HP 40gs hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf
HP 40gs - Graphing Calculator Class Manual
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- HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 1
hp40g+.book Page i Friday, December 9, 2005 1:03 AM HP 40gs graphing calculator user's guide Edition1 Part Number F2225AA-90001 - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 2
hp.com THIS MANUAL AND ANY EXAMPLES CONTAINED HEREIN ARE PROVIDED "AS IS" AND ARE SUBJECT TO CHANGE WITHOUT NOTICE. HEWLETT-PACKARD COMPANY MAKES NO WARRANTY OF ANY KIND WITH REGARD TO THIS MANUAL CONNECTION WITH THE FURNISHING, PERFORMANCE, OR USE OF THIS MANUAL of this manual is prohibited without - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 3
The display 1-2 The keyboard 1-3 Menus 1-8 Input forms 1-9 Mode settings 1-10 Setting a mode 1-11 Aplets (E-lessons 1-12 Aplet library 1-16 Aplet views 1-16 Aplet view configuration 1-18 Mathematical calculations 1-19 Using fractions 1-25 Complex numbers 1-29 Catalogs and editors 1-30 - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 4
10-14 Plotting 10-15 Plot types 10-16 Fitting a curve to 2VAR data 10-17 Setting up the plot (Plot setup view 10-18 Trouble-shooting a plot 10-19 Exploring the graph 10-19 Calculating predicted values 10-20 11 Inference aplet iv - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 5
hp40g+.book Page v Friday, December 9, 2005 1:03 AM About the Inference aplet 11-1 Getting started with the Inference aplet 11-1 Importing sample statistics from the Statistics aplet -1 Performing TVM calculations 12-4 Calculating Amortizations 12-7 13 Using mathematical functions Math functions - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 6
hp40g+.book Page vi Friday, December 9, 2005 1:03 AM Symbolic calculations 13-20 Finding derivatives 13-21 Program constants and physical constants 13-24 Program constants 13-25 Physical constants 13-25 14 Computer Algebra System (CAS) What is a CAS 14-1 Performing symbolic calculations 14-1 - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 7
Finding statistical values for list elements 19-9 20 Notes and sketches Introduction 20-1 Aplet note view 20-1 Aplet sketch view 20-3 The notepad 20-6 21 Programming Introduction 21-1 Program catalog 21-2 Creating and editing programs 21-4 Using programs 21-7 Customizing an aplet 21-9 vii - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 8
Resetting the HP 40gs R-3 To erase all memory and reset defaults R-3 If the calculator does not turn on R-4 Operating details R-4 Batteries R-4 Variables R-6 Home variables R-6 Function aplet variables R-7 Parametric aplet variables R-8 Polar aplet variables R-9 Sequence aplet variables - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 9
hp40g+.book Page ix Friday, December 9, 2005 1:03 AM Solve aplet variables R-11 Statistics aplet variables R-12 MATH menu categories R-13 Math functions R-13 Program constants R-15 Physical Constants R-16 CAS functions R-17 Program commands R-19 Status messages R-20 Limited Warranty Service - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 10
hp40g+.book Page x Friday, December 9, 2005 1:03 AM - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 11
hp40g+.book Page 1 Friday, December 9, 2005 1:03 AM 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 - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 12
or for incidental or consequential damage in connection with the furnishing, performance or use of this manual and the examples herein. © Copyright 1994-1995, 1999-2000, 2003, 2006 Hewlett-Packard Development Company, L.P. The programs that control your HP 40gs are copyrighted and all rights are - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 13
or you want to quit the current activity (such as an aplet, a program, or an editor), press . All mathematical functions are available in the HOME. The name of the current aplet is displayed in the title of the home view. The calculator is provided with a slide cover to protect the display and - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 14
hp40g+.book Page press the first menu key, that is, the leftmost top-row key on the calculator keyboard. Edit line. The line of current entry. History. The HOME display display but are retained in memory. Title. The name of the current aplet is displayed at the top of the HOME view. RAD, GRD, - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 15
keystroke. To cancel, press again. Alpha in effect for next keystroke. To cancel, press again. Low battery power. Busy. Data is being transferred. The keyboard HP 40gs Graphing Calculator Menu Key Labels Menu Keys Aplet Control Keys Cursor Keys Alpha Key Shift Key Enter Key Getting - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 16
hp40g+.book Page 4 Friday, December 9, 2005 1:03 AM Menu keys Aplet control keys • On the calculator keyboard, the top row of keys are called menu keys. Their meanings depend on the context-that's why they are blank. The menu keys are - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 17
hp40g+.book Page 5 Friday, December 9, 2005 1:03 AM Entry/Edit keys The entry and edit keys are: Key (CANCEL) CLEAR ,, , Meaning Cancels the current operation if the calculator is on by pressing . Pressing , then OFF turns the calculator on the current active aplet. Deletes the character - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 18
hp40g+.book Page 6 to hold down when you press HOME. This action is depicted in this manual as "press MODES." To cancel a shift, press again. The alphabetic keys orange to the lower right of each key.) To cancel Alpha, press again. For a lower case letter, press . For a string - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 19
2005 2:20 PM HELPWITH Example The HP 40gs built-in help is available in HOME CAS system, pressing the will show the CAS help menu. SYNTAX HOME ( ) is the place to do non-symbolic calculations. (For symbolic calculations, use the computer algebra system, referred throughout this manual as CAS - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 20
in calculations. (pSee "Physical constants" on page 13-25 for more information.) • Pressing takes you to the beginning of the MATH menu. See "Math functions by category" on page 13-2 for details of the math functions. When using the MATH menu, or any menu on the HP 40gs, pressing an alpha key - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 21
hp40g+.book Page 9 Friday, December 9, 2005 1:03 AM To search a menu To cancel a speed-search a list, type the first letter of the word. For example, to find the Matrix category in , press , the Alpha "M" key. • To go up a page, you can press down a page, press . . To go Press (for CANCEL - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 22
grads in a circle. The angle mode you set is the angle setting used in both HOME and the current aplet. This is done to ensure that trigonometric calculations done in the current aplet and HOME give the same result. The number format mode you set is the number format used in both HOME - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 23
hp40g+.book Page 11 Friday, December 9, 2005 1:03 AM Setting Decimal Mark Options ( 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. Press form. MODES - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 24
environments where you explore different classes of mathematical operations. You select the aplet that you want to work with. Aplets come from a variety of sources: • Built-in the HP 40gs (initial purchase). • Aplets created by saving existing aplets, which have been modified, with specific - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 25
, which can be used in a variety of applications, the HP 40gs is supplied with two teaching aplets: Quad Explorer and Trig Explorer. You cannot modify configuration settings for these aplets. A great many more teaching aplets can be found at HP's web site and other web sites created by educators - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 26
transferred to the HP 40gs using the provided Connectivity Kit. Quad Explorer aplet HINT The Quad Explorer aplet is used to investigate the behaviour of y = a(x + h)2 + v as the values of a, h and v change, both by manipulating the equation and seeing the change in the graph, and by manipulating - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 27
hp40g+.book Page 15 Friday, December 9, 2005 1:03 AM Trig Explorer aplet The Trig Explorer aplet is used to investigate the behaviour of the graph of y = a sin(bx + c) + d as the values of a, b, c and d change, both by manipulating the equation and seeing the change in the graph, or by - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 28
are illustrations of the three major aplet views (Symbolic, Plot, and Numeric), the six supporting aplet views (from the VIEWS menu), and the two user-defined views (Note and Sketch). Note: some aplets-such as the Linear Solver aplet and the Triangle Solver aplet-only have a single view, the Numeric - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 29
hp40g+.book Page 17 Friday, December 9, 2005 1:03 AM Numeric view Plot-Table view Press to display the aplet's Numeric view. In this the plot and the data table. See "Other views for scaling and splitting the graph" on page 2-13 for futher information. The VIEWS menu contains the Plot-Detail - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 30
hp40g+.book Page 18 Friday, December 9, 2005 1:03 AM Note view Sketch 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 sketches" on page 20-1 - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 31
other HP 40gs calculators. See "Creating new aplets based on existing aplets" on page 22-1. Mathematical calculations The most commonly used math operations are available from the keyboard. Access to other math functions is via the MATH menu ( ). You can also CAS for symbolic calculations. See - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 32
hp40g+.book Page 20 Friday, December 9, 2005 1:03 AM Example Calculate -2--3----2---------1---4--------8- ln (45) : -3 23 14 8 3 45 Long , use EEX. (This is easier than using 10 .) Calculate -(--4----×-----1---0-------1--3---)--(---6----×-----1---0---2---3--)3 × 10-5 4 EEX 13 6 EEX 23 3 - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 33
