5) that defines the regression model, or “fit”, to use for the regression analysis of each two-variable data set. There are three ways to select a regression model: • Accept the d efault option to f it th e data to a str aight line.
Statistics aplet 10-13 To define your own fit 1. In Numeri c vi ew , mak e sur e is set. 2 . Display the S ymbolic v iew . 3 . Highli ght the F it e xpres sion ( Fit1 , etc .) for the desired data set . 4. T ype in an e xpr ess ion and pr ess . The independent variable must be X , and the expr ession mus t not contain an y unknow n var iables .
10-14 Statistics aplet Computed statistics One-variable When the data set contains an odd number of values, the data set’s median value is no t used when calculating Q1 and Q3 in the table abo ve.
Statistics aplet 10-15 Two-variable Plotting You can plot: • histogr ams ( ) • box - and-whisk er plots ( ) • scat ter p lots ( ). Once you have entere d your data ( ), defined your data set ( ), and defined your F it model for two- variable statistics ( SETUP - SYMB ), you can plot your data.
10-16 Statistics aplet To plot statistical data 1. In S ymbo lic v ie w ( ) , select ( ) the data sets y ou w ant to plot . 2 . F or one-var iable data ( ) , select the plo t type in Plot Setup ( SETUP - PLOT ) . Highli ght ST A TPLOT , pres s , select either Histogram or BoxWhisker , and pr ess .
Statistics aplet 10-17 Scatter Plot Two-v ariable statistics . The numbers below the plot indicate that the cursor is at the first data point for S2, at (1, 6). Press to move to the next data point and display information about it. To connect the data points as they are plotted, checkmark CONNECT in the second page of the Plot Setup.
10-18 Statistics aplet Relative Error The relative error is a measure of the erro r between predicted values and actual va lues based on the specified Fit.
Statistics aplet 10-19 For instance, the data set (1,1 ), (3,9), (4,16), (2,4) would be plotted and traced in the order (1,1), (2,4), (3,9), (4,16). Trouble-shooting a plot If you have problems plotting, check that you have the following: • The co rr ect or menu label o n (Numeric view ) .
10-20 Statistics aplet Calculating predicted values The functions PREDX and PREDY estimate (predict ) values for X or Y given a hypothetical value for the other . The estimation is made based on the curve that has been calculated to fit the data a ccording to the specified fit.
Statistics aplet 10-21 • Enter P RED Y( x-value ) to find the pr edic ted va lue of the dependent var iable gi ven a h ypothetical independent vari ab le. You can type PREDX and PREDY into the edit line, or you can copy these function names from the MATH menu under the Stat-Two category.
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Inference aplet 11-1 11 Inference aplet About the Inference aplet The Inference capabilities include calculation of confidence intervals and hy pothesis tests based on the Normal Z-distribution or Student’s t-distribution.
11-2 Inference apl et Inference aplet’s SYMB view keys The table below summarizes the options available in Symbolic view. If you choose one of the hypoth esis tests, you can choose the alternative hypothesis to test against the null hypothesis.
Inference aplet 11-3 Select the inferential method 2. Select the Hypothesis Test inferential method. Select HYPOTH TEST 3. Define the type of test. Z–Test: 1 μ 4. Select an alternative hypothesis. μ< μ0 Enter data 5. Enter the sample statistics and population parameters.
11-4 Inference apl et By default, each field already contains a value. These values constitute the ex ample database and are explained i n the feature of this aplet. Display on-line help 6. To display the on-line help, press 7. To close the on-line help, press .
Inference aplet 11-5 A calculator produces the following 6 random numbers: 0.529, 0.295, 0.952, 0.2 59, 0.925, and 0.592 Open the Statistics aplet 1. Open the Statistics aplet and reset the current settings. Select Statistics The Statistics aplet opens in the Numeric view.
11-6 Inference apl et Open Inference aplet 6. Open the Infere nce aplet and cle ar current setting s. Select Inference Select inference method and type 7. Select an inference method. Select CONF INTERVAL 8. Select a distribution statistic type. Select T-Int: 1 μ Set up the interval calculation 9.
Inference aplet 11-7 Import the data 10. Import the data from the Statistics aplet. Note: The data from C1 is displayed by default. Note: Press to see the statistics before importing them into the Numeric Setup view. Also, if there is more than one aplet b ased on the Statistics aplet, you are prompted to choose one.
11-8 Inference apl et Hypothesis tests You use hypothesis tests to test the validity of hypotheses that relate to the statistical parameters of one or two populations. The tests are base d on statistics of samples of the populations. The HP 40gs hypothesis tests use the Normal Z-distribution or Student’s t-distribution to calculate probabilities.
Inference aplet 11-9 Results The results are: Two-Sample Z-Test Menu name Z-Test: μ 1– μ 2 On the basis of two samples, each from a separate population, this test measures t he strength of the evidence for a selected hypothesis against the null hypothesis.
11-10 Inference apl et Results The results are: One-Proportion Z-Test Menu name Z-Test: 1π On the basis of statistics from a single sample, this test measures the strength of the evidence for a selected hypothesis against the null hypothesis.
Inference aplet 11-11 Inputs The inputs are: Results The results are: Two-Proportion Z-Test Menu name Z-Test: π 1 – π 2 On the basis of statistics from two samples, each from a different population, the Two-Proportion Z-Test measures the strengt h of the evide nce for a selected hypothesis against the null hypothesis.
11-12 Inference apl et Inputs The inputs are: Results The results are: One-Sample T-Test Menu name T-Test: 1 μ The One-sample T-Test is used when the population standard deviation is not know n. On the basis of statistics from a single sample, this test measures the strength of the evidence for a selected hypothesis against the null hypothesis.
Inference aplet 11-13 Inputs The inputs are: Results The results are: Field name Definition Sample mean. Sx Sample standard deviat ion. n Sample size. μ0 Hypothetical population mean. α Significance level. x Result Description Test T T-Test statistic.
11-14 Inference apl et Two-Sample T-Test Menu name T-Test: μ 1 – μ 2 The Two-sample T-Test is used when the population standard deviation is not know n. On the basis of statistics from two samples, each sample from a different population, this test measures the strength of the evidence for a selected hypothesis against the null hypothesis.
Inference aplet 11-15 Results The results are: Confidence intervals The confidence interval calc ulations that the HP 40gs can perform are based on the Normal Z-distribution or Student’s t-distribution.
11-16 Inference apl et Results The results are: Two-Sample Z-Interval Menu name Z-IN T: μ1 – μ2 This option uses the Normal Z- distribution to calculate a confidence interval for the difference between the means of two populations, μ 1 – μ 2 , when the population standard deviations, σ 1 and σ 2 , are known.
Inference aplet 11-17 One-Proportion Z-Interval Menu name Z-INT: 1 π This option uses the Normal Z-distribution to calculate a confidence interval for the proportion of successes in a population for the case in which a sample of size, n , has a number of successes, x .
11-18 Inference apl et Results The results are: One-Sample T-Interval Menu name T-INT: 1 μ This option uses the Student’s t-distribution to calculate a confidence interval for m, the true mean o f a population, for the case in which the true population standard deviation, s, is unknown.
Inference aplet 11-19 Results The results are: Two-Sample T-Interval Menu name T-INT: μ 1 – μ 2 This option uses the Student’s t-distribution to calculate a confidence interval for the difference between the means of two populations, μ 1 – μ 2, when the population standard deviations, s1and s2 , are unknown.
11-20 Inference apl et Results The results are: Result Description Critical T Critical value for T. μ Min Lower bound for μ 1 – μ 2 . μ Max Upper bound for μ 1 – μ 2 .
Using the Finance Solver 12-1 12 Using the Finance Solver The Finance Solver, or Finance aplet , is available by using the APLET key in your calculator. Use the up and down arrow keys to select the Finance aplet. Your screen should look as follows: Press the key or the soft menu key to activate the aplet.
12-2 Using the Finance Sol ver combined amount earns interest at a certain rate. Financial calculations involving compound interest include savings accounts, mo rtgages, pension funds, leases, and annuities.
Using the Finance Solver 12-3 flow diagram shows lease payments at the beginning of each period. The following cash flow diagram shows deposits into an account at the end of each period.
12-4 Using the Finance Sol ver Performing TVM calculations 1. Launc h the F inanc ial Sol ver as indi cated at the beginning of this secti on. 2 . Use the arr o w ke y s to highli ght the differ ent f ields and enter the kno wn v aria bles in the T VM calculati ons, pres sing the soft-menu ke y after enter ing each kno wn va lue.
Using the Finance Solver 12-5 Example 1 - Loan calculations Suppose you finance the purcha se of a car with a 5-year loan at 5.5% annual intere st, compounded monthly.
12-6 Using the Finance Sol ver Example 2 - Mortgage with balloon payment Suppose you have taken out a 30-year, $ 150,000 house mortgage at 6.5% annual interest. You expect to sell the house in 10 years, repay ing the loan in a balloon payment. Find the size of the balloon payment, the value of the mortgage after 10 years of payment.
Using the Finance Solver 12-7 Calculating Amortizations Amortization calculations, which also use the TVM variables, determine the amounts applied towards principal and interest in a payment or series of payments. To calculate amortizations: 1. Start the F inance Solv er as indicated at the beginning of t his sec tion.
12-8 Using the Finance Sol ver 3 . Pre ss the soft menu k ey to amorti z e the ne w batch of pa yments . Repeat step s 1 through 3 as often as needed. Example 4 - Amortization for home mortgage For the results of Example 3, show the amortization of the next 10 years of the mortgage loan.
Using mathematical fun ctions 13-1 13 Using mathematical func tions Math functions The HP 40gs contains many math functions. The function s are grouped in categories. For example, the Matrix category contains functions for manipulating matrices. The Probability category (shown as Prob.
13-2 Using mathematical functio ns To select a function 1. Pr ess to displa y the MA TH menu. T he categorie s appear in alphabetical or der . 2 . Pr ess or to scr oll thr ough the categor ies. T o jum p direc tly to a category , pr ess the f irst letter of the category’s name.
Using mathematical fun ctions 13-3 Functions common to keyboard and menus These functions are common to the keyboard and MATH menu. Keyboard functions The most frequently used functions are available directly from the keyboard. Many of the keyboard functions also accept complex numbers as arguments.
13-4 Using mathematical functio ns ,, , Add, Subtract, Multiply, Di vide. Also accepts complex numbers, lists and matrices. val u e1 + va lu e 2 , etc. e x Natural exponential. Also accepts complex numbers. e^ val u e Example e^5 ret u rn s 148.413159103 Natural logarithm.
Using mathematical fun ctions 13-5 Example ASIN(1) r eturns 90 (Degr ees mode) . ACOS Arc cosine: cos –1 x . Output range is from 0° to 180°, 0 to π , or 0 to 200 grads. Inputs and outputs depend on the current angle format. Also accepts complex numbers.