Instead an error message is displayed: "Invalid User Function". This is because the calculator interprets A(B+4) as meaning 'evaluate function A at calculator inserts it automatically. Parentheses are also important in specifying the order of operation. Without parentheses, the HP 40gs calculates - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 34
hp40g+.book Page 22 Friday, December 9, 2005 1:03 AM Algebraic precedence order AND and NOT. 8. OR and XOR. 9. Left argument of | (where). 10.Equals, =. The smallest number the HP 40gs can represent is 1 × 10-499(1E-499). A smaller result is displayed as zero. The largest number is 9.99999999999 × - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 35
hp40g+.book Page 23 Friday, December 9, 2005 1:03 AM When you highlight a previous input the previous line is an expression containing the ANS, the calculation is repeated iteratively. See how (50), and 50 ANS retrieves and reuses the last result updates ANS (from 50 to 75 to 100). 25 You can - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 36
hp40g+.book Page 24 Friday, December 9, 2005 1:03 AM HINT When you retrieve a line. Storing a value in a variable You can save an answer in a variable and use the variable in later calculations. There are 27 variables available for storing real values. These are A to Z and θ. See Chapter 17, " - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 37
hp40g+. in the edit line. Displays the current expression in standard mathematical form. Deletes the highlighted expression from the display history, unless ( CLEAR) whenever you have finished working in HOME. It saves calculator memory to clear the display history. Remember that all your previous - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 38
hp40g+.book Page 26 Friday, December 9, 2005 1:03 AM 2. Select Number Format, fraction precision" below for more information. The fraction precision setting determines the precision in which the HP 40gs converts a decimal value to a fraction. The greater the precision value that is set, the - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 39
hp40g+.book Page 27 Friday, December 9, 2005 1:03 AM • Precision set to 1: • Precision set to 2: • Precision set to 3: • Precision set to 4 Fraction calculations Getting started When entering fractions: • You use the key to separate the numerator part and the denominator part of the fraction. • - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 40
hp40g+.book Page 28 Friday, December 9, 2005 1:03 AM Converting decimals to fractions 2. Enter the calculation. 3 4 8 23 57 Note: Ensure you are in the HOME view. 3. Evaluate the calculation. Note that if you had selected Mixed Fraction instead of Fraction as the Number format, the answer - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 41
hp40g+.book Page 29 Friday, December 9, 2005 1:03 AM In this example, the fraction precision is set to 6. Complex numbers Complex results To enter complex numbers Storing complex numbers The HP 40gs can return a complex number as a result for some math functions. A complex number appears as an - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 42
hp40g+.book Page 30 Friday, December 9, 2005 1:03 AM 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 (numbers or text or other items) that are independent of aplets. • A catalog lists items, - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 43
10 different definitions for each Function, Parametric, Polar, and Sequence aplet. You can graph any of the relations (in the same aplet) simultaneously by selecting them. Defining an expression (Symbolic view) Choose the aplet from the Aplet Library. Aplets and their views Press or to select an - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 44
sequences with integer domains. Or define the nth term as a non-recursive expression in terms of n only. In this case, the calculator inserts the first two terms based on the expression that you define. - Note: You will have to enter the second term if the hp40gs is unable to calculate - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 45
hp40g+.book Page 3 Friday, December 9, 2005 1:03 AM Evaluating expressions In aplets In the Symbolic view, a variable is a symbol only, and does not represent one specific value. To evaluate a function in Symbolic view, press . If a function calls - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 46
hp40g+.book Page 4 Friday, December 9, 2005 1:03 AM In HOME You can the key on the keyboard. Enters the independent variable in the Polar aplet. Or, you can use the key on the keyboard. Enters the independent variable in the Sequence aplet. Or, you can use the key on the keyboard. Displays the - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 47
hp40g+.book Page 5 Friday, December 9, 2005 1:03 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 done, press to view the new plot. Aplets and their views 2-5 - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 48
hp40g+.book Page 6 Friday, December 9, 2005 1:03 AM Plot view settings 2-6 The plot TRNG Parametric aplet: Specifies the tvalues (T) for the graph. θRNG Polar aplet: Specifies the angle (θ) value range for the graph. NRNG Sequence aplet: Specifies the index (N) values for the graph. TSTEP - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 49
hp40g+.book Page 7 Friday, December 9, 2005 1:03 AM Reset plot settings Field CONNECT LABELS AXES GRID Meaning (Continued) Connect the plotted points. (The Sequence aplet always connects them.) Label the axes with XRNG and YRNG values. Draw the axes. Draw grid points using XTICK and YTICK spacing - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 50
hp40g+.book Page 8 Friday, December 9, 2005 1:03 AM Trace a graph To move between relations Key Meaning ( FASTER plots in only every other column, whereas tracing always uses every column. In Function and Sequence Aplets: You can also scroll (move the cursor) left or right beyond the edge of the - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 51
hp40g+.book Page option, and press is not displayed, press .) Not all available in all aplets. . (If options are Option Center Box... In Out X-Zoom In X- to zoom in on. See "Other views for scaling and splitting the graph" on page 2-13. Divides horizontal and vertical scales by the X-factor and - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 52
hp40g+.book Page 10 Friday, December 9, 2005 1:03 AM Option Y-Zoom In Y-Zoom for the supplied x axis settings. (For Sequence and Statistics aplets, autoscaling rescales both axes.) The autoscale process uses the first selected function only to determine the best scale to use. Rescales both axes so - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 53
hp40g+.book Page 11 Friday, December 9, 2005 1:03 AM ZOOM examples Option Un-zoom Meaning (Continued) Returns the display to the previous zoom, or if there has been only one zoom, un-zoom displays the graph : X-Zoom In Now un-zoom. X-Zoom Out: X-Zoom Out Now un-zoom. Aplets and their views 2-11 - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 54
hp40g+.book Page 12 Friday, December 9, 2005 1:03 AM Y-Zoom In: Y-Zoom In Now un-zoom. Y-Zoom Out: Y-Zoom Out Zoom Square: Square To of the rectangle. Press . 4. Use the cursor keys ( , etc.) to drag to the opposite corner. 5. Press to zoom in on the boxed area. 2-12 Aplets and their views - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 55
hp40g+.book Page 13 Friday, December on the screen. Other views for scaling and splitting the graph The preset viewing options menu ( ) contains options for preset viewing options menu can also contain options that relate to the aplet. VIEWS menu options Press , select an option, and press - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 56
7.58, or 81/3 grads; rescales vertical axis so 1 pixel = 0.1 unit. (Not in Sequence or Statistics aplets.) The Plot-Detail view can give you two simultaneous views of the plot. 1. Press . Select Plot-Detail and press . The graph is plotted twice. You can now zoom in on the right side. 2. Press - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 57
hp40g+.book Page 15 Friday, December 9, 2005 1:03 AM Overlay plots Decimal scaling Integer scaling Trigonometric scaling Aplets and their views To move between functions, use the and cursor keys to move the cursor from one graph to another. 4. To return to a full Numeric (or Plot) view, press ( - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 58
hp40g+.book Page 16 Friday, December 9, 2005 1:03 Effectively, the menu key allows you to make the table match the pixel columns in the graph view. 2. When done, press numbers. to view the table of Numeric view settings The independent variable value to the next. 2-16 Aplets and their views - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 59
hp40g+.book Page 17 Friday, December 9, 2005 1:03 AM Reset numeric settings Field NUMTYPE NUMZOOM Meaning (Continued) Type of Toggles between two character sizes. Displays the defining function expression for the highlighted column. To cancel this display, press . Aplets and their views 2-17 - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 60
hp40g+.book Page 18 Friday, December 9, 2005 1:03 AM Zoom within a table ZOOM options Zooming redraws the table of numbers in greater or lesser the table, use the arrow keys to place the cursor in the independent variable column, then enter the value to jump to. 2-18 Aplets and their views - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 61
hp40g+.book Page 19 Friday, December 9, 2005 1:03 AM Automatic recalculation You can values are then calculated and displayed. Build a table 1. Start with an expression defined (in Symbolic view) in the aplet of your choice. Note: Function, Polar, Parametric, and Sequence aplets only. 2. In - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 62
hp40g+.book Page 20 Friday, December 9, 2005 1:03 AM "Build Your Own" menu keys Key CLEAR Meaning Puts both the positive and negative y values, you need to define two equations as follows: y = 9 - x2 and y = - 9 - x2 1. In the Function aplet, specify the functions. 2-20 Aplets and their views - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 63
Function 9 9 2. Reset the graph setup to the default settings. SETUP-PLOT CLEAR 3. Plot the two functions and hide the menu so that you can see all the circle. 4. Reset the numeric setup to the default settings. SETUP-NUM CLEAR 5. Display the functions in numeric form. Aplets and their views 2-21 - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 64
hp40g+.book Page 22 Friday, December 9, 2005 1:03 AM - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 65
hp40g+.book Page 1 Friday, December 9, 2005 1:03 AM 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. For example y = 2x + 3 . Once you have defined a function you can: • create graphs to find roots, - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 66
aplet's Symbolic view screen. They are labeled F1(X) to F0(X). Highlight the function definition field you want to use, and enter an expression. (You can press to delete an existing line, or clear all lines.) CLEAR to 1 3 2 Set up the plot You can change the scales of the x and y axes, graph - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 67
hp40g+.book Page 3 Friday, December 9, 2005 1:03 AM Change the scale 6. You can change the scale to see more or less of your graphs. In this example, choose Auto Scale. (See "VIEWS menu options" on page 2-13 for a description of Auto Scale). Select Auto Scale Trace a graph 7. Trace the linear - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 68
hp40g+.book Page 4 Friday, December 9, 2005 1:03 AM 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- - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 69
hp40g+.book Page 5 Friday, December 9, 2005 1:03 AM 12.Choose the linear function whose intersection with the -2 ≤ x ≤ -1, first move the cursor to F1(x) = 1 - x and select the signed area option. Select Signed area Function aplet 15.Move the cursor to x = -2 by pressing the or key. 3-5 - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 70
hp40g+.book Page 6 Friday, December 9, 2005 1:03 AM 16.Press to accept using F2(x) = (x + 3) find the extremum of the quadratic Note: See "Shading area" on page 3-11 for another method of calculating area. 19. Move the cursor to the quadratic equation and find the extremum of the quadratic. Select - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 71
hp40g+.book Page 7 Friday, December 9, 2005 1:03 AM HINT The Root and Extremum functions return one value only even view setup)" on page 2-16 for more information. 22. Match the table settings to the pixel columns in the graph view. Explore the table 23. Display the table of values. Function - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 72
hp40g+.book Page 8 Friday, December 9, 2005 1:03 AM To navigate around a table 24.Move to X = -5.9. 6 times To go directly to a value 25. Move directly to X the symbolic definition for the F1 column. The symbolic definition of F1 is displayed at the bottom of the screen. 3-8 Function aplet - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 73
selected graph. The results of the FCN functions are saved in the following variables: • Area • Extremum • Isect • Root • Slope For example, if you use the Root function to find the root of a plot, you can use the result in calculations in HOME. Access FCN variables Function aplet The - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 74
hp40g+.book Page 10 Friday, December 9, 2005 1:03 AM FCN functions The FCN an extremum, then the result is labeled EXTR: instead of ROOT:. (The root-finder is also used in the Solve aplet. See also "Interpreting results" on page 7-6.) The cursor is moved to the root value on the x-axis and the - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 75
hp40g+.book Page 11 Friday, December 9, 2005 1:03 AM Function Intersection Description (Continued) Select Intersection to find the intersection of two graphs Open the Function aplet. The Function aplet opens in the the area. 9. Press to calculate the area. The area measurement is displayed - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 76
hp40g+.book Page 12 Friday, December 9, 2005 1:03 AM Plotting a piecewise-defined function Suppose you wanted to plot the following piecewisedefined function. f(x) = x+2 x2 ⎩ 4-x ;x ≤ -1 ;-1 < x ≤ 1 ;x ≥ 1 1. Open the Function aplet. Select Function 2. Highlight the line you want to use, - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 77
hp40g+.book Page 1 Friday, December 9, 2005 1:03 AM 4 Parametric aplet 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. They take the forms x = f(t) and y = g(t) . Getting started - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 78
hp40g+.book Page 2 Friday, December 9, 2005 1:03 AM Set angle measure 3. Set the angle measure to degrees. MODES Select Degrees Set up the plot 4. Display the graphing options. PLOT The Plot Setup input form has two fields not included in the Function aplet, TRNG and TSTEP. TRNG specifies the - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 79
hp40g+.book Page 3 Friday, December 9, 2005 1:03 AM Overlay plot 8. Plot a triangle graph over the existing circle graph. PLOT 120 Select able to explore the graph using trace, zoom, split screen, and scaling functionality available in the Function aplet. See "Exploring the graph" on page 27 for - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 80
hp40g+.book Page 4 Friday, December 9, 2005 1:03 AM - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 81
hp40g+.book Page 1 Friday, December 9, 2005 1:03 AM 5 Polar aplet Getting started with the Polar aplet Open the Polar aplet 1. Open the Polar aplet. Select Polar Define the expression Like the Function aplet, the Polar aplet opens in the Symbolic view. 2. Define the polar equation r = 2π cos - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 82
hp40g+.book Page 2 Friday, December 9, 2005 1:03 AM Explore the graph Display the numbers 5. Display the Plot view menu key labels. The Plot view options available are the same as those found in the Function aplet. See "Exploring the graph" on page 2-7 for further information. 6. Display the table - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 83
specifying just the first term and the rule for generating all subsequent terms. You will, though,have to enter the second term if the hp40gs is unable to calculate it automatically. Typically if the nth term in the sequence depends on n-2, then you must enter the second term. Sequence aplet 6-1 - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 84
hp40g+.book Page 2 Friday, December 9, 2005 1:03 AM Open the Sequence aplet 1. Open the Sequence aplet. Select Sequence Define the expression The Sequence aplet starts in the Symbolic view. 2. Define the Fibonacci sequence, in which each term (after the first two) is the sum of the preceding - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 85
hp40g+.book Page 3 Friday, December 9, 2005 1:03 AM Plot the sequence 4. Plot the Fibonacci sequence. 5. In Plot Setup, set the SEQPLOT option to Cobweb. SETUP-PLOT Select Cobweb Display the table 6. Display the table of values for this example. Sequence aplet 6-3 - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 86
hp40g+.book Page 4 Friday, December 9, 2005 1:03 AM - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 87
hp40g+.book Page 1 Friday, December 9, 2005 1:03 AM 7 Solve aplet About the Solve aplet The Solve aplet solves an equation or an expression for its unknown variable. equations, for example, should be solved using the Linear Solver aplet,matrices or graphs in the Function aplet. Solve aplet 7-1 - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 88
hp40g+.book Page 2 Friday, December 9, 2005 1:03 AM Getting started with the Solve aplet Suppose you want to find the acceleration needed to increase the speed of a car from 16.67 m/sec (60 kph) to 27.78 m/sec (100 - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 89
hp40g look for any other solutions. The Plot view shows one graph for each side of the selected equation. You can choose any 771.7284 . This graph will be a horizontal line. The other graph will be Y = U2 + 2AD, with U = 16.67 and D = 100 , that is, Y = 200A + 277.8889 . This graph is also a line. - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 90
hp40g+.book Page 4 Friday, December 9, 2005 1:03 AM 6. Plot the equation for variable A. Select Auto Scale 7. Trace along the graph find guesses" on page 7-7 for more information. Solve aplet's NUM view keys The Solve aplet's NUM view keys are: Key Meaning Copies the highlighted value - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 91
hp40g+.book Page 5 Friday, December 9, 2005 1:03 AM Key CLEAR Meaning (Continued) solution closest to the initial guess is returned. Number format You can change the number format for the Solve aplet in the Numeric Setup view. The options are the same as in HOME MODES: Standard, Fixed, Scientific - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 92
hp40g+.book Page 6 aplet found a point where both sides of the equation were equal, or where the expression was zero (a root), within the calculator's the equation or expression is continuously real, this point is Solve's best approximation of an actual solution. Solve found a point where the value - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 93
hp40g+.book to the solve process. For example, the solution that the Solve aplet finds is not a solution, but the closest that the function gets Root-Finder at work You can watch the process of the root-finder calculating and searching for a root. Immediately after pressing to start the root- - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 94
hp40g+.book Page 8 Friday, December solutions, since only positive distance makes sense. 1. Select the Solve aplet and enter the equation. Select Solve X V T A T 2 equation X = V x T + A x T 2 /2, the plot will produce two graphs: one for Y = X and one for X = V x T + A x T 2 /2. Since we - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 95
hp40g+.book Page 9 Friday, December 9, 2005 1:03 AM 5. Move the cursor near the positive (right-side) intersection. This cursor value will be an initial it to travel 50 m within 3 seconds? Assume the same acceleration, 4 m/s2. Leave the last value of V as the initial guess. 3 50 Solve aplet 7-9 - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 96