13-6 Using mathematical functio ns Example 2^8 r eturns 256 ABS Absolute value. For a co mplex number, this is . ABS ( val ue ) ABS (( x , y )) Example ABS(–1 ) r eturns 1 ABS((1,2)) r eturns 2.
Using mathematical fun ctions 13-7 Example (0,s1,2*X+3,X) finds the inde finite r esult 3*s1+2* (s1^2/2) See “T o find the indef inite integral u sing for mal var iables ” on page 13- 2 3 f or more inf ormati on on finding indef inite integr als.
13-8 Using mathematical functio ns Example IM((3,4)) r eturns 4 RE Real part x , of a complex number, ( x, y ). RE (( x, y )) Example RE((3,4)) r eturns 3 Constants The constants available from the MATH FUNCTIONS menu are mathematical constants. These are des cribed in this section.
Using mathematical fun ctions 13-9 → C Convert from Fahrenheit to Celcius. Example → C(212) r eturns 100 → F Convert from Celcius to Fahrenheit. Example → F(0) r eturns 32 → CM Convert from inches to centimeters. → IN Convert from centimeters to inches.
13-10 Using mathematical functions COSH Hyperboli c cosine COSH ( val ue ) SINH Hyperbolic sine. SINH ( val ue ) TANH Hyperbolic tangent. TANH ( val ue ) ALOG Antilogarithm (exponential). Th is is more accurate than 10^x due to limitations of the power function.
Using mathematical fun ctions 13-11 RECURSE Prov ides a method of defining a sequence without using the Symbolic view of the Sequ ence aplet. If used with | (“where”), RECURSE will step through the evaluation.
13-12 Using mathematical functions Example Fo r x 4 +2x 3 –25x 2 –26x+120 : POLYEVAL([1,2,-25,-26,120],8) ret u r n s 3432 . POLYFORM Polynomi al form. Creates a polynomial in var iable1 from expression. POLYFORM ( e xpression , vari ab l e1 ) Example POLYFORM((X+1)^2+1,X) ret u r n s X^2+2*X+2 .
Using mathematical fun ctions 13-13 Factorial of a positive integer. For non-integers, ! = Γ (x + 1) . This calculates the gamma function. value! PERM Number of permutations (with regard to order) o f n things taken r at a time: n!/(r!(n-r)! PERM ( n, r ) Example PERM(5,2) r eturns 20 .
13-14 Using mathematical functions UTPT Upper-Tail Student’s t-Probability given degrees of freedom, evaluated at value. Returns the probability that the Student's t- random variable is greater than va lue. UTPT ( degr ees , valu e ) Real-number functions Some real-number functions can also take complex arguments.
Using mathematical fun ctions 13-15 HMS → H ours-minutes-seconds to deci mal. Converts a number or expression in H.MMSSs format (time or angle that can include fractions of a second) to x.x format (number of hours or degrees with a decimal fraction).
13-16 Using mathematical functions Example 9 MOD 4 re turns 1 % x percent of y ; that is, x /100* y . % ( x , y ) Example % (20,50) r eturns 10 %CHANGE Percent change from x to y , that is, 100( y–x )/ x . % CHANGE ( x , y ) Example % CHANGE(20,50) r eturns 150 %TOTAL Percent total : (100) y/ x .
Using mathematical fun ctions 13-17 Examples SIGN (–2) ret u rn s –1 SIGN((3,4)) r eturns (.6,.8) TRUNCATE Truncates value to decimal places . Accepts complex numbers. TRUNCATE ( val ue , places ) Example TRUNCATE(2.3678,2) r eturns 2.36 XPON Exponent of value .
13-18 Using mathematical functions Examples ISOLATE(2*X+8,X) r eturns -4 ISOLATE(A+B*X/C,X) r eturns -(A* C/B) LINEAR? Tests whet her expression is linear for the specified variable .
Using mathematical fun ctions 13-19 Test functions The test functions are logical operators that always return either a 1 ( true ) or a 0 ( false ). < Less than. Returns 1 if true, 0 if false. val u e1 < va lu e 2 ≤ Less than or equal to. Returns 1 if true, 0 if false.
13-20 Using mathematical functions XOR Exclusive OR. Returns 1 if either value1 or value2 —but not both of them—is non-zero, otherwise returns 0. val u e1 XOR val ue2 Trigonometry functions The trigonometry functions can also take complex numbers as arguments.
Using mathematical fun ctions 13-21 names. The HP 40gs has six formal names available for use in symbolic calculations. These are S1 to S5. When you perform a calculation that contains a formal name, the HP 40gs does not carry out any substitutions. You can mix formal names and real variables.
13-22 Using mathematical functions differentiation function substi tutes the value that X holds, and returns a numeric result. For example, consider the function: 1. Enter the differ entiati on functi on onto the command line , substituting S1 in place of X .
Using mathematical fun ctions 13-23 F1 3. Se l e c t F 2 ( X ) and eval u a te i t. 4. Pres s to display the r esult . Note: Use the arr o w ke y s to vi ew the entir e functi on . | Y ou coul d also ju st def ine . To find the indefinite integral using formal variables F or ex ample, to find the indefinite inte gral of use: 1.
13-24 Using mathematical functions 4. Cop y the r esult and eva lu a te. Th us, sub stituting X for S1, it can be seen that: This result is derived from substituting X =S 1 and X =0 into the original expression found in step 1. However, substituting X =0 will not always evaluate to zero and may result in an unwanted constant.
Using mathematical fun ctions 13-25 Program constants The program constants are numbers that have been assigned to various calculat or settings to enable you to test for or specify such a setting in a program.
13-26 Using mathematical functions 3 . Use the ar r ow k e y s to nav igate thr ough the opti ons. 4. T o see the sy mbol and v alue of a selec ted constant , pr ess . (Cli ck to clos e the infor mation w indow that appears .) The f ollo wi ng ex ample sho w s the informati on av ailabl e about the speed of light (one of the phy sics constants).
Using mathematical fun ctions 13-27 3. Se l e c t light s... fr om the Ph ysi cs menu . 4. Pr ess . The menu c loses and the v alue of the select ed constant is copied t o the edit line. 5 . Co mplete the equati on as y ou w ould no rmally and pr ess to get the r esult .
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Computer Al gebra System (CAS) 14-1 14 Computer Algebra S y stem (CAS) What is a CAS? A computer al gebra system ( hereafter C AS) enables y ou to perform symbolic calculations.
14-2 Computer Algebra System (CAS) using vector s and matrices. (Vectors and matrices cannot be entered using the Equation Writer). To open the Equation Writer, press the soft- key on the menu bar of the HOME screen. The illustration at the right shows an expression being written in the Equation Writer.
Computer Al gebra System (CAS) 14-3 3. P re s s a n d t o select j ust the 20 in the term . 4. Pres s the menu ke y and choose FACTOR . Then pr ess . Note that the FACTOR functi on is added to the sele cted t erm. 5. Press to factor the selected term.
14-4 Computer Algebra System (CAS) 10. Pres s three times to select the entire expression and then press to simplify it to the form required. CAS variables When you use the symbolic calculation functions, y ou are working with symbolic variab les (variables that do not contain a permanent value).
Computer Al gebra System (CAS) 14-5 CAS modes The modes that determine how CAS operates can be set on CAS MODES scre en. To display CAS MODES screen, press: ·To navigate through the options in CAS MODES screen, press the arrow keys.
14-6 Computer Algebra System (CAS) calculated as closed-form algebraic expressions, whenever possible. [Default: u nselected.] Num. Factor mode When the NUM FACTOR setting is selected, approximate roots are used when factoring . For example, is irreducible over the intege rs but has approximate roots over the reals.
Computer Al gebra System (CAS) 14-7 Using CAS functions in HOME You can use many computer algebra functions directly in the HOME screen, as long as you take certain precautions. CAS functions th at take matrices as an argument work only from HOME. CAS functions can be accessed by pressing when MATH menu is displayed.
14-8 Computer Algebra System (CAS) Symbolic matrices are stored as a list of lists and therefore must be stored in L0, L1…L 9 (whereas numeric matric es are stored in M0, M1,…M9).
Computer Al gebra System (CAS) 14-9 HELP and press . The menu of help topi cs appears. Each help topic includes the required syntax, along with real sample values. You can copy the syntax, with the sample values, to the HOME screen or to the Equation Writer, by pressing .
14-10 Computer Alge bra System (CAS) For example, suppose y ou have stored the expression x 2 in G, and have defined the function F(x) a s x 2 . Suppose now you want to calculate INTVX(X 2 ). You could: • enter INTVX(X 2 ) direc tly , or • enter INTVX(G) , or • enter INTVX(F(X)) .
Computer Algebra Sys tem (CAS) 14-11 Typing: DEF(U(N) = 2N+1) produces the result: U(N) = 2N+1 Typing: U(3) then returns: 7 Example Calculate the first six Fermat numbers F1...F6 and determine whether they are prime. So, you want to calculate: for k = 1.
14-12 Computer Alge bra System (CAS) which gives 4294967297 You can factor F(5) with FACTOR , which you’ll find in the ALGB menu on the menu bar. Typing: FACTOR(F(5)) gives: 641·6700417 Typing: F(6.
Computer Algebra Sys tem (CAS) 14-13 In real mode, the result is: In complex mode (using CFG ), the result is: PARTFRAC Partial fraction expansion PARTFRAC has a rational fraction as an argument. PARTFRAC returns the partial fraction decomposition of this rational fraction.
14-14 Computer Alge bra System (CAS) Example 2 Typing: SUBST(QUOTE(CONJ(Z)),Z=1+i) gives: CONJ(1+i) STORE Store an object in a variable STORE stores an object in a variable.
Computer Algebra Sys tem (CAS) 14-15 SUBST Substi tute a value for a variable SUBST has two parameters: an expression depe ndent on a parameter, and an equality (parameter=substitute value). SUBST substitutes the specifie d value for the variable in the expression.
14-16 Computer Alge bra System (CAS) DIFF menu DERIV Derivative and partial deri vative DERIV has two arguments: an expression (or a functi on) and a variable. DERIV returns the derivative of the expression (or the function) with respect to th e variable given as the second parameter (used for calculating partial derivatives).
Computer Algebra Sys tem (CAS) 14-17 DERVX(F) Or, if you have defined F(X) using DEF , that is, if you have typed: then type: DERVX(F(X)) Simplify the result to get: DIVPC Division in increasing order by exponent DIVPC has three ar guments: two polynomials A(X) and B(X) (where B(0) ≠ 0), and a whole number n.
14-18 Computer Alge bra System (CAS) and with period T ( T being equal to the contents of the variable PERIOD ). If f(x) is a discrete series, then: Example Determine the Fourier coefficients of a periodic function f with period 2 π and defined over interval [0, 2 π ] by f(x)=x 2 .
Computer Algebra Sys tem (CAS) 14-19 IBP returns the AND of and of that is, the terms that are calculated when performing a partial integration. It remains then to calculate the integral of the second term of the AND, then add it to the first term of the AND to obtain a primitive of .