are global, which means they are shared throughout the different aplets of the calculator. A value that is assigned to a home variable anywhere same problem in different places (such as HOME and the Solve aplet) without having to update the value whenever it is recalculated. As the Solve aplet - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 97
and the Linear Solver aplet will attempt to solve for x and y (and z in threeequation sets). The hp40gs will alert you if aplet 1. Open the Linear Sequence aplet. Select Linear Solver The Linear Equation Solver opens. Choose the equation set 2. If the last time you used the Linear Solver aplet - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 98
hp40g+.book Page 2 Friday, December 9, 2005 1:03 AM Define and solve the equations example in the previous step). To solve a three- equation set, press . solver was able to find solutions for x, y, and z as soon as the first co-efficient of the last equation was entered. 8-2 Linear Solver aplet - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 99
hp40g+.book Page 3 Friday, December 9, 2005 1:03 AM As you enter each of the remaining known values, the solution changes. The example at the right shows the final solution once all the co-efficients and constants are entered for the set of equations we set out to solve. Linear Solver aplet 8-3 - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 100
hp40g+.book Page 4 Friday, December 9, 2005 1:03 AM - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 101
hp40g+.book Page 1 Friday, December 9, 2005 1:03 AM 9 Triangle Solve aplet About the Triangle Solver aplet The Triangle Solver aplet will calculate the remaining lengths or angles. The HP 40gs will instructions.) Because the angle measure mode is associated with the aplet, you should start the aplet - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 102
hp40g+.book Page 2 Friday, December 9, 2005 1:03 AM Open the Triangle Solver aplet 1. Open the Triangle Solver aplet. Select Triangle Solver Choose the triangle type Specify the known values 9-2 The Triangle Solver aplet opens. Note: if you have already used the Triangle Solver, the entries and - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 103
hp40g+.book Page 3 Friday, December 9, 2005 1:03 AM Errors Triangle Solve aplet lengths as B and C, we would press MODES, change the mode, and then press to return to the aplet. 4. Press . The solver calculates the values of the unknown variables and displays. As the illustration at the - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 104
hp40g+.book Page 4 Friday, December 9, 2005 1:03 AM Not enough data If you are using the general input form, you need to specify at least three values for the Triangle Solver to be able to calculate the remaining attributes of the triangle. If you specify less than three, Not enough data appears on - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 105
hp40g+.book Page 1 Friday, December 9, 2005 1:03 AM 10 Statistics aplet About the Statistics aplet The Statistics aplet can store up to ten data sets at one time. It can perform one-variable or two-variable statistical analysis of one or more sets of data. The Statistics aplet starts with the - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 106
hp40g+.book Page 2 Friday, December 9, 2005 1:03 AM Open the Statistics aplet 1. Open the Statistics aplet and clear existing data by pressing . Select Statistics Enter data The Statistics aplet starts in the Numerical view. 1VAR/2VAR menu key label At any time the Statistics aplet aplet - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 107
hp40g+.book Page 3 Friday, December 9, 2005 1:03 AM Choose fit and data columns 4. Select a fit in the Symbolic setup view. SETUP-SYMB Select the correlation coefficient (CORR). The CORR value indicates how well the linear model fits the data. 9 times The value is .8995. Statistics aplet 10-3 - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 108
mark, if you wish). SETUP-PLOT 7 100 4000 9. Plot the graph. Draw the 10.Draw the regression curve (a curve to fit the data regression curve points). Display the equation for best linear fit This draws the regression line for the best linear fit. 11.Return to the Symbolic view. 12.Display the - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 109
hp40g+.book Page 5 Friday, December 9, 2005 1:03 AM Predict values 13.To find the predicted sales figure if advertising were to go up to 6 minutes: 15.Jump to the indicated point on the regression line. 6 Observe the predicted y-value in the left bottom corner of the screen. Statistics aplet 10-5 - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 110
hp40g+.book Page 6 Friday, December 9, 2005 1:03 AM Entering and editing statistical data The Numeric view ( ) is used to enter data into the Statistics aplet. or two-variable statistics. This setting affects the statistical calculations and plots. The label indicates which setting is current - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 111
hp40g+.book Page 7 Friday, December 9, 2005 1:03 AM Example Key Meaning (Continued) Deletes the first five students have the following measurements 160cm, 165cm, 170cm, 175cm, 180cm. 1. Open the Statistics aplet. Select Statistics 2. Enter the measurement data. 160 165 170 175 180 Statistics - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 112
hp40g+.book Page 8 Friday, December 9, 2005 1:03 AM 3. Find the mean of the sample. Ensure the / menu key label reads . Press to see the statistics calculated from the sample data in C1. Note that the title for the column variables ( ) or for the Fit expressions ( ). 10-8 Statistics aplet - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 113
hp40g+.book Page 9 Friday, December 9, 2005 1:03 AM Statistics aplet Key CLEAR Meaning (Continued) Displays the current variable expression in standard mathematical form. Press when done. Evaluates the variables in the highlighted column (C1, etc.) expression. Displays the menu for entering - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 114
hp40g+.book Page 10 Friday, December 9, 2005 1:03 AM 5. Move the highlight bar into the right column of the H1 definition and replace . When you are finished entering data values, you can press a key for another Statistics view (like ), or you can switch to another aplet or HOME. Statistics - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 115
hp40g+.book Page 11 Friday, December 9, 2005 1:03 AM Edit a data set Delete data Insert data Sort data values In the Numeric view of the Statistics aplet, highlight the data value to change. Type a new value and press , or press to copy the value to the edit line for modification. Press - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 116
hp40g+.book Page 12 Friday, December Select one of the available fit options in Symbolic Setup view. • Enter your own mathematical expression in Symbolic view. This expression will be plotted, but it will not be an exponential curve, y = bemx. Fits to a power curve, y = bxm. 10-12 Statistics aplet - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 117
hp40g+.book Page 13 Friday, December 9, 2005 1:03 AM To define your own fit Fit model Quadratic Cubic Logistic Exponent Trigonometric User Defined Meaning (Continued) Fits to a quadratic curve, y = ax2+ the Fit type (S1FIT, etc.) in the Symbolic Setup view to User Defined. Statistics aplet 10-13 - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 118
hp40g+.book Page 14 Friday, December 9, 2005 1:03 AM Computed statistics One-variable . When the data set contains an odd number of values, the data set's median value is not used when calculating Q1 and Q3 in the table above. For example, for the following data set: {3,5,7,8,15,16,17} only - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 119
hp40g+.book Page 15 Friday, December 9, 2005 1:03 AM Two- fit only (regardless of the Fit chosen). Returns a value from 0 to 1, where 1 is the best fit. The relative error for the selected fit. Provides a measure of accuracy for the fit. You can only one histogram at a time. Statistics aplet 10-15 - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 120
hp40g+.book Page 16 Friday, December 9, 2005 1:03 AM To plot statistical data Plot types Histogram Box and Whisker Plot 1. In Symbolic view ( sets you want . The right whisker marks the maximum data value. The numbers below the plot mean that this column has a median of 13. 10-16 Statistics aplet - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 121
, checkmark CONNECT in the second page of the Plot Setup. This is not a regression curve. Fitting a curve to 2VAR data In the Plot view, press . This draws a curve to fit the checked two-variable data set(s). See "To choose the fit" on page 10-12. Correlation coefficient Statistics aplet The - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 122
hp40g the other built-in aplets. See "Setting up the plot (Plot view setup)" on page 2-5. Settings unique to the Statistics aplet are as follows: Plot to change the highlighted setting. Connected points (2VAR) CONNECT (on the second page), when checkmarked, connects the data points as they are - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 123
hp40g+.book Page 19 Friday, December 9, 2005 1:03 AM 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 in"Exploring the graph" on page 2-7. Statistics aplet's PLOT view keys - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 124
hp40g 2var statistics only) Enables you to specify a value on the line of best fit to jump to or a data point number to jump to. Displays the other. The estimation is made based on the curve that has been calculated to fit the data according to the specified fit. Find predicted values 1. aplet - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 125
hp40g+.book Page 21 Friday, December 9, 2005 1:03 AM HINT • Enter PREDY(x-value) to category. In cases where more than one fit curve is displayed, the PREDY function uses the most recently calculated curve. In order to avoid errors with this function, uncheck all fits except the one that you want - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 126
hp40g+.book Page 22 Friday, December 9, 2005 1:03 AM - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 127
hp40g+.book Page 1 Friday, December 9, 2005 1:03 AM 11 Inference aplet About the Inference aplet The Inference capabilities include calculation of confidence intervals and hypothesis tests based on the Normal Z-distribution or Student's t-distribution. Based on the statistics from one or two - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 128
hp40g+.book Page 2 Friday, December 9, 2005 1:03 AM Inference aplet's SYMB view keys The table below summarizes the options available in Symbolic view. Hypothesis Tests Z: 1 μ, the Z-Test on 1 mean Z: μ1 - μ2, the Z-Test on the difference of - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 129
hp40g+.book Page 3 Friday, December 9, 2005 1:03 AM Select the inferential 4. Select an alternative hypothesis. μ< μ0 5. Enter the sample statistics and population parameters. setup-NUM Inference aplet The table below lists the fields in this view for our current Z-Test: 1 μ example. Field name - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 130
hp40g+.book Page 4 Friday, December 9, 2005 1:03 AM Display on-line help By default, each field already contains a value. These values constitute the example database and are explained in the feature of this aplet 9. Display a graphic view of the aplet The Inference aplet supports the calculation - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 131
hp40g+.book Page 5 Friday, December 9, 2005 1:03 AM Open the Statistics aplet A calculator produces the following 6 random numbers: 0.529, 0.295, 0.952, 0.259, 0.925, and 0.592 1. Open the Statistics aplet and reset the current settings. Select Statistics The Statistics aplet opens in the Numeric - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 132
1:03 AM Open Inference aplet 6. Open the Inference aplet and clear current settings. 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. Set up the - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 133
hp40g+.book Page 7 Friday, December 9, 2005 1:03 AM 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 based on the - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 134
of one or two populations. The tests are based 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. One-Sample Z-Test Menu name Inputs Z-Test: 1 μ On the basis of statistics from a single - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 135
hp40g+.book Page 9 Friday, December 9, 2005 1:03 AM Results The results are: Result Test Z Prob Critical Z Critical x μ2 The inputs are: Field name x1 x2 n1 n2 σ1 Definition Sample 1 mean. Sample 2 mean. Sample 1 size. Sample 2 size. Population 1 standard deviation. Inference aplet 11-9 - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 136
hp40g+.book Page 10 Friday, December 9, 2005 1:03 AM Results Field name σ2 α The results are: Result Test Z Prob Critical Z Definition Population You select one of the following alternative hypotheses against which to test the null hypothesis: H1:π < π0 H1:π > π0 H1:π ≠ π0 11-10 Inference aplet - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 137
hp40g+.book Page 11 Friday, December 9, 2005 1:03 AM Inputs The inputs are: Field name x n π0 α Definition Number of successes in the π1= π2. You select one of the following alternative hypotheses against which to test the null hypothesis: H1:π1 < π2 H1:π1 > π2 H1:π1 ≠ π2 Inference aplet 11-11 - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 138
hp40g+.book Page 12 Friday, December 9, 2005 1:03 AM Inputs Results The inputs are: Field name X1 X2 n1 n2 α The results are: assumed value, Η0 :μ = μ0 You select one of the following alternative hypotheses against which to test the null hypothesis: H1:μ < μ0 H1:μ > μ0 H1:μ ≠ μ0 Inference aplet - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 139
hp40g+.book Page 13 Friday, December 9, 2005 1:03 AM Inputs Results The inputs are: Field name x Sx n μ0 α The results are: Result Test T Prob . Boundary value of T associated with the α level that you supplied. Boundary value of x required by the α value that you supplied. Inference aplet 11-13 - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 140
hp40g+.book Page 14 Friday, December 9, 2005 1:03 AM Two-Sample T-Test Menu name Inputs T-Test: μ1 - μ2 The Two-sample T-Test is Sample 1 size. n2 Sample 2 size. α Significance level. _Pooled? Check this option to pool samples based on their standard deviations. 11-14 Inference aplet - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 141
calculations that the HP 40gs calculate a confidence interval for m, the true mean of a population, when the true population standard deviation, s, is known. The inputs are: Field name x σ n C Definition Sample mean. Population standard deviation. Sample size. Confidence level. Inference aplet - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 142
hp40g+.book Page 16 Friday, December 9, 2005 1:03 AM Results The results are: Result Critical Z μ min μ max Description Critical value for Z. Lower bound for μ. Upper bound for μ. Two-Sample Z-Interval Menu name Inputs Z-INT: μ1- μ2 This option uses the Normal Z-distribution to calculate aplet - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 143
hp40g+.book Page 17 Friday, December 9, 2005 1:03 AM One-Proportion Z-Interval Menu name Inputs Z-INT: 1 π This option uses the Normal Z-distribution to calculate π1 - π2 This option uses the Normal Z-distribution to calculate a confidence interval for the difference between the proportions of - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 144
hp40g+.book Page 18 Friday, December 9, 2005 1:03 AM Results Field name n1 n2 C Definition (Continued -Sample T-Interval Menu name Inputs T-INT: 1 μ This option uses the Student's t-distribution to calculate a confidence interval for m, the true mean of a population, for the case in which the - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 145
hp40g+.book Page 19 Friday, December 9, 2005 1:03 AM Results The results are: Result Critical T μ Min μ Max Description Critical value for T. Lower bound for μ. Upper bound for μ. Two-Sample T-Interval Menu name Inputs T-INT: μ1 - μ2 This option uses the Student's t-distribution to calculate - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 146
hp40g+.book Page 20 Friday, December 9, 2005 1:03 AM Results The results are: Result Critical T Δ μ Min Δ μ Max Description Critical value for T. Lower bound for μ1 - μ2. Upper bound for μ1 - μ2. 11-20 Inference aplet - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 147
key or the soft menu key to activate the aplet. The resulting screen shows the different elements involved in the solution of financial problems with your HP 40gs calculator. Background information on and applications of financial calculations are provided next. Background The Finance Solver - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 148
hp40g+.book Page 2 Friday, December 9, 2005 1:03 AM combined amount earns interest at a certain rate. Financial calculations involving compound interest include savings accounts, mortgages, pension funds, leases, and annuities. Time Value of Money (TVM) calculations, as the name implies, make use - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 149
hp40g+.book Page 3 Friday, December 9, 2005 1:03 AM flow diagram shows lease payments to compute the nominal interest rate per compounding period -- which is the interest rate actually used in TVM calculations. The present value of the initial cash flow. To a lender or borrower, PV is the amount of - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 150
hp40g+.book Page 4 Friday, December 9, 2005 1:03 AM The periodic payment amount. The payments are the same amount each period and the TVM calculation assumes PMT that no payments are skipped. Payments can occur at the beginning or the end of each compounding period -- an option you control by - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 151
hp40g+.book Page 5 Friday, December 9, 2005 1:03 AM Example 1 - Loan calculations Suppose you finance the purchase of a car with a 5-year loan at 5.5% annual interest, compounded monthly. The purchase price of the car is $19,500, and the down payment is $3,000. What are the required monthly - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 152
hp40g+.book Page 6 Friday, December 9, 2005 1:03 AM Example 2 - Mortgage with balloon option. • Enter the known TVM variables as shown in the diagram above. Your input form, for calculating monthly payments for the 30-yr mortgage, should look as follows: • Highlighting the PMT field, press - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 153
hp40g+.book Page 7 Friday, December 9, 2005 1:03 AM 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 Finance Solver as - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 154
hp40g+.book Page 8 Friday, shown below. To amortize a series of future payments starting at payment p: 1. Calculate the balance of the loan at payment p-1. 2. Store the new balance in to the current display mode, then calculates the amortization rounded to the same setting. The original variables are not - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 155
hp40g+.book Page 1 Friday, December 9, 2005 1:03 AM 13 Using mathematical functions Math functions The HP 40gs contains many math functions. The functions are grouped in categories. For example, the Matrix category contains functions for manipulating matrices. The Probability category (shown as - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 156
hp40g+.book Page 2 Friday, December 9, 2005 1:03 AM edit line. If you press while the MATH menu is open, CAS functions and commands are displayed. You can select a CAS function or command in the same way that you select a a function does not require spaces. 13-2 Using mathematical functions - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 157
hp40g+.book Page 3 Friday, December 9, 2005 1:03 AM Functions common to keyboard and menus These functions are common to the keyboard and functions are available directly from the keyboard. Many of the keyboard functions also accept complex numbers as arguments. Using mathematical functions 13-3 - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 158