14-20 Computer Alge bra System (CAS) Example Given: calculate a primitive of f . Type: Or, if you have stored f(x) in F, that is, if you have already typed: then type: INTVX(F) Or, if you have used DE.
Computer Algebra Sys tem (CAS) 14-21 gives a primitive: Note You can also type which gives the primitive which is zero for x = 1 Example Calculate: Typing: gives th e result: NOTE: If the argument to INTVX is the AND of two elements, INTVX concerns itself only with the se cond element of the AND, and adds the result to the first argument.
14-22 Computer Alge bra System (CAS) QUOTE(expression), to avoid rewriting the expression i n normal form (i.e., not to have a rational simplification of the arguments) during the execution of the LIMIT command.
Computer Algebra Sys tem (CAS) 14-23 Typing: gives: 2 NOTE: To find the limit as x approaches a + (resp a – ), the second argument is written: X=A+0(resp X=A-0) For the following expression, find the limi t as x approaches + ∞ : Typing: produces (after a short wait): NOTE: the symbol ∞ is obtained by typing SHIFT 0.
14-24 Computer Alge bra System (CAS) PREVAL is used for calculatin g an integral defined from a primitive: it evaluates this pr imitive between the two limits of the integral. Typing: PREVAL(X 2 +X,2,3) gives: 6 RISCH Primitive and defined integra l RISCH has two parameters: an expression and the name of a variable.
Computer Algebra Sys tem (CAS) 14-25 Typing: gives: • Ex amp le — Expansion in the vic init y of x=+ ∞ or x=– ∞ Example 1 Give a 5th-order expansion of arctan(x) in the vic inity of x =+ ∞ , taking as infinitely small .
14-26 Computer Alge bra System (CAS) You must be in Rigorous (not Sloppy) mode to apply SERIES with unidirectional expansion. (See “CAS modes” on page 14-5 for instructions on setting and changing modes. Example 1 Give a 3rd-order expansion of in the vicinity of x = 0 + .
Computer Algebra Sys tem (CAS) 14-27 TABVAR Variation table TABVAR has as a parameter an ex pression with a rational derivative. TABVAR returns the variation table for the expression in terms of the current variable.
14-28 Computer Alge bra System (CAS) Typing: gives: Note ‘th-order’ means that the numerator and the denominator are expanded to the 4th relative order (here, the 5th absolute order for the numerator, and fo r the denominator, which is given in the end, the 2nd order (5 − 3), seeing that the exponent of the denominator is 3).
Computer Algebra Sys tem (CAS) 14-29 Typing: DISTRIB((X+1)·(X+2)·(X+3)) gi ves: EPSX0 Disregard small values EPSX0 has as a parameter an ex pres sion in X, and returns the same expression with the values less than EPS replaced by zeroes. Typing: EPSX0(0.
14-30 Computer Alge bra System (CAS) Typing: EXP2POW(EXP(N · LN(X))) gives: FDISTRIB Distributivity FDISTRIB has an expression as argument. FDISTRIB enables you to appl y the distributivity of multiplication with respec t to addition all at once.
Computer Algebra Sys tem (CAS) 14-31 Example 3 Typing: LIN(SIN(X)) gives: LNCOLLECT Regroup the logarithms LNCOLLECT has as an argument an expression containing logarithms. LNCOLLECT regroups the terms in the logarithms. It is therefore preferable to use an expression that has already been factored (using FACTOR ).
14-32 Computer Alge bra System (CAS) Typing: SINCOS(EXP(i·X)) gives after turning on complex mode, if necessary: cos(x) + i · sin(x) SIMPLIFY Simplify SIMPLIFY simplifies an expres sion automatically. Typing: gives, after simplification: 4 · cos(x) 2 − 2 XNUM Evaluation of reals XNUM has an expression as a parameter.
Computer Algebra Sys tem (CAS) 14-33 Typing: XQ(1.414213562) gives: √ 2 SOLV menu The SOLV menu contains functions that enable you to solve equations, linear systems, and differential equations. DESOLVE Solve differential equations DESOLVE enables you to solve differential equations.
14-34 Computer Alge bra System (CAS) To produce the solutions for y(0) = 1, type: which gives: Example 2 Solve: y” + y = cos(x) y(0) = 1 y’(0) = 1 It is possible to solve for the constants from the outset.
Computer Algebra Sys tem (CAS) 14-35 LDEC Linear diffe rential equations having constant coefficients LDEC enables you to directly solve linear differential equations having cons tant coefficients. The parameters are the second member and the characteristic equation.
14-36 Computer Alge bra System (CAS) L1=2L1+L2 ENTER Reduction Result then press ENTER. The following is then written to the Equation Writer: (x = − 2) AND (y = − 1) Example 2 Type: (2·X+Y+Z=1)AND(X+Y+2·Z=1)AND(X+2·Y+Z=4) Then, invoke LINSOLVE and type the unknowns: X AND Y AND Z and press the ENTER key.
Computer Algebra Sys tem (CAS) 14-37 then press ENTER. The following is then written to the Equation Writer: SOLVE Solve equations SOLVE has as two parameters: (1) either an equality between two expressions, or a single expression (in which case = 0 is implied), and (2) the name of a variable.
14-38 Computer Alge bra System (CAS) SOLVEVX Solve equations SOLVEVX has as a parameter either: (1) an equality between two expressions in the variable contained in VX, or (2) a single such expression (in which case = 0 is implied). SOLVEVX solves the equation.
Computer Algebra Sys tem (CAS) 14-39 Typing: ACOS2S(ACOS(X) + ASIN(X)) gives, when simplified: ASIN2C Transform the arcsi n into arccos ASIN2C has as a trigonometric expression as an argument. ASIN2C transforms the express ion by re placing arcsin (x) with − ar ccos(x) .
14-40 Computer Alge bra System (CAS) Typing: ATAN2S(ATAN(X)) gives: HALFTAN Transform in terms of tan(x/2) HALFTAN has a trigonometric expression as an argument. HALFTAN transforms sin(x), cos(x) and tan(x) in the expression, rewriting them in terms of tan(x/2).
Computer Algebra Sys tem (CAS) 14-41 TAN2CS2 transforms this expr ession by replacing tan(x) with . Typing: TAN2CS2(TAN(X)) gives: TAN2SC Replace tan(x) with sin(x)/cos(x) TAN2SC has a trigonometric expression as an argument. TAN2SC transforms this expr ession by replacing tan(x) with .
14-42 Computer Alge bra System (CAS) TCOLLECT linearizes this ex pression in terms of sin( n x ) and cos( n x ), then (in Real mode) reconstructs the sine and cosine of the same angle.
Computer Algebra Sys tem (CAS) 14-43 gives: 4·cos(x) 3 –3·cos(x) TLIN Linea rize a trigonomet ric expression TLIN has as an argument a trigonometric expression.
14-44 Computer Alge bra System (CAS) Typing: TRIG(SIN(X) 2 + COS(X) 2 + 1) gives: 2 TRIGCOS Simplify using the cosines TRIGCOS has as an argument a trigonometri c expression. TRIGCOS simplifies this expression, using the identity sin(x) 2 +cos(x) 2 = 1 to rewrite it in terms of cosines.
Computer Algebra Sys tem (CAS) 14-45 CAS Functions on the MATH menu When you are in the Equation Writer and press , a menu of additional CAS functions available to you is displayed.
14-46 Computer Alge bra System (CAS) returns: Y = X –1 + 2 Pressing simplifies this to: Y = X + 1 IM See “IM” on pag e 13-7. – Specifies the negation of the argument. RE See “RE” on page 13-8. SIGN Determines the quotient of the argument divided by its modulus.
Computer Algebra Sys tem (CAS) 14-47 DIVIS Gives the divisors of an integer. Example Typing: DIVIS(12) gives: 12 OR 6 OR 3 OR 4 OR 2 OR 1 Note: DIVIS(0) returns 0 OR 1. EULER Returns the Euler index of a whole number. The Euler index of n is the number of whole numbers less than n that are prime with n .
14-48 Computer Alge bra System (CAS) In step-by-step mode, there ar e a number of intermediate results: 18 mod 15 = 3 15 mod 3 = 0 Res ul t : 3 Pressing or then causes 3 to be written to the Equation Writer. Note that the last non-zero remainder in the sequence of remainders shown in the intermediate steps is the GCD.
Computer Algebra Sys tem (CAS) 14-49 [48, 1 ,0 ] [30, 0,1]*–1 [18 ,1,–1]*–1 [12 ,–1,2]*–1 [6,2 ,–3]*–2 Re sult: [6,2 ,–3] Pressing or then causes 2 AND –3 = 6 to be written to the Equation Writer. The intermediate steps shown are the combination of lines.
14-50 Computer Alge bra System (CAS) IREMAINDER works with integers and with Gaussian integers. This is what disti nguishes it from MOD. Example 2 Typing: IREMAINDER(2 + 3·i, 1 + i) gives: i ISPRIME? Returns a value indicating whether an integer is a prime number.
Computer Algebra Sys tem (CAS) 14-51 NEXTPRIME NEXTPR IME( n ) returns the smallest prime or pseudo-prime greater than n . Example Typing: NEXTP RIME(7 5 ) gives: 79 PREVPRIME PREVPRIME( n ) returns the greatest prime or pseudo-prime less than n .
14-52 Computer Alge bra System (CAS) DIVMOD Division in Z/pZ or Z/pZ[X]. Example 1 In Z/pZ, the arguments are two integers: A and B. When B has an inverse in Z/pZ, the result is A/B simplified as Z/pZ. Typing: DIV MOD(5 , 3) gives: 6 Example 2 In Z/pZ[X], the arguments are two polynomials: A[X] and B[X].
Computer Algebra Sys tem (CAS) 14-53 FACTORMOD Factors a polynomial in Z/ pZ[X], providing that p ≤ 97, p is prime and the order of the multiple factors is less than the modu lo. Example Typing: FA C T O R M O D ( – ( 3 X 3 – 5X 2 + 5X – 4)) gives: GCDMOD Calculates the GCD of the two polynomials in Z/pZ[X].
14-54 Computer Alge bra System (CAS) MULTMOD Performs a multiplication in Z/pZ or in Z/pZ[ X]. Example 1 Typing: MUL TMO D(11, 8) gives: –3 Example 2 Typing: MUL TMOD(11X + 5, 8X + 6) gives: POWMOD Calculates A to the power of N in Z/pZ[X], and A(X) to the power of N in Z/pZ[X].
Computer Algebra Sys tem (CAS) 14-55 SUBTMOD Performs a subtraction in Z/pZ or Z/pZ[X]. Example 1 Typing: SU BTM O D ( 29 , 8 ) gives: –5 Example 2 Typing: S UB TMOD(11X + 5, 8X + 6) gives: Polynomial menu EGCD Returns Bézout’s Identity, the Extended Greatest Common Divisor (EGCD).