hp40g+.book Page 4 Friday, December 9, 2005 1:03 AM ,, , ex 10x ,, ASIN 13-4 Add, Subtract, Multiply, Divide. Also accepts complex numbers, lists π/2, or -100 to 100 grads. Inputs and outputs depend on the current angle format. Also accepts complex numbers. ASIN(value) Using mathematical functions - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 159
hp40g+.book Page 5 Friday, December 9, 2005 1:03 AM ACOS ATAN Example ASIN(1) returns 90 (Degrees mode). Arc cosine: cos-1x. . Also accepts complex numbers. -value Example -(1,2) returns (-1,-2) Power (x raised to y). Also accepts complex numbers. value^power Using mathematical functions 13-5 - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 160
hp40g+.book Page 6 Friday, December 9, 2005 1:03 AM Example 2^8 returns 256 ABS Absolute value. For a complex number, this is x2 + y2 . variable (s1, etc). ∫ (lower, upper, expression, variable) See "Using formal variables" on page 13-20 for further details. 13-6 Using mathematical functions - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 161
hp40g+.book Page 7 Friday, December 9, 2005 1:03 AM TAYLOR Example ∫ (0,s1,2*X+3,X) finds the indefinite result 3*s1+2*(s1^2/2) See "To find the indefinite integral using formal variables" on page 13-23 for more information on finding indefinite integrals. Calculates mathematical functions 13-7 - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 162
3 The constants available from the MATH FUNCTIONS menu are mathematical constants. These are described in this section. The HP 40gs has two other menus of constants: program constants and physical constants. These are described in "Program constants and physical constants" on page 13-24. Natural - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 163
hp40g+.book Page 9 Friday, December 9, 2005 1:03 AM →C →F →CM →IN →L →LGAL →KG →LBS →KM →MILE →DEG →RAD Convert from Fahrenheit to -1x. ACOSH(value) ASINH Inverse hyperbolic sine : sinh-1x. ASINH(value) ATANH Inverse hyperbolic tangent : tanh-1x. ATANH(value) Using mathematical functions 13-9 - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 164
hp40g+.book Page 10 Friday, December 9, 2005 1:03 AM COSH SINH TANH ALOG EXP ITERATE Repeatedly for #times evaluates an expression in terms of variable. The value for variable is updated each time, starting with initialvalue. ITERATE(expression, variable, initialvalue, #times) Example ITERATE(X2 - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 165
Sequence aplet. If used with | ("where"), RECURSE will step through the evaluation. RECURSE(sequencename, termn, term1, term2) Example RECURSE(U,U(N-1)*N,1,2) U1(N) Stores a factorial-calculating coefficients for the value of x. POLYEVAL([coefficients], value) Using mathematical functions 13-11 - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 166
hp40g+.book Page 12 Friday, December can see them easily by going to the Matrix Catalog. and access them individually in calculations by referring to M1(1), M1(2) etc. Probability functions COMB Number of combinations (without regard combined two at a time.! 13-12 Using mathematical functions - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 167
Produced by a pseudo-random number sequence. The algorithm used in the RANDOM function uses a seed number to begin its sequence. To ensure that two calculators must produce different results for the square of the standard deviation. UTPN(mean, variance, value) Using mathematical functions 13-13 - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 168
hp40g+.book Page 14 Friday, December 9, 2005 FLOOR(value) Example FLOOR(-3.2) returns -4 FNROOT Function root-finder (like the Solve aplet). Finds the value for the given variable at which expression most nearly evaluates to value) Example FRAC (23.2) returns .2 13-14 Using mathematical functions - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 169
hp40g+.book Page 15 Friday, December 9, 2005 1:03 AM HMS→ →HMS INT MANT MAX MIN MOD Hours-minutes-seconds to decimal. Converts a number of two values. MIN(value1, value2) Example MIN(210,25) returns 25 Modulo. The remainder of value1/value2. value1 MOD value2 Using mathematical functions 13-15 - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 170
hp40g+.book Page 16 Friday, December 9, 2005 1:03 AM % %CHANGE %TOTAL RAD→DEG ROUND SIGN 13-16 Example 9 MOD 4 returns 1 x percent of y; that is, zero, result is zero. For a complex number, this is the unit vector in the direction of the number. SIGN(value) SIGN((x, y)) Using mathematical functions - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 171
hp40g+.book Page 17 Friday, December 9, 2005 1:03 AM TRUNCATE XPON Examples SIGN (-2) returns -1 SIGN((3,4)) returns (.6,.8) Truncates value to decimal the (formal) variables S1 to represent any sign and n1 to represent any integer. ISOLATE(expression, variable) Using mathematical functions 13-17 - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 172
hp40g+.book Page 18 Friday, December 9, 2005 1:03 AM LINEAR? QUAD QUOTE | (where) 13-18 quotes. For example, X^3+2*X F1(X) puts the expression X^3+2*X into F1(X) in the Function aplet. Evaluates expression where each given variable is set to the given value. Defines numeric evaluation of - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 173
hp40g+.book Page 19 Friday, December 9, 2005 1:03 AM Test functions AND IFTE NOT OR The test functions are logical operators that zero, otherwise returns 0. NOT value Returns 1 if either value1 or value2 is non-zero, otherwise returns 0. value1 OR value2 Using mathematical functions 13-19 - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 174
sinx CSC(value) SEC Secant: 1/cosx. SEC(value) Symbolic calculations Although CAS provides the richest environment for performing symbolic calculations, you can perform some symbolic calculations in HOME and with the Function aplet. CAS functions that you can perform in HOME (such as DERVX and - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 175
hp40g+.book Page 21 Friday, December 9, 2005 1:03 AM 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 - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 176
hp40g+.book Page 22 Friday, December 9, 2005 1:03 AM differentiation function substitutes the value . For example, to differentiate sin (x2) + 2 cosx : 1. Access the Function aplet's Symbolic view and define F1. 2 2. Define F2(X) as the derivative of F(1). 13-22 Using mathematical functions - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 177
hp40g+.book Page 23 Friday, December 9, 2005 1:03 AM F1 3. Select F2(X) and evaluate it. 4. Press to display the 3x2 - 5dx use: ∫ (0, S1, 3 X 2 − 5, X ) 1. Enter the function. 0 S1 3 X 5 X 2. Show the result format. 3. Press to close the show window. Using mathematical functions 13-23 - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 178
hp40g+.book Page 24 Friday, December 9, 2005 1:03 and should be disregarded if an indefinite integral is required. Program constants and physical constants When you press , three menus math functions menu (which appears by default) • the program constants menu, and • the physical constants menu. - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 179
hp40g+.book Page 25 Friday, December 9, 2005 1:03 AM Program constants The program constants are numbers that have been assigned to various calculator settings to enable you to test for or specify such a setting in a program. For example, the various display formats are assigned the following - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 180
hp40g+.book Page 26 Friday, December 9, 2005 1:03 AM 3. Use the arrow keys to navigate about the speed of light (one of the physics constants). 5. To use the selected constant in a calculation, press . The constant appears at the position of the cursor on the edit line. Example Suppose you want - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 181
hp40g+.book Page 27 Friday, December 9, 2005 1:03 AM 3. Select light s...from the Physics menu. 4. Press . The menu closes and the value of the selected constant is copied to the edit line. 5. Complete the equation as you would normally and press to get the result. Using mathematical functions - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 182
hp40g+.book Page 28 Friday, December 9, 2005 1:03 AM - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 183
mode, giving you infinite precision. On the other hand, non-CAS calculations, such as those performed in HOME view or by an aplet, are numerical calculations and are limited by the precision of the calculator (to 10-12 in the case of the HP 40gs). For example, with Standard as your numerical format - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 184
hp40g+.book Page 2 Friday, December 9, 2005 1:03 AM using vectors and matrices. ( history when you leave the Equation Writer. (You can, however, manually copy them to HOME: see page 14-8). CAS functions are described in detail in "CAS functions in the Equation Writer" on page 14-9. Chapter 15, - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 185
hp40g+.book Page 3 Friday, December 9, 2005 1:03 AM 3. Press and to select just the 20 in the 20 term. 4. Press the menu key and choose press and to factor the selected term. 9. Press to select the entire second term, and then press to simplify it. Computer Algebra System (CAS) 14-3 - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 186
hp40g+.book Page 4 Friday, December 9, 2005 1:03 AM 10.Press 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, you are working with symbolic variables (variables that do not contain a - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 187
any other letter, or combination of letters and numbers, by editing the INDEP VAR field in CAS MODES screen. To change the setting, press , enter a new value and then press . The variable VX in the calculator's {HOME CASDIR} directory takes, by default, the value of 'X'. This is the name of the - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 188
hp40g+.book Page 6 Friday, December 9, 2005 1:03 AM Num. Factor mode Complex vs. Real mode Verbose vs. nonverbose mode Step-by-step mode Increasing-powers mode Rigorous setting Simplify nonrational setting calculated calculator will report an error. [Default: unselected.] When in COMPLEX mode, CAS - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 189
take matrices as an argument work only from HOME. CAS functions can be accessed by pressing when MATH menu is displayed. You can also directly type a function name when you are in alpha mode. Note that certain calculations will be performed in approximate mode because numbers are interpreted - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 190
are stored as a list of lists and therefore must be stored in L0, L1...L9 (whereas numeric matrices are stored in M0, M1,...M9). CAS linear algebra instructions accept lists of lists as input. For example, if you type in HOME: XQ({{S2 + 1, 1}, { 2 , 1}}) L1 then you have: TRAN(L1) = {{S2 - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 191
hp40g+.book English. For instructions, see "Online Help language" on page 15-4. CAS functions in the Equation Writer You can display a menu of CAS functions in directly type the name of a CAS function when you are in ALPHA mode. Note that in this section, CAS functions available from the sot-key - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 192
hp40g+.book Page 10 Friday, December 9, 2005 1:03 AM ALGB menu COLLECT DEF 14-10 For example, suppose you have stored the expression x2 in G, and have defined the function F(x) as x2. Suppose now you want to calculate DEF defines this function and returns the equality. Computer Algebra System (CAS) - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 193
hp40g+.book Page 11 Friday, December 9, 2005 1:03 AM 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 Computer Algebra System (CAS) 14-11 - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 194
hp40g+.book Page 12 Friday, December 9, 2005 1:03 AM EXPAND FACTOR 14-12 which gives 4294967297 You can factor F(5) - 2 ⋅ X + 1) gives: x4 + 1 Factorization FACTOR factors an expression. Example To factor: x4 + 1 type: FACTOR(X4+1) FACTOR is located in the ALGB menu. Computer Algebra System (CAS) - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 195
hp40g+.book Page 13 Friday, December 9, 2005 1:03 AM PARTFRAC QUOTE In real mode, the result is: (x2 + 2 ⋅ x expression from being evaluated or simplified. Example 1 Typing: i m ⎛⎝ Q U O T E ( ( 2 X - 1) ⋅ E X P ( -1-X - 1 ), X = +∞⎠⎞ gives: +∞ Computer Algebra System (CAS) 14-13 - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 196
hp40g+.book Page 14 Friday, December 9, 2005 1:03 AM STORE | 14-14 Example 2 Typing: SUBST(QUOTE(CONJ(Z)),Z=1+i) gives: CONJ(1+i) Store parameter=substitute value). | substitutes the specified value for the variable in the expression. Typing: X2 - 1 X = 2 gives: 22 - 1 Computer Algebra System (CAS) - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 197
hp40g+.book Page 15 Friday, December 9, 2005 1:03 AM SUBST TEXPAND UNASSIGN Substitute a value for a variable SUBST has Typing: TEXPAND(COS(3·X)) gives: 4 ⋅ cos (x)3 - 3 ⋅ cos (x) Clear a variable UNASSIGN is used to clear a variable, for example: UNASSIGN(ABC) Computer Algebra System (CAS) 14-15 - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 198
hp40g+. example, given: f(x) = ------x------x2 - 1 + ln ⎛ ⎝ x-x----+-----1-1-⎠⎞ calculate the derivative of f. Type: D E RVX ⎛ ⎝ ------X-------X2 - is, if you have typed: TOR E⎛⎝ ------X-------X2 - 1 + L N ⎛ ⎝ X-X-----+-----1-1-⎠⎞ ,F⎠⎞ then type: Computer Algebra System (CAS) - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 199
hp40g+.book Page 17 Friday, December 9, 2005 1:03 AM 0. Typing: DIVPC(1+X2+X3,1+X2,5) gives: 1 + x3 - x5 When the calculator displays a request to change to increasing powers mode, respond yes. FOURIER Fourier coefficients function defined over interval [0, T] Computer Algebra System (CAS) 14-17 - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 200
hp40g+.book Page 18 Friday, December 9, over interval [0, 2π] by f(x)=x2. Typing: STORE(2π,PERIOD) FOURIER(X2,N) The calculator does not know that N is a whole number, so you have to replace IBP has two parameters: an expression of the form u(x) ⋅ v'(x) and v(x) . Computer Algebra System (CAS) - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 201
hp40g+.book Page 19 Friday, December 9, 2005 1:03 AM NOTE: IBP returns the AND of u(x) ⋅ v(x) and of -v(x) ⋅ u'(x) 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 - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 202
hp40g+.book Page 20 Friday, December 9, 2005 1:03 AM 14-20 Example Given: f(x) = ------x------x2 - 1 + LN⎝⎛ x-x----+-----1-1-⎠⎞ calculate values only in Rigorous mode. (See "CAS modes" on page 14-5 for instructions on setting and changing modes.) Example Calculate: 2 x6 + 2 ⋅ x4 + x2 - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 203
hp40g+.book Page 21 Friday, December 9, 2005 1:03 AM NT V 4--+-----1---0-⎠⎞ Example Calculate: ∫ the result to the first argument. lim Calculate limits LIMIT or lim has two arguments: an variable = the value to which you want to calculate the limit). You can omit the name of the - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 204
hp40g+.book Page 22 Friday, December 9, 2005 1:03 AM 14-22 QUOTE(expression), to avoid rewriting the expression in normal the limit as x approaches 0: -ns--i--⋅n---t-(-a-n--n---⋅(---xx nt--a--⋅n----s(--i-n-n---⋅(---xx---))- You can use the LIMIT command to do this. Computer Algebra System (CAS) - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 205
hp40g+.book Page 23 Friday, December 9, 2005 1:03 AM PREVAL Typing: lim⎝⎛-N--S---⋅I---NT----A(--N--N----⋅(--X-X TN---A--⋅--N-S----(I--NN-----(-⋅-X--X--)--)-, 0⎠⎞ gives: For example, if VX contains X, and if F is a function, PREVAL (F(X),A,B) returns F(B)-F(A). Computer Algebra System (CAS) 14-23 - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 206
hp40g+.book Page 24 Friday, December 9, 2005 1:03 AM RISCH NOTE: PREVAL is used for calculating an integral defined from a primitive: it evaluates this primitive between the two limits of of cos(2 · x)2 in the 6 For this you use the SERIES command. 14-24 Computer Algebra System (CAS) - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 207
hp40g+.book Page 25 Friday, December 9, 2005 1:03 AM Typing: S E R I E S ⎝⎛ C O S ( 2 ⋅ X)2, X = π-- , 6 4⎠⎞ gives: 〈1-4 - 3h + 2h2 + 8--------3- h3 3 - 8-- h4 3 + 0⎝⎛h--4--5⎠⎞ |h = X - < a, use a negative real (such as -4.0) for the order. Computer Algebra System (CAS) 14-25 - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 208
hp40g+.book Page 26 Friday, December 9, 2005 1:03 AM 14-26 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. when exploring in the vicinity of x = 0+: Computer Algebra System (CAS) - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 209
hp40g+.book Page 27 Friday, December 9, 2005 1:03 AM TABVAR TAYLOR0 --1--- ⋅ h4 + -----1- ⋅ h3 + 1-- ⋅ h2 + h + 0(h5) (h = x) 16 8 2 Variation table TABVAR 's limited 4th-relative-order expansion in the vicinity of x=0 (if x is the current variable). Computer Algebra System (CAS) 14-27 - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 210
hp40g+.book Page 28 Friday, December 9, 2005 1:03 AM Note Typing: T A Y L O R 0 ⎝⎛ TT---AA--NN--((-PQ---⋅⋅--XX--))-------SS--II--NN--((--PQ--⋅⋅--XX--))⎠⎞ gives: -P----3- + when you apply it several times, to carry out the distributivity step by step. 14-28 Computer Algebra System (CAS) - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 211
hp40g+.book Page 29 Friday, December 9, 2005 1:03 AM EPSX0 EXPLN EXP2POW Typing: DISTRIB((X+1)·(X+2)·(X+3)) gives: x ⋅ (x + 2) ⋅ (x + 3) + 1 ⋅ (x exponentials and logarithms without linearizing it. EXPLN puts the calculator into complex mode. Typing: EXPLN(SIN(X)) gives: -e---x---p---(---i---⋅---x - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 212
hp40g+.book Page 30 Friday, December 9, 2005 1:03 AM FDISTRIB LIN 14-30 but converts a trigonometric expression to exponentials and then linearizes the complex exponentials. LIN puts the calculator into complex mode when dealing with trigonometric functions. Example 1 Typing: LIN((EXP(X)+1)3) gives: - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 213
hp40g+.book Page 31 Friday, December 9, 2005 1:03 AM LNCOLLECT POWEXPAND SINCOS 1-- ⋅ exp(-(2 ⋅ i ⋅ x)) + 1-- + 1-- ⋅ exp(2 ⋅ i ⋅ x) 4 24 Example 3 Typing: LIN(SIN(X)) gives: --i- ⋅ expi ⋅ x + then rewrites this expression in terms of sin(x) and cos(x). Computer Algebra System (CAS) 14-31 - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 214
hp40g+.book Page 32 Friday, December 9, 2005 XNUM has an expression as a parameter. XNUM puts the calculator into approximate mode and returns the numeric value of the has a real numeric expression as a parameter. XQ puts the calculator into exact mode and gives a rational or real approximation of - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 215
hp40g+.book Page 33 Friday, December 9, 2005 1:03 AM SOLV menu DESOLVE Typing: XQ(1.414213562) gives: √2 The SOLV menu 2 cC0 and cC1 are integration constants (y(0) = cC0 y'(0) = cC1). You can then assign values to the constants using the SUBST command. Computer Algebra System (CAS) 14-33 - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 216
hp40g+.book Page 34 Friday, December 9, 2005 1:03 AM ISOLATE 14-34 To produce the solutions for y(0) = 1, type: SUBST(Y(X) = cC0 ⋅ COS(X) + -X--+---2---⋅--c--C---1 ⋅ : (x = √2) OR (x = −√2) and in complex mode: (x = √2 · i) OR (x = −√2) OR (x = −(√2 · i)) OR (x = √2) Computer Algebra System (CAS) - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 217
hp40g+.book Page 35 Friday, December 9, 2005 1:03 AM LDEC Linear differential equations having constant coefficients LDEC enables LINSOLVE(X+Y+3 AND X-Y+1, X AND Y) gives: (x = −2) AND (y = −1) or, in Step-by-step mode (CFG, etc.): L2=L2−L1 113 1 -1 1 Computer Algebra System (CAS) ENTER 14-35 - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 218
hp40g+.book Page 36 Friday, December 9, 2005 1:03 AM 14-36 L1=2L1+L2 11 3 0 -2 -2 ENTER Reduction Result 20 4 0 -2 -2 L2=2L2−L1 2 1 1 -1 1 1 2 -1 1 2 1 -4 ENTER L3=2L3−L1 2 1 1 -1 0 1 3 -1 1 2 1 -4 and so on until, finally: Reduction Result 80 0 4 0 8 0 -20 0 0 -8 -4 Computer Algebra System (CAS) - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 219
hp40g+.book Page 37 Friday, December 9, 2005 1:03 AM SOLVE then press ENTER. The following is then written to the Equation Writer: ⎝⎛ x = -12--⎠⎞ AND ⎛ ⎝ by AND. Typing: SOLVE(X2+Y2-3 AND X-Y2+1,X AND Y) gives: (x = 1) AND (y = −√2) OR (x = 1) AND (y = √2) Computer Algebra System (CAS) 14-37 - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 220