14-56 Computer Alge bra System (CAS) FACTOR Factors a polynomial. Example 1 Typing: F A CT OR(X 2 – 2) gives: Example 2 Typing: F A CT OR(X 2 + 2·X + 1) gives: GCD Returns the GCD (Greatest Common Divisor) of two polynomials.
Computer Algebra Sys tem (CAS) 14-57 LCM Returns the LCM (Least Common Multiple) of two polynomials. Example Typing: LC M ( X 2 + 2·X + 1, X 2 – 1) gives: LEGENDRE Returns the polynomial L n , a non-null solution of the differential equation: where n is a whole number.
14-58 Computer Alge bra System (CAS) PROPFRAC PROPFRAC rewrites a rational fr action so as to bring out its whole number part. PROPFRAC(A(X)/ B(X)) writes th e rational fraction A(X)/ B(X) in the form: where R”(X) = 0, or 0 ≤ deg (R(X) < deg (B(X).
Computer Algebra Sys tem (CAS) 14-59 Note that in step-by-step mode, synthetic division is shown, with each polynomial represented as the list of its coefficients in descending order of power. REMAINDER Returns the remainder from the division of the two polynomials, A(X) and B(X), divided in decreasing order by exponent.
14-60 Computer Alge bra System (CAS) Example 1 Typing: T CHEB Y CHEFF(4) gives: Example 2 Typing: T CHEB Y CHEFF(–4) gives: Real menu CEILING See “CEILING” on page 13-14. FLOOR See “FLOOR” on page 13-14. FRAC See “FRAC” on page 13-14. INT Se e “INT” on page 13-15.
Computer Algebra Sys tem (CAS) 14-61 Tests menu ASSUME Use this function to make a hypothesis about a specified argument or variable. Example Typing: ASSUM E( X > Y) sets an assumption that X is greater than Y.
14-62 Computer Alge bra System (CAS) CAS Functions on the CMDS menu When you are in the Equation Writer and press , a menu of the full set of CAS functions available to you is displayed.
Computer Algebra Sys tem (CAS) 14-63 Example Find the solutions P(X) of: P(X) = X (mod X 2 + 1) P(X) = X – 1 (mod X 2 – 1) Typing: CHINREM((X) AND (X 2 + 1) , (X – 1) AND (X 2 – 1)) gives: That is: CYCLOTOMIC Returns the cyclotomic polynomial of or der n .
14-64 Computer Alge bra System (CAS) Example 1 Typing: EXP 2HY P (EXP (A)) gives: sinh( a) + co sh(a ) Example 2 Typing: EXP 2HY P( EXP (– A) + EXP(A) ) gives: 2 · cosh( a) GAMMA Returns the values of the Γ function at a given point.
Computer Algebra Sys tem (CAS) 14-65 Example Typing: I AB CU V (48, 3 0, 1 8 ) gives: 6 AND –9 IBERNOULLI Returns the n th Bernoulli ’s number B( n ) where: Example Typing: IBERNOULLI(6) gives: ICHINREM Chinese Remainders: ICHINREM(A AND P,B AND Q) returns C AND R, where A, B, P and Q are whole numbers.
14-66 Computer Alge bra System (CAS) ILAP is the inverse Laplace transform of a given expression. Again, the expression is the value of a function of the variable stored in VX.
Computer Algebra Sys tem (CAS) 14-67 Typing: gives: LAP See ILAP above. PA2B2 Decomposes a prime integer p congruent to 1 modulo 4, as follows: p = a 2 + b 2 .
14-68 Computer Alge bra System (CAS) gives: Psi Returns the value of the Digamma function at a . The Digamma function is defined as the derivative of ln( Γ (x)), so we have PSI( a ,0) = Psi( a ).
Computer Algebra Sys tem (CAS) 14-69 Example Typing: SIGM A(X · X!, X) gives: X! because (X + 1)! – X! = X · X!. SIGMAVX Returns the discrete antideriva tive of the input function, that is a function, G, that satisfies the relation: G( x + 1) – G( x ) = f( x ).
14-70 Computer Alge bra System (CAS) TSIMP Simplifies a given expression by rewriting it as a function of complex exponentials, and then reduc ing the number of variables (enabling complex mode in the process). Example Typing: gives: VER Returns the version number of your CAS.
Equation Writer 15-1 15 Equation W riter Using CAS in the Equation Writer The Equation Writer enables yo u to type expre ssions that you want to simplify, factor, differentiate, integrate, and so on, and then work them through as if on paper. The key on the HOME screen menu bar opens the Equation Writer, and the key closes it.
15-2 Equation Writer ALGB menu The menu contains functions that enable you to perform algebra, such as factoring, expansion, simplification, substitution, and so on. DIFF menu The menu contains functions that enable you to perform differential calculus, such as differentiation, integration, series expansion, limits, and so on.
Equation Writer 15-3 REWRI menu The menu contains functions that enable you to rewrite an expression in another form. SOLV menu The menu contains functions that enable you to solve equation s, linear systems, and differential equations. TRIG menu The menu contains functions that enable you to transform trigonometric expressions.
15-4 Equation Writer • Th e fo u r th sym bo l, S , in the abo ve e xam ple, indi cates that y ou ar e in step-b y-step mode . If you w ere not in step-b y-step mode , this sy mbol wo uld be D (whi ch stands fo r Direct ). The first line of an Equation Writer me nu only indica tes some of the mode settings.
Equation Writer 15-5 Entering expressions and subexpressions You type expressions in the Equation Writer is much the same way as you type them in the HOME screen, using the keys to directly enter numbers, letters and operators, and menus to select various functions and commands.
15-6 Equation Writer this case, you have to press to select elements in the expression. The following illustration shows how an expression c an be viewed as a tree in the Eq uation Writer. It illustrates a tree view of the expression: Suppose that the cursor is positioned to the right of 3: • If you pr ess once, the 3 component is selected.
Equation Writer 15-7 • Pres s again an d again to progre ssiv ely select mor e of the top-most br anch , and then low er branc hes (5 x , 5 x + 3, and then the entire numerator and finall y the entir e expr essi on). More Examples Example1 If you enter: 2 + X × 3– X and press the entire expr ession is select ed.
15-8 Equation Writer (– X) apply to it. As a result, the entered expression is interpreted, and displayed, as (2 + X)(3 – X). Select the entire expression by pressing and evaluate it by pressing .
Equation Writer 15-9 Select the fifth branch by pressing . At this point, the desired expression is in the Equation Writer, as shown at t he righ t. Suppose that you want to select the second and third branches, that is: . Firs t press . This selects , the second term.
15-10 Equation Writer Pressing produces the result of the partial calculation. Summing up Pressing enables you to select the current element and its neighbour to the right. enables you to exchange the selected element with its neighbour to the left. The selected element remains selected after you move it.
Equation Writer 15-11 How to modify an expression If you’re typing an expression, the key enables you to erase what you’ve typed. If you’re selecting, you can: • Cancel the sele ction w ithout de leting the expr essi on by pre ssing . T he c ursor mo v es to the end o f the deselected portion .
15-12 Equation Writer Accessing CAS functions While you are in the Equation Writer, you can access all CAS functions, and you can ac cess them in various ways.
Equation Writer 15-13 select the entire expression and press , you obtain: However, if you type: select the entire expression and press , you obtain 1. How to enter infix functio ns An infix function is one that is typed between its arguments. For example, AND , | and MOD are infix functions.
15-14 Equation Writer First option: function first, then arguments In the Equation Writer, press , select FACTOR and then press or . FACTOR() is displayed in the Equation Writer, with the cursor between the parentheses (as shown at the right). Enter your expression, using the rules of selection described earlier.
Equation Writer 15-15 Press to obtain th e an intermediate result (4 2 – 4) and again to evaluate the intermediate result. The final answer is 12. Second option: arguments first, then function Enter your expression, using the rules of selection described earlie r.
15-16 Equation Writer Press to obtain an intermediate result, (4– 2)(4 + 2), and again to evaluate the intermediate result. The final answer, as before, is 12. Note If you call a CAS function while you’r e writing an expression, whatever is cu rrentl y selected is copied to the function’s first or main argument.
Equation Writer 15-17 • MODULO contains the v alue of p fo r performing symbolic c al culat ion s i n Z/pZ or in Z/pZ [ X ]. Y ou can change the value of p eithe r with the MODSTO command on the MODULAR menu , (by typ ing, f or ex ample , MODS T O( n ) to gi ve p a va lue of n ), o r f r o m CAS M ODE S scr een (s ee page 14- 5).
15-18 Equation Writer Diff&Int () , Rewrite () , Solve () and Trig () . • Th e Complex menu , pr ov iding f unctions spec if ic to manipulating with com plex number s. • Th e Constant menu , containing e , i, ∞ and π . • Th e Hyperb . menu , containing hy perboli c functio ns.
Equation Writer 15-19 Press to clear the value of the highlighted variable. Press to change the name of the highlighted variable. Press to define a new variable (which you do by specifying an object and a name for the object. SYMB key Pressing the key in the Equation Writer gives you access to CAS history.
15-20 Equation Writer NOTE This operation supposes that the c urrent variable is also the variable of the function or curve you want to graph. When the expression is copied, it is evaluated, and the current variable (contained in VX) is changed to X, T, or θ , depending on the type of plot you chose.
Equation Writer 15-21 Short-cut keys In the Equation Writer, the following are short-cut keys to the symbols indicated: 0 for ∞ 1 for i 3 for π 5 for < 6 for > 8 for ≤ 9 for ≥ hp40g+.
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Step-by-Step Examples 16-1 16 Step-b y- Step Examples Introduction This chapter illustrates the power of CAS, and the Equation Writer, by working though a number of examples. Some of these examples are variations on questions from senior math examination papers.
16-2 Step-by-Step Examples Press to simplify the numerator. Press to select the entire fraction. Press to simplify the selected fraction, giving the result shown at the right. Example 2 Given that write C in the form , where d is a whole number. Solution: In the Equation Writer, enter C by typing: 2 45 3 12 20 6 3 Pres s to select .
Step-by-Step Examples 16-3 Pres s to factor 20 into . Pre ss to selec t and to simplify it. Pre ss to selec t and to e xc hange with . Pre ss to selec t and to select 45 . Pres s , sele ct FACTOR and pres s . Press to factor 45 i n t o . Pre ss to selec t and to simplify the selecti on.
16-4 Step-by-Step Examples Pres s to ev aluate the select ion . It re mains to transf orm and combine it w ith . Follo w the same procedur e as undertaken a number of times abo ve . Y ou w ill find that is equal to , and so the final tw o terms cancel each o ther out.
Step-by-Step Examples 16-5 Press to select the entire equation, then press to reduce it to . Press , select FACTOR, press and then . The r esult is as shown at the right. Now press , select SOLVEVX, press and press . The result is shown at t he righ t.
16-6 Step-by-Step Examples Pres s , select LINSOLVE and pr ess . Enter 17 X 20 Y 90 10 X 25 Y 90 X Y If you are working in step by step mode, pressing produces the result at the right.
Step-by-Step Examples 16-7 1. F ind the ex act le ngth of AB in ce ntimet re s. 2 . Deter mine the equation o f the line AB . First method Type: STORE((-1,3),A) and press . Accept the change to Complex mode, if necessary. Note that pressing returns the coordinates in complex form: –1+3i.
16-8 Step-by-Step Examples Press again to simplify the result to Y = 2X+5. Second method Type: (-3,-1 )-(-1,3) The answer is –(2+4i). With the answer still selected, apply the ABS command by pressing . Pressing gives , the same answer as with method 1 above.
Step-by-Step Examples 16-9 4. Show that for e very integer n > 0, b n × c n = a 2n . 5 . Deduce the prime factor decompositi on of a 6 . 6. S h ow t h a t G CD ( b n , c n ) = GCD( c n ,2). Deduce that b n and c n ar e prime together . Solution: Begin by entering the three definitions.
16-10 Step-by-Step Examples Show that the whole numbers k such that: have digits in decimal notation. We have: so have digits in decimal notation. Moreover, is divisible by 9, since its decimal notation can only end in 9. We also have: and so and are both divisible b y 3.
Step-by-Step Examples 16-11 Now consider the product of two of the definitions entered above: B(N) × C(N): B N C N . Press , to select EXP2POW and press . Press to evaluate the expression, yielding the result of B(N) × C(N). Consider now the decomposition of A(6) into its pr ime factors.
16-12 Step-by-Step Examples Part 2 Given the equation: [1] where the integers x and y are unkn own and b 3 and c 3 are defined as in part 1 above: 1. Sho w that [1] has at least one so lution . 2 . Appl y Euc lid’s algo rithm to b 3 and c 3 and find a solutio n to [1].
Step-by-Step Examples 16-13 so , , or The calculator is not needed for finding the general solution to equation [1]. We started with and have established that . So, by subtraction we have: or According to Gauss’s Theorem, is prime with , so is a divisor of .
16-14 Step-by-Step Examples the circle C , M will move on a curve Γ . In this exercise we will study and plot Γ . 1. Let and m be the point on C of affix . F ind the coor dinates of M in terms o f t . 2 . Co mpare x(–t) w ith x(t) and y(–t) with y(t).
Step-by-Step Examples 16-15 Selecting the entire expression and pressing gives the result at the right: Now linearize the result by applying the LIN command (which can be found on the me nu). The result, after accepting the switch to complex mode, is shown at the right: Now store t he result in variable M.
16-16 Step-by-Step Examples DEF command to it. Press to complete the definition. To calculate the real part of the expression, apply the IM command (available on the COMPLEX submenu of the MATH menu) to the stored variable M.
Step-by-Step Examples 16-17 Then press to produce the result at the right: In other words, . If is part of , then is also part of . Since and are symmetrical with respect to the x- axis, we can deduce that the x-axis i s an axis of symmetry for . Part 3 Calculate by typing: DERVX X t .
16-18 Step-by-Step Examples Part 4 To calculate , begin by typing: DERVX(Y(t)) . Pressing returns: Press again to simplify the result: Select FACTOR and press . You can now define the function (in the same way that you defined ). Part 5 To show the variations of and , we will trace and on the same graph.
Step-by-Step Examples 16-19 Now press to see the graphs. Part 6 To find the values of and for return to CAS, type each function in turn and press . (You may need to press twice for further simplification).
16-20 Step-by-Step Examples The example at the right shows the case for t = 0. Select the entire expression and press to get the answer: 0 The example at the right shows the case for t = π /3. Selecting the entire expression and pressing displays the message shown at the right.
Step-by-Step Examples 16-21 Now we will graph Γ , which is a parametric curve. In the Equation Writer, type X(t) + i × Y(t) . Select the entire expression and press . Now press , select Parametric and press . Select X1,Y1 as the destination and press .
16-22 Step-by-Step Examples Exercise 8 For this exercise, make sure that the calculator is in exact real mode with X as the current variable. Part 1 For an integer, n , define the following: Define g over [0,2] where: 1. F ind the var iati ons of g o ver [0,2].
Step-by-Step Examples 16-23 Solution 1 Start by defining G(X): DEF G X = 2 X 3 X 2 Now press : Press and to select the numerator and denominator, and then press . This leaves G(X) displayed: Finally, apply the TABVAR function: TABVAR and pres s a number of times until the var iation table appears (sho w n abov e) .
16-24 Step-by-Step Examples Now press and scroll down the screen to: Now press to obtain the table of variations. If you are not in step-by -step mode, you can also get the calculation of the derivative by typing: DERVX(G(X)) which produces the preceding result.
Step-by-Step Examples 16-25 We can now see that: To justify the preceding calculation, we must assume that is a primitive of . If you are not sure, you can use the INTVX function as illustrated at the right: Note that the INTVX command is on the menu.
16-26 Step-by-Step Examples NOTE : The variable VX is now set to N . Reset it to X by pressing (to display CAS MODES screen) and change the INDEP VAR s etting. To check the result, we can say that: and that therefore: or, simplifying: If the limit of exists as approaches + in the inequalities in solution 2 above, we get: Part 2 1.
Step-by-Step Examples 16-27 Solution 1 Start by defining the following: Now type PROPFRAC(G(X)) . Note that PROPFRAC can be found on the POLYNOMIAL submenu of th e MATH menu. Pressing yields the result shown at the right. Solution 2 Enter the integral: .
16-28 Step-by-Step Examples Solution 3 The calculator is not needed here. Simply stating that increases for is sufficient to yield the inequality: Solution 4 Since is positive over [0, 2 ], through multiplication we get: and then, integrating: Solution 5 First find the limit of when → + .
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Variables and me mory management 17-1 17 V ar iables and memory manag ement Introduction The HP 40gs has approximately 200K of user memory. The calculator uses this memory to store variables, perform computations, and store history. A v a r i a b l e i s a n o b j e c t t h a t y o u c r e a t e i n m e m o r y t o h o l d data.
17-2 Variables and memory management Storing and recalling variables You can store numbers or expressions from a pr evious input or result into variables. Numeric Precision A number stored in a variable is always stored as a 12- digit mantissa with a 3-digit exponent.
Variables and me mory management 17-3 5 . Enter a name f or the var iable . A 6 . Pr ess to stor e the r esult . The results of a calculation can also be stored directly to a variable. For example: 2 5 3 B To recall a value To recall a variable’s value, type the name of the variable and press .
17-4 Variables and memory management The VARS menu You use the VARS menu to access all variables in the calculator. The VARS menu is organised by category. For each variable category in the left column, there is a list of variables in the right colu mn.
Variables and me mory management 17-5 5 . Choos e whether to place the v ari able name or the var iab le value on the command line . – Press to indicate that y ou want the var iable ’s contents to a ppear on the command line. – Press to indicate that y ou w ant the var iable ’s name to appear on the co mmand line.
17-6 Variables and memory management 4. Enter data for L2 . 55 48 86 90 77 5 . Pres s to access HOME . 6 . Open the var iable men u and select L1. 7 . Cop y it to the command line. Note: Because the option is highli ghted, the v ar iable ’s name , rather than its conten ts, is copi ed to the command line .
Variables and me mory management 17-7 Home variables It is not possible to store data of one type in a variable of another type. For example, yo u use the Matrix catalog to create matrices. You can crea te up to ten matrices, and you can store these in variables M0 to M9.
17-8 Variables and memory management Aplet variables Most aplet va riables stor e values that are unique t o a particular aplet. These include symbolic expressions and equations (see below), settings for the Plot and Numeric views, and the results of some calculations such as roots and intersections.
Variables and me mory management 17-9 Memory Manager You can use the Memory Manager to determine the amount of available memory on the calculator. You can also use Memory Manager to organize memory. For example, if the available memory is low, you can use the Memory Manager to determine which aplets or variables consume large amounts of memory.
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Matrices 18-1 18 M atrices Introduction You can perform matrix calc ulations i n HOME and in programs. The matrix and each row of a matrix appear in brackets, and the elements and rows are separated by commas.
18-2 Matri ces Creating and storing matrices You can create, edit, delete, send, and receive matrices in the Matrix catalog. To open the Matrix catalog, press MATRIX .
Matrices 18-3 2 . Highli ght the matr ix v ari able name you w ant to use and pres s . 3 . Selec t the type of matr ix t o cr eate . – For a v ect or (one -dimension al array) , select Real vector or Complex vector .
18-4 Matri ces To transmit a matrix You can send matrices between calculators just as you can send aplets, programs, lists, and notes. 1. Connec t the calculat ors using an appr opr iate cable . 2 . Open the Matr ix catalogs on both calc ulators . 3 .
Matrices 18-5 To display a matrix • In the Matri x catalog ( MATRIX ), highlight the matri x name and pr ess . • In HOME , enter the name of the matr ix v aria ble and pres s . To display one element In HOME, enter matrixname ( row,column ). For example, if M2 is [[3,4],[5,6]] , then M2(1,2) returns 4 .
18-6 Matri ces To store one element In HOME, enter, value matrixname ( row, column ). For example, to change the element in the first row and second column of M5 to 728, then display the resulting matrix: 728 M 512 M5 . An attempt to store an element to a row or column beyond the size of the matrix results in an error message.
Matrices 18-7 M1 M2 To multiply and divide by a scalar For division by a scalar, enter the matrix first, then the operator, then the scalar. For multiplication, the order of the operands does not matter. The matrix and the sc alar can be real or complex.
18-8 Matri ces To divide by a square matrix For division of a matrix or a vector by a square matrix, the number of rows of the dividend (or the number of elements, if it is a vector) must equal the number of rows in the divisor. This operation is not a mathematical division: it is a left- multiplication by the inverse of the divi sor.
Matrices 18-9 3 . Retu rn to the Matri x Cat al og. MATRIX In this ex ample , the vec tor you c reated is listed a s M1. 4. Cr eate a new matr ix . Select Real matrix 5 . Enter the eq uation coeffi ci ents. 23 4 11 1 4 12 In this ex ample , the matr ix y ou c reat ed is listed as M2 .
18-10 Matri ces Matrix functions and commands About functions • Fu n c t io n s c a n b e u s e d i n a n y a p l e t o r i n H O M E. T h ey ar e listed in the MA TH menu under the Matr i x categor y . The y can be used in mathematical ex pressi ons —primaril y in HOME—as w ell as in progr ams.
Matrices 18-11 COND Condition Number. Finds the 1-norm (column norm) of a square matr ix . COND ( matri x ) CROSS Cross Product of vector1 with vecto r2 . CROSS ( vec to r 1 , ve ct or 2 ) DET Determinant of a square matrix . DET ( matri x ) DOT Dot Product of two arrays, matrix1 matrix2 .
18-12 Matri ces LU LU Deco mposition. Factors a square matrix into three matrices: {[[ lowertriangular ]],[[ uppertriangular ]],[[ permutation ]]} The uppertriangular has ones on its diagonal. LU ( matri x ) MAKEMAT Make Matr ix. Creates a matrix of dimension rows × columns , using expression to calculate each element.
Matrices 18-13 SPECNORM Sp ectral Norm of matrix . SPECNORM ( matri x ) SPECRAD Spect ral Radius o f a square matri x . SPECRAD ( matri x ) SVD Singular Value Decomp osition. Factors an m × n matrix into two matrices and a vector: {[[ m × m square orthogonal ]],[[ n × n square orthogonal ]], [ real ]}.
18-14 Matri ces column 2) is swapped with element 2,1; element 2,3 is swapped with element 3,2; and so on. For exampl e, TRN([[1,2],[3,4]]) creates the matrix [[1,3],[2,4]] . Reduced-Row Echelon Form The following set of equations can be written as the augmented matrix which can then stored as a real matrix in any matrix variable.
Matrices 18-15 The final row of zeros in the reduced-row echelon form of the augmented matrix indicates an inconsistent system with infinite solutions .
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Lists 19-1 19 L ists You can do list operations in HOME and in programs. A list consists of comma-separated real or complex numbers, expressions, or matr ices, all enclosed in braces. A list may, for example, contain a sequence of real numbers such as {1,2,3} .
19-2 Lists 3. E nter t he values you want i n th e l ist, pressin g after each one. V alues can be r eal or comple x number s (or an expr ession). If you enter a calculati on, it is ev aluated and the re sult is inserted in the list . 4. When done , pr ess LIST to see the List catalog, or pres s to r eturn to HOME .
Lists 19-3 List edit keys When you press to create or change a list, the following keys are available to you: Create a list in HOME 1. Enter the list on the edit line. Start and end t he list w ith brace s (the shifted and ke ys) and separate each element w ith a comma.
19-4 Lists Displaying and editing lists To display a list • In the List catalog , highligh t the list name and pres s . • In HOME , enter the name of the list and pr ess . To display one element In HOME, enter listname ( element# ). For example, if L2 is {3,4,5,6}, then L2(2) returns 4 .
Lists 19-5 To insert an element in a list 1. Open the List catalog. LIST . 2. P r e s s o r t o highligh t the name of the list y ou wa nt to edit (L1, etc.) and pr ess to display the lis t contents . New elements are inserted above the highlighted positio n.
19-6 Lists Deleting lists To delete a list In the List catalog, highli ght the list name and press . You are prompted to confirm that you want to delete the contents of the highlighted list variable. Press to delete the contents. To delete all lists In the List catalog, press CLEAR .
Lists 19-7 var iable name (su ch as L1) or the actual list . F or ex ample , REVERSE({1,2,3}) . • If Dec imal Mark in Modes is set to C omma, use peri ods to separ ate arguments . F or e xample , CONCAT(L1.L2) . Common operators like +, –, ×, and / can take lists as arguments.
19-8 Lists MAKELIST Calculates a sequence of elements for a new list. Evaluates expression with variable from begin to end values, taken at increment steps. MAKELIST( expression , va ri ab le , begin , end , incr ement ) The MAKELIST function generates a series by automatically producing a list from the repeated evaluation of an expression.
Lists 19-9 SIZE Calculates the number of elements i n a list. SIZE( list ) Also works with matrices. Σ LIST Calculates the sum of all elements in list. Σ LIST( list ) Example Σ LIST({2,3,4}) ret u rn s 9 . SORT Sor ts element s in ascending o rder.
19-10 Lists 3 . Start the S tatistic s aplet, and se lect 1-var iable mode (pre ss , if necess ary , to displa y ). Select Statistics Note: Y our list v alues are no w in column 1 (C1). 4. In the S ymbo lic vi ew , define H1 (for e xam ple) as C1 (sample) and 1 (freq uency).
Notes and sketches 20-1 20 Notes and sk etch es Introduction The HP 40gs has text and pi cture editors for entering notes and sk etches. • E ach aplet has its o wn independent No te vie w and Sk etch vie w . Notes and sk etc hes that y ou c reat e in these vi ews ar e associ ated with the aplet.
20-2 Notes and sketches Note edit keys Key M e a n i n g Space key for text entry. Displays next page o f a multi-page note. Alpha-lock for letter entry. Lower-case alpha-lock for letter entry. Backspaces cursor and deletes character. Deletes current character.
Notes and sketches 20-3 Aplet sketch view You can attach pictures to an aplet in its Sketch view ( SKETCH ). Y our w ork is aut omatically s av ed with the aplet . Pres s any other v ie w ke y or to ex it the Sketc h vie w Sketch keys To dra w a line 1.
20-4 Notes and sketches To draw a box 1. In Sketc h v iew , press and mo ve the curs or to wher e you w ant any corner of the bo x to be. 2. P r e s s . 3 . Mov e the cu rsor to mark the oppo site corner for the bo x. Y ou can adjust the siz e of the bo x by mov ing the cu rs or.
Notes and sketches 20-5 To label parts of a sketch 1. Pres s and type the te xt on the edit line . T o lock the Alpha shift on, pr ess (for upper case) or (fo r low er case). T o make the label a smaller c har acter si ze , turn o ff befor e pr essing .
20-6 Notes and sketches To import a graphics variable You can copy the contents of a graphics v ariable into the Sketch view of an aplet. 1. Open the Sketch v iew o f the aplet ( SKETCH ). The gr aphic w ill be copied her e . 2 . Pr ess , . 3 . Highli ght Graphic , then pr ess and highli ght the name of the var iable ( G1 , etc .
Notes and sketches 20-7 4. W rite your note . See “Note edit k e ys ” on page 20 - 2 for mor e infor mation on the entry and editing of notes. 5 . When you ar e finished, press or an aplet key to e xit Not epad. Y our wor k is automaticall y sa ved .
20-8 Notes and sketches To import a note You can import a note from the Notepa d into an aplet’s Note view, and vice versa. Suppose you wan t to copy a note named “Assignments” fr om the Notepad into the Function Note view: 1. In the F unction aplet , displa y the Note v ie w ( NOTE ).
Programming 21-1 21 Pr ogramming Introduction This chapter describes how to program using the HP 40gs. In this chapter you’ll learn about: • using the Pr ogram catalog to c r eate and edit progr ams • progr amming commands • stor ing and r etrie v ing var iables in pr ogr ams • progr amming v ariab les.
21-2 Programming Example RUN GETVALUE: RUN CALCULATE: RUN " SHOW ANSWER " : This program is separated into three main tasks, each an individual program. Within each program, the task can be simple—or it can be di vided further into other programs that perform smaller tasks.
Programming 21-3 Program catalog keys The program catalog keys are: Key M e a n i n g Opens the highlighted program for editing. Prompts for a new program name, then opens an empty program. Transmits the highlighted program to another HP 40gs or to a disk drive.
21-4 Programming Creating and editing programs Create a new program 1. Pres s PROGRM t o open the Progr am catalog . 2. P r e s s . The HP 40gs pr ompts yo u fo r a n am e.
Programming 21-5 2 . On the left , use or to highligh t a command category , then press to access the commands in the category . Select the command that y ou w ant . 3 . Pres s to paste the command into the pr ogr am editor . Edit a program 1. Press PROGRM to open the Progr am catalog.
21-6 Programming Editing keys The editing keys are: Key M e a n i n g Inserts the character at the editing point. Inserts space into text. Displays previous page of the program. Displays next page of the program. Moves up or down one line. Moves right or left one character.
Programming 21-7 Using programs Run a program From HOME, type RUN program_name. or From the Program catalog, highlight the program you want to run and press Regardless of where you star t the program, all programs run in HOME. What you see will differ slightly depending on where you started the program.
21-8 Programming Copy a program You can use the following procedure if you want to make a copy of your work before editing—or if you want to use one program as a template for another. 1. Pres s PROGRM to open the Progr am catalog . 2. P r e s s . 3 .
Programming 21-9 Delete a program To delete a program: 1. Pres s PROGRM to open the Progr am catalog. 2 . Hi ghlight a pr ogr am to delete , then pr ess . Delete all programs You can delete all programs at once. 1. In the Pr ogram catalog , pr ess CLEAR .
21-10 Programm ing 4. Dev elop a progr am that use s the SETVIEWS command to modify the aplet’s VIEW S menu . The menu options pr ovi de links to ass oci ated pr ograms . Y ou can spec ify any ot her progr ams that y ou want trans ferr ed w ith the aplet .
Programming 21-11 Save the aplet 1. Open the Functi on aplet and sa ve it as “EXP ERIMENT ” . The ne w aplet appear s in the Aplet library . Select Function EXP ERIMENT 2 . Cr eate a progr am called EXP .ME1 w ith contents as shown . This progr am conf igur es the plot ra nges, then runs a progr am that allo w s y ou to set the angle f ormat .
21-12 Programm ing 6 . Open the Pr ogram cat alog and cr eate a pr ogram named “EXP . S V” . Include the follow ing c ode in the progr am . E ach entry line after the command SE T VIEW S is a tr i.
Programming 21-13 ’ ’ ’ ’ ;’ ’ EXP.ANG’ ’ ;0; The pr ogram EXP .ANG is a small routine that is called by other pr ogr ams that the aplet use s. T his entry specif ies that the progr am EXP.ANG is transferr ed when the aplet is tr ansfer red , but the space in the fir st quote s ensur es that no entry appears on the menu .
21-14 Programm ing Aplet commands CHECK Checks (selects) the correspon ding function in the current aplet. For example, Check 3 would check F3 if the current aplet is Function. Then a checkmark would app ear next to F3 in Symbolic view, F3 would be plotted in Plot view, and evaluated in Numeric view.
Programming 21-15 options us e , or the pr ogram that def ines the aplet ’s VIEW S menu . • Y ou can inclu de a “Start” opti on in the VIEW S menu to spec ify a progr am that y ou want to r un automati cally w hen the aplet starts. This pr ogr am typically sets up the aplet’s initial configur ation.
21-16 Programm ing ProgramName ProgramName is the name of the program that runs when the corresponding menu entry is selected. All programs that are identified in the aplet’s SETVIEW S command are transferred when the aplet is transmitted. ViewNumber V iewNumber is the number of a view to start after the program finishes running.
Programming 21-17 View numbers The Function aplet views are numbered as fo llows: View numbers from 15 on will vary according to the parent aplet. The list shown above is for the Function aplet. Whatever the normal VIEWS menu for the parent aplet, the first entry will become number 15, the second number 16 and so on.
21-18 Programm ing Example 1 X A : IF A==1 THEN MSGBOX " A EQUALS 1" : END: IF... THEN... ELSE... END Executes the true-clause seque nce of commands if the test- clause is true, or the false-clause sequ ence of commands if the test-clause is false.
Programming 21-19 IFERR...THEN...ELSE...END allows a program to intercept error conditions that otherwise would cause the program to abort. Its syntax is: IFERR tr ap-claus e THEN clause _1 ELSE clause _2 END : Example IFERR 60/X X Y: THEN MSGBOX "Error: X is zero.
21-20 Programm ing Example ARC 0;0;2;0;2 π : FREEZE: Dr aw s a c ir cle cente red at (0, 0) of r adius 2 . The FREEZE command causes the c irc le to remain display ed on the screen until y ou press a k ey . BOX Draws a box with diagonally opposite corners ( x1,y1 ) and ( x2,y2 ).
Programming 21-21 Example TLINE 0;0;3;3: Er ases pr ev iously dr a wn 4 5 degr ee line fr om (0, 0) to (3, 3), or draw s that line if it doesn ’t alr eady e xist . Graphic commands The graphic commands use th e graphics variables G0 through G9—or the Page variable from Sketch—as graphicname arguments.
21-22 Programm ing GROBXOR Using the logical XOR, superimpos es graphicname2 onto graphicname1 . The upper left corner of graphicname2 is placed at position . GROBXOR gr aphicname1 ; ( position ) ; graphi cname2 : MAKEGROB Creates graphic with given width, height, and hexadecimal data, and stores it in graphicname .
Programming 21-23 Loop commands Loop hp allow a program to execute a routine repeatedly. The HP 40gs has three loop structures. The example programs below illustrate each of these structures incrementing the variable A from 1 to 12. DO…UNTIL …E ND Do .
21-24 Programm ing Matrix commands The matrix commands take variables M0–M9 as arguments. ADDCOL Add Column. Inserts values into a column before column_number in the specified matrix . You enter the values as a vector. The values must be separated by commas and the number of valu es must be the same as the number of rows in the matrix name .
Programming 21-25 REPLACE Replaces portion of a matrix or vector stored in name with an object starting at position start . start for a matrix is a list containing two numbers; for a vector, it is a single number. Replace also works with lists and graphics.
21-26 Programm ing PRVAR Prints name and co ntents of variablename . PRVAR var iablename : You can also use the PRVAR command to print th e contents of a program or a note. PRVAR pr ogramname ;PROG: PRVAR note name ; NOTE: Prompt commands BEEP Beeps at the frequency and for the time you specify.
Programming 21-27 Example If you have stored {1,2,3,4} in variable L1, entering CLVAR L1 w ill clear L1. DISP Dis plays textitem in a row of the display at the line_number . A text item consists of any number of expressions and quoted strings of text.
21-28 Programm ing Examples 5.152000 X DATE( sets the date to May 15, 2000) . 10.1500 X TIME (sets the time to 10:15 am). EDITMAT Matrix Editor. Opens the Matr ix editor for the specified matrix. Returns to the program when user presses EDITMAT matr ixname : The EDITMAT command can also be used to create matrices.
Programming 21-29 Example INPUT R; "Circular Area"; "Radius"; "Enter Number";1: MSGBOX Displays a mess age box containing textitem. A text item consists of any number of expressions and quoted strings of text. The expressions are evalu ated and turned into strings of text.
21-30 Programm ing Stat-One commands DO1VSTATS Calculates STATS using datase tname and stores the results in the corresponding variables: N Σ , Tot Σ , Mean Σ , PVar Σ , SVar Σ , PSDev, SSDev, Min Σ , Q1, Median, Q3, and Max Σ . Datasetname can be H1, H2, .
Programming 21-31 Storing and retrieving variables in programs The HP 40gs has both Ho me variables and Aplet variables. Home variables ar e used for real numbers, complex numbers, graphics, lists, and matrices. Home variables keep the same values in HOME and in aplets.
21-32 Programm ing Coord Function Parametric Polar Sequence Solve Statistics Turns the coordinate-display mode in Plot view on o r off. From Plot view, use the Menu mean key to toggle coordinate display on an off. In a program, type 1 X Coord —to turn coor dinate displa y on (defa ult) .
Programming 21-33 Hwidth Statistics Sets the width of histogram bars. From Plot Setup in 1VAR stats set a value for Hwidth or In a program, type n X Hwidth Indep All Aplets Defines the value of the independent variable used in tracing mode. In a program, type n X Indep InvCross All Aplets Toggles between solid crosshai rs or inverted crosshairs.
21-34 Programm ing Nmin / Nmax Sequence Defines the minimum and maxi mum independent variable values. Appears as the NRNG fields in the Plot Setup input form. From Plot Setup, enter values for NRNG . or In a program, type X Nmin X Nmax whe re Recenter All Aplets Recenters at the crosshairs locations when zooming.
Programming 21-35 Simult Function Parametric Polar Sequence Enables you to choose between simultaneous and sequential graphing of all selected expressions. From Plot Setup, check (or uncheck) _ SIMULT or In a program, type 1 X Simult —fo r simultaneous gr aphing (defa ult) .
21-36 Programm ing Tmin / Tmax Parametric Sets the minimum and maxi mum independent variable values. Appears as the TRNG field in the Plot S etup input form. From Plot Setup, enter values for TRNG . or In a pr ogram , type X Tmin X Tmax wher e Tracing All Aplets Turns the tracing mode on or off in Plot view.
Programming 21-37 Xtick AAll Aplets Sets the distance between tick marks for the horizontal axis. From the Plot Setup input form, enter a value for Xtick . or In a program, type n X Xtick whe re Ytick All Aplets Sets the distance between tick marks for the vertical axis.
21-38 Programm ing Xzoom All Aplets Sets the horizontal zoom factor. From Plot-ZOOM-Set Factors, enter the value for XZOOM . or In a program, type n X XZOOM wher e The default value is 4. Yzoom All Aplets Sets the vertical zoom factor. From Plot-ZOOM-Set Factors, enter the value for YZOOM .
Programming 21-39 X1, Y1...X9,Y9 X0,Y0 Parametric Can contain any expression. Independent variable is T. Example 'SIN(4*T)' X Y1(T):'2*SIN(6*T)' X X1(T) R1...R9, R0 Polar Can contain any expression. Independent variable is θ . Example '2*SIN(2* θ )' X R1( θ ) U1.
21-40 Programm ing Example Cubic X S2fit or 6 X S2fit Numeric-view variables The following aplet variable s control the Numeric view. The value of the variable applies to the current aplet only. C1...C9, C0 Statistics C0 through C9 , for columns of data.
Programming 21-41 1 Standard 2 Fixed 3 Sci 4 Eng 5 Fraction 6 MixFraction Note: if Fraction or Mixed Fracti on is chosen, the setting will be disregarded when labeling axes in the Plot view.
21-42 Programm ing NumStart Function Parametric Polar Sequence Sets the starting value for a table in Numeric view. From Num Setup, enter a value for NUMSTART . or In a program, type n X NumStart NumStep Function Parametric Polar Sequence Sets the step size (increment value) for an independ ent variable in Numeric view.
Programming 21-43 Example 1VAR X StatMode or 1 X StatMode Note variables The following aplet variable is availa ble in Note view. NoteText All Aplets Use NoteText to recall text previously entered in Note view. Sketch variables The following aplet variables are available in Sketch view.
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Extending aplets 22-1 22 Extending aplets Aplets are the application environments where you explore different classes of m athematical operations. You can extend the capabili ty of the HP 40gs i n the.
22-2 Ext ending aplets 1. Open the Solve aplet and sav e it under th e new name . Solve | T R I A N G L E S 2 . Ent er t he fou r fo rmu la s: θ O H θ A H θ OA AB C 3 . Dec ide whether y ou w ant the aplet to oper ate in Degr ees, R adians, or Grads .
Extending aplets 22-3 Using a customized aplet To use the “Triangles ” aplet, simply select the approp riate formula, change to the Numeric view and solve for the missing variable. Find the length of a ladder leaning against a vertical wall if it forms an angle of 35 o with the horizontal and extends 5 metres up the wall.
22-4 Ext ending aplets Annotating an aplet with notes The Note view ( NOTE ) attaches a note to the current aplet. See Chapter 2 0, “Notes and sketches” . Annotating an aplet with sketches The Sketch view ( SKETCH ) attaches a picture to the current aplet.
Extending aplets 22-5 To transmit an aplet 1. Connec t the PC o r aplet disk dr iv e to the calc ulator b y an appropr iate cable. 2 . Sending calc ulator : Open the L ibr ar y , highligh t the aplet to send , and pres s .
22-6 Ext ending aplets If you are using the PC Connectivity Kit to download aplets from a PC, you will see a list of aplets in the PC’s current directory. Check as ma ny items a s you would li ke to receive. Sorting items in the aplet library menu list Once you have entered information into an aplet, you have defined a new version of an aplet.
R-1 R Re ference inf ormation Glossary aplet A small application, limited to one topic. The built-in aplet types are Function, Parametric, Polar, Sequence, Solve, Statistics, Inference, Finance, Trig Explorer, Quad Explorer, Linear Explorer and Triangle Solve.
R-2 list A set of values separated by commas (periods if the Decimal Mark mode is set to Comma ) and enclosed in braces. Lists are commonly used to enter statistical data and to evaluate a function with multiple values. Created and manipulated b y the List editor and catalog.
R-3 Resetting the HP 40gs If the calculator “locks up” and seems to be stuck, you must reset it. This is much like resetting a PC. It cancels certain operations, restores ce rtain conditions, and clears temporary memory locations.
R-4 If the calculator does not turn on If the HP 40gs does not turn on follow the steps below until the calculator turns on. You may find that the calculator turns on before you have completed the procedure. If the calculator still does not turn on, please contact Customer Support for further information.
R-5 To install the main batteries a. Slide up the battery compartment cover as illustrated. b. Insert 4 new AAA (LR03) batteries into the main compartment. Make sure each batte ry is inserted in the indicated direction. To install the backup battery a.
R-6 Variables Home variables The home variables are: Category Available name Complex Z1 ... Z9 , Z0 Graphic G1 ... G9 , G0 Library Function Parametric Polar Sequence Solve Statistics User-named List L1 ... L9 , L0 Matrix M1 ... M9 , M0 Modes Ans Date HAngle HDigits HFormat Ierr Time Notepad User-named Program Editline User-named Real A.
R-7 Function aplet variables The function aplet variables are: Category Availa ble name Plot A xes Connect Coord FastRes Grid Indep InvCross Labels Recenter Simult Tracing Xcross Ycross Xtick Ytick Xm.
R-8 Parametric aplet variables The parametric aplet variables are: Category Available name Plot Axe s Connect Coord Grid Indep InvCross Labels Recenter Simult Tmin Tmax Tracing Tstep Xcross Ycross Xti.
R-9 Polar aplet variables The polar aplet variables are: Category Availa ble names Plot A xes Connect Coord Grid Indep InvCross Labels Recenter Simult Umin Umax θ step Tracing Xcross Ycross Xtick Yti.
R-10 Sequence aplet variables The sequence aplet variables are: Category Available name Plot Axe s Coord Grid Indep InvCross Labels Nmin Nmax Recenter SeqPlot Simult Tracing Xcross Ycross Xtick Ytick .
R-11 Solve aplet variables The solve aplet variables are: Category Availa ble name Plot A xes 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 Numer ic Digits Format NumCol NumRow Note NoteText Sketch Page PageNum hp40g+.
R-12 Statistics aplet variables The statistics aplet variables are: Category Available name Plot Axe s 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,.
R-13 MATH menu categories Math functions The math functions are: Category Availa ble name 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 Δ LIST MAKELIST π LIST POS REVERSE SIZE Σ LIST SORT Loop ITERATE RECURSE Σ ∂ ∫ hp40g+.
R-14 Matrix COLNORM COND CROSS DET DOT EIGENVAL EIGENVV IDENMAT INVERSE LQ LSQ LU MAKEMAT QR RANK ROWNORM RREF SCHUR SIZE SPECNORM SPECRAD SVD SVL TRACE TRN Polynom.
R-15 Program constants The program constants are: Tests < ≤ = = ≠ > ≥ AND IFTE NOT OR XOR Trig ACOT ACSC ASEC COT CSC SEC Category Av ailable name (Continued) Category Availa ble name Angle Degrees Grads Radians Format Standard Fixed Sci Eng Fraction SeqPlot Cobweb Stairstep S1.
R-16 Physical Constants The physical constants are: Category Available Nam e Chemist • Avog adro (A vagadr o ’s Number , NA) • Boltz . (Boltmann, k) • mol.
R-17 CAS functions CAS functions are: Category Function Algebra COLLECT DEF EXPAND FACTOR PARTFRAC QUOTE STORE | SUBST TEXPAND UNASSIGN Complex i ABS ARG CONJ DROITE IM – RE SIGN Constant e i ∞ π Diff & Int DERIV DERVX DIVPC FOURIER IBP INTVX lim PREVAL RISCH SERIES TABVAR TAYLOR0 TRUNC Hyperb .
R-18 Polynom. EGCD FACTOR GCD HERMITE LCM LEGENDRE PARTFRAC PROPFRAC PTAYL QUOT REMAINDER TCHEBYCHEFF Real CEILING FLOOR FRAC INT MAX MIN Rewrite DISTRIB EPSX0 EXPLN EXP2POW FDISTRIB LIN LNCOLLECT POW.
R-19 Program commands The program commands are: Category Command Aplet CHECK SELECT SETVIEWS UNCHECK Branch IF THEN ELSE END CASE IFERR RUN STOP Drawing ARC BOX ERASE FREEZE LINE PIXOFF PIXON TLINE Gr.
Status messages Stat-Two DO2VSTATS SETDEPEND SETINDEP Category Command (Continued) Message Meaning Bad Argument Type Incorrect input for this operation. Bad Argument Value The value is out of range for this operation. Infinite Result Math exception, such as 1/0.
R-21 Invalid Syntax The function or command you entered does not include the proper arguments or order of arguments. The delimiters (parentheses, commas, periods, and semi-colons) must also be correct. Look up the function name in the index to find its proper syntax.
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W-1 L imited W arranty HP 40gs Graphing Calculator; Warranty peri od: 12 months 1. HP war rants to y ou, the end-user c ustomer , that HP hard war e , accessor ies and suppli es will be f ree fr om defec ts in materi als and wo rkmanship after the date of pur chase , f or the period spec ifi ed abov e .
W-2 6 . HP MAKE S NO O THER EXP RE S S W ARR ANTY OR CONDIT ION WHE THER WRITTEN OR ORAL. T O THE EXTENT ALL OWED B Y L OCAL L A W , ANY IMPLIED W ARRANTY OR CONDI TION OF MERCHANT ABILITY , S A TI SF AC T OR Y QU ALITY , OR FITNE SS FOR A P AR TICULAR PURP OSE IS LIMI TED T O THE DURA TION OF THE EXPRE SS W ARRANT Y SET F ORTH AB OVE .
W-3 Service Europe Countr y : T elephone numbers Austr ia +43-1-36 0 2 7 71203 Belgium +3 2 - 2 - 712 6 219 D e n m a r k + 45 - 8 - 233 284 4 Ea st e r n Eu ro p e countr ies +4 20 -5- 414 2 2 5 2 3 .
W-4 P lease logon to http://www .hp .com for th e l atest ser vice and suppo rt informati on .h L.Ame ri ca Country: T elephone numbers Ar gentina 0 -810 -5 5 5-5 5 20 Bra zil Sao P aulo 3 7 4 7 - 77 .
W-5 Regulatory Notices Federal Commu- nications Commission Notice This equipment has been tested and found to comply with the limits for a Class B digital device , pursuant to Part 15 of the FCC Rules. These limi ts are designed to provide reasonable protection agains t harmful interference in a residential installation.
W-6 Hewlett-Packard Company P. O. Box 692000, Mail Stop 530113 Houston, Texas 77269-2000 Or, call 1-800-474-6836 For questions regarding this FCC declaration, co ntact: Hewlett-Packard Company P.
W-7 Japanese Notice こ の 装置は、 情報 処理装置等電波障害自主規制協議 会 （VCCI） の基準 に 基 づ く ク ラ ス B 情報技術装置 で す 。 こ の装 置は、.
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I-1 Index A ABCUV 14-62 ABS 14-45 absolute value 13-6 ACOS2S 14-38 add 13-4 ADDTMOD 14-51 ALGB menu 14-10 algebraic entry 1-19 alpha characters typing 1-6 alphabetical sorting 22-6 angle measure 1-10 .
I-2 bad guesses error message 7-7 batteries R-4 Bernoulli’s number 14-65 box-and-whisker plot 10-16 branch commands CASE...END 21-18 IF...THEN...ELSE.
I-3 cosine 13-4 inverse hyperbolic 13-9 cotangent 13-20 covariance statistical 10-15 creating aplet 22-1 lists 19-1 matrices 18-2 notes in Notepad 20-6 programs 21-4 sketches 20-3 critical value(s) di.
I-4 notes 20-2 programs 21-5 Editline Program catalog 21-2 editors 1-30 EGCD 14-55 eigenvalues 18-11 eigenvectors 18-11 element storing 18-6 E-lessons 1-12 engineering number format 1-11 EPSX0 14-29 e.
I-5 glossary R-1 graph analyzing statistical data in 10-19 auto scale 2-14 box-and-wh isker 10-16 capture current display 21-21 cobweb 6-1 comparing 2-5 connected points 10-17 defining the independent.
I-6 using symbolic variables 13-23 independent values adding to table 2-19 independent variable defined for Tracing mode 21-33 inference confidence intervals 11-15 hypothesis tests 11-8 One-Proportion.
I-7 finding statistical values in list ele- ments 19-9 generate a series 19-8 list function syntax 19-6 list variables 19-1 returning position of element in 19-8 reversing order in 19-8 sending and re.
I-8 redimension 21-24 replacing portion of matrix or vec- tor 21-25 sending or receiving 18-4 singular value decomposition 18-13 singular values 18-13 size 18-12 spectral norm 18-13 spectral radius 18.
I-9 mixed fraction 1-11 scientific 1-10 Standard 1-10 numeric precision 17-9 Numeric view adding values 2-19 automatic 2-16 build your own table 2-19 display defining function for col- umn 2-17 recalc.
I-10 labels 21-34 recent er 21-34 root 21-34 s1mark-s5mark 21-34 statplot 21-35 tracing 21-33 umin/umax 21-35 ustep 21-35 polar variables axes 21-31 connect 21-31 grid 21-32 in menu map R-9 indep 21-3.
I-11 RE 13-8 real number maximum 13-8 minimum 13-8 real part 13-8 real-number functions 13-14 % 13-16 %CHANGE 13-16 %TOTAL 13-16 CEILING 13-14 DEGtoRAD 13-14 FNROOT 13-14 HMSto 13-15 INT 13-15 MANT 13.
I-12 date 21-27 time 21-27 SEVAL 14-68 SIGMA 14-68 SIGMAVX 14-69 SIGN 14-46 sign revers al 7-6 SIMPLIFY 14-32 simplify 14-68 , 14-70 SINCOS 14-31 , 14-40 sine 13-4 inverse hy perbolic 13-9 singular va.
I-13 Labels 21-34 Recenter 21-34 S1mark-S5mark 21-34 Ycross 21-37 step size of independent variable 21-36 step-by-step 14-6 STORE 14-14 storing list elements 19-1 , 19- 4 , 19-5 , 19-6 matrix eleme nt.
I-14 COT 13-2 0 CSC 13-20 HALFTAN 14-40 SEC 13-20 SINCOS 14-40 TAN2CS2 14-40 TAN2SC 14-41 TAN2SC2 14-41 TRIGCOS 14-44 TRIGSIN 14-44 TRIGTAN 14-44 TRIGSIN 14-44 TRIGTAN 14- 44 TRUNC 14-28 truncating va.
I-15 in 2-9 options 2-9 , 3-8 options within a table 2-18 out 2-9 redrawing table of numbers op- tions 2-18 square 2-10 un-zoom 2-11 within Numeric view 2-18 X-zoom 2-9 Y-zoom 2-10 hp40g+.
hp40g+.book Page 16 Friday, December 9, 2005 1:03 AM.
Un punto importante, dopo l’acquisto del dispositivo (o anche prima di acquisto) è quello di leggere il manuale. Dobbiamo farlo per diversi motivi semplici:
Se non hai ancora comprato il HP F2225AA 40gs è un buon momento per familiarizzare con i dati di base del prodotto. Prime consultare le pagine iniziali del manuale d’uso, che si trova al di sopra. Dovresti trovare lì i dati tecnici più importanti del HP F2225AA 40gs - in questo modo è possibile verificare se l’apparecchio soddisfa le tue esigenze. Esplorando le pagine segenti del manuali d’uso HP F2225AA 40gs imparerai tutte le caratteristiche del prodotto e le informazioni sul suo funzionamento. Le informazioni sul HP F2225AA 40gs ti aiuteranno sicuramente a prendere una decisione relativa all’acquisto.
In una situazione in cui hai già il HP F2225AA 40gs, ma non hai ancora letto il manuale d’uso, dovresti farlo per le ragioni sopra descritte. Saprai quindi se hai correttamente usato le funzioni disponibili, e se hai commesso errori che possono ridurre la durata di vita del HP F2225AA 40gs.
Tuttavia, uno dei ruoli più importanti per l’utente svolti dal manuale d’uso è quello di aiutare a risolvere i problemi con il HP F2225AA 40gs. Quasi sempre, ci troverai Troubleshooting, cioè i guasti più frequenti e malfunzionamenti del dispositivo HP F2225AA 40gs insieme con le istruzioni su come risolverli. Anche se non si riesci a risolvere il problema, il manuale d’uso ti mostrerà il percorso di ulteriori procedimenti – il contatto con il centro servizio clienti o il servizio più vicino.