hp40g+.book Page 38 Friday, December 9, 2005 1:03 AM SOLVEVX TRIG menu ACOS2S Solve equations SOLVEVX has as a parameter either: (1) an a trigonometric expression as an argument. ACOS2S transforms the expression by replacing arccos(x) with π-2 − arcsin(x). 14-38 Computer Algebra System (CAS) - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 221
hp40g+.book Page 39 Friday, December 9, 2005 1:03 AM ASIN2C ASIN2T Typing: ACOS2S(ACOS(X) + ASIN(X)) gives, when simplified: π-2 as an argument. ATAN2S transforms the expression by replacing arctan(x) with arc sin ⎛ ⎜ ---------x . ⎝ 1 + x2⎠ Computer Algebra System (CAS) 14-39 - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 222
hp40g+.book Page 40 Friday, December 9, 2005 1:03 AM HALFTAN SINCOS TAN2CS2 14-40 Typing: ATAN2S(ATAN(X)) gives: asin ⎛ ⎜ ---------x ⎝ x2 + 1⎠ (x) + i · sin(x) Transform tan(x) with sin(2x) and cos(2x) TAN2CS2 has a trigonometric expression as an argument. Computer Algebra System (CAS) - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 223
hp40g+.book Page 41 Friday, December 9, 2005 1:03 AM TAN2SC TAN2SC2 TCOLLECT TAN2CS2 transforms this expression by replacing tan(x) with the cosine of the same angle TCOLLECT has a trigonometric expression as an argument. Computer Algebra System (CAS) 14-41 - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 224
hp40g+.book Page 42 Friday, December 9, 2005 1:03 AM TEXPAND 14-42 TCOLLECT linearizes this expression in terms of sin(n x) and cos (LN(X·Y)) gives: ln(y) + ln(x) Example 3 Typing: TEXPAND(COS(X+Y)) gives: cos(y)·cos(x)-sin(y)·sin(x) Example 4 Typing: TEXPAND(COS(3·X)) Computer Algebra System (CAS) - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 225
hp40g+.book Page 43 Friday, December 9, 2005 1:03 AM TLIN TRIG gives: 4·cos(x)3-3·cos(x) Linearize a trigonometric + cos(x)2 = 1 TRIG has as an argument a trigonometric expression. TRIG simplifies this expression using the identity sin(x)2 + cos(x)2 = 1. Computer Algebra System (CAS) 14-43 - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 226
hp40g+.book Page 44 Friday, December 9, 2005 1:03 AM TRIGCOS TRIGSIN TRIGTAN 14-44 Typing: terms of tangents. Typing: TRIGTAN(SIN(X)4 + COS(X)2 + 1) gives: 2-----⋅---t--a---n---(---x---)--4----+-----3----⋅----t-a---n----(--x---)--2----+-----2tan (x)4 + 2 ⋅ tan (x)2 + 1 Computer Algebra System (CAS) - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 227
hp40g+.book Page 45 Friday, December 9, 2005 1:03 AM 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. Many of the functions in this menu match the functions available from the soft-key menus in - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 228
hp40g+.book Page 46 Friday, December 9, 2005 1:03 AM returns: Y = X -1 + 2 Pressing simplifies this to: Y = X + 1 IM See "IM" on page 13-7. - Specifies Note that many integer functions also work with Gaussian integers (a + bi where a and b are integers). 14-46 Computer Algebra System (CAS) - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 229
hp40g+.book Page 47 Friday, December 9, 2005 1:03 AM DIVIS Gives the divisors of an integer. Example Typing: DIVIS(12) gives: 12 OR 6 OR 3 (90) gives: 2·32·5 GCD Returns the greatest common divisor of two integers. Example Typing: GCD(18, 15) gives: 3 Computer Algebra System (CAS) 14-47 - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 230
hp40g to the Note that the last non-zero remainder in the sequence of remainders shown in the intermediate steps is the GCD. gives: 29 AND 3 In step-by-step mode, the calculator shows the division process in longhand. Returns the value of Bézout : [z,u,v]:z=u*48+v*30 Computer Algebra System (CAS) - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 231
hp40g+.book Page 49 Friday, December 9, 2005 1:03 AM IQUOT IREMAINDER quotient of the integers at the beginning of the vector, these integers being the sequence of remainders). Returns the integer quotient of the Euclidean division of two integers. Example : 3 Computer Algebra System (CAS) 14-49 - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 232
hp40g+.book Page 50 Friday, December 9, 2005 1:03 AM ISPRIME? LCM MOD 14-50 IREMAINDER works with integers and with Gaussian integers. This is what : 0. Returns the least common multiple of two integers. Example Typing: LCM(18, 15) gives: 90 See "MOD" on page 13-15. Computer Algebra System (CAS) - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 233
hp40g+.book Page 51 Friday, December 9, 2005 1:03 AM NEXTPRIME NEXTPRIME(n) returns =13; that is, you have entered MODSTO(13) or STORE(13,MODULO), or have specified 13 for Modulo in CAS MODES screen (as explained on page 15-16). ADDTMOD Performs an addition in Z/pZ. Example 1 Typing: ADDTMOD(2, - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 234
hp40g+.book Page 52 Friday, December 9, 2005 1:03 AM DIVMOD EXPANDMOD 14-52 Division in Z/pZ or Z/pZ[X]. Example 1 In 3 + 5 · 4) gives: 0 Example 2 In Z/pZ[X], the argument is a polynomial. Typing: EXPANDMOD((2X2 + 12)·(5X - 4)) gives: -(3 ⋅ x3 - 5 ⋅ x2 + 5 ⋅ x - 4) Computer Algebra System (CAS) - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 235
hp40g+.book + 5X - 4)) gives: -((3x - 5) ⋅ (x2 + 6)) Calculates the GCD of the two polynomials in Z/pZ[X]. Example Typing: GCDMOD(2X2 + 5, 5X2 + 2X - 3) gives: -(6x - 1) Calculates the inverse of an integer in Z/pZ. Example Typing: INVMOD(5) gives: -5 since - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 236
hp40g+.book Page 54 Friday, December 9, 2005 1:03 AM MULTMOD POWMOD Performs a multiplication in Z/pZ or in Z/pZ[X]. Example 1 Typing: MULTMOD(11, 8) gives: -3 Example 2 Typing: MULTMOD(11X + 5, 8X + 6) gives: -(3x2 - 2x - 4) Calculates 13), 10 = -3 (mod 13). 14-54 Computer Algebra System (CAS) - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 237
hp40g+.book Page 55 Friday, December 9, 2005 1:03 AM SUBTMOD Performs a subtraction in Z/pZ or Z/pZ[X]. Example 1 Typing: EGCD(X2 + 2 · X + 1, X2 - 1) gives: -1 AND -1 = 2x + 2 Example 2 Typing: EGCD(X2 + 2 · X + 1, X3 + 1) gives: -(x - 2) AND 1 = 3x + 3 Computer Algebra System (CAS) 14-55 - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 238
hp40g+.book Page 56 Friday, December 9, 2005 1:03 AM FACTOR GCD HERMITE 14-56 Factors a polynomial. Example 1 Typing: FACTOR(X2 - 2) gives: (x + 2) ⋅ (x = (-1)n ⋅ e x---22 --d---n-- - -x--2- e2 dxn Example Typing: HERMITE(6) gives: 64x6 - 480x4 + 720x2 - 120 Computer Algebra System (CAS) - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 239
hp40g+.book Page 57 Friday, December 9, 2005 1:03 AM LCM LEGENDRE PARTFRAC Returns the 2x2 + 2 + ---------1-----2x - 2 and gives, in complex mode: 1----------3-----⋅---i -----1- 1-----+-----3----⋅---i x + 2 + --------4 2 4---------- x+i x-1 x-i Computer Algebra System (CAS) 14-57 - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 240
hp40g+.book Page 58 Friday, December 9, 2005 1:03 AM PROPFRAC PTAYL QUOT 14-58 PROPFRAC rewrites a rational fraction QUOT returns the quotient of two polynomials, A(X) and B(X), divided in decreasing order by exponent. Example Typing: QUOT(X2 + 2·X + 1, X) gives: x+2 Computer Algebra System (CAS) - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 241
hp40g+.book Page 59 Friday, December 9, 2005 1:03 AM 0 For n ≥ 1, we have: Tn + 1(x) = 2xTn(x) - Tn - 1(x) If n < 0, TCHEBYCHEFF returns the 2nd-species Tchebycheff polynomial: Tn(x) = -s--i--sn--i-(-n--n-(---a⋅--r-a-c--r-c-c--o-c--so--(-s--x-(--)x--)--)--) Computer Algebra System (CAS) 14-59 - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 242
hp40g+.book Page 60 Friday, December 9, 2005 1:03 AM Example 1 Typing: TCHEBYCHEFF(4) gives: 8x4 - 8x2 + 1 Example 2 Typing: TCHEBYCHEFF(-4) gives: 8x3 - 4x Real menu in the Equation Writer. See "SOLV menu" on page 14-33 for a description of these functions. 14-60 Computer Algebra System (CAS) - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 243
hp40g+.book Page 61 Friday, December 9, 2005 1:03 AM Tests menu ASSUME UNASSUME AND OR NOT IFTE Use this function to make a hypothesis about a specified argument or variable. Example Typing: ASSUME(X>Y) sets an assumption that X is greater than Y. In fact, the calculator System (CAS) 14-61 - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 244
hp40g+.book Page 62 Friday, December 9, 2005 1:03 AM 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. Many of the functions in this menu match the functions available from the soft-key menus - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 245
hp40g+.book Page 63 Friday, December 9, 2005 1:03 AM CYCLOTOMIC EXP2HYP Example Find the solutions P(X) of: P(X) = X (mod X2 + 1) P(X) = X - 1 (mod X2 - 1) Typing: as an argument. It transforms that expression with the relation: exp(a) = sinh(a) + cosh(a). Computer Algebra System (CAS) 14-63 - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 246
hp40g+.book Page 64 Friday, December 9, 2005 1:03 AM GAMMA IABCUV 14-64 Example 1 Typing: EXP2HYP(EXP(A)) gives: sinh(a) + cosh(a) Example 2 Typing: AND V such that AU + BV = C where A, B and C are whole numbers. C must be a multiple of GCD(A,B) to obtain a solution. Computer Algebra System (CAS) - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 247
hp40g+.book Page 65 Friday, December 9, 2005 1:03 AM IBERNOULLI ICHINREM ILAP Example Typing: IABCUV(48, 30, 18) gives: 6 AND -9 Returns the nth Bernoulli's number of a given expression. The expression is the value of a function of the variable stored in VX. Computer Algebra System (CAS) 14-65 - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 248
hp40g+.book Page 66 Friday, December 9, 2005 1:03 AM P ⎝⎛ L-----A----P----(--f--(---xx---)2--)--+--+---p--(-x-x----++-----qp a-----+----b--⎠⎞ Example To solve: y″-6 ⋅ y′ + 9 ⋅ y = x ⋅ e3x, y(0) = a, y′(0) = b c type: LAP(X · EXP(3 · X)) The result is 1 x2 - 6x + 9 Computer Algebra System (CAS) - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 249
hp40g+.book Page 67 Friday, December 9, 2005 1:03 AM Typing: 1 X-6) ⋅ a + b⎞ IL A P ⎜ ⎜ ⎜ PA2B2 Decomposes a prime integer p congruent to 1 modulo 4, as follows: p = a2 + b2. The calculator gives the result as a + b · i. Example 1 Typing: PA2B2(17) gives: 4 + i that CAS) 14-67 - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 250
hp40g+.book Page 68 Friday, December 9, 2005 1:03 AM Psi REORDER SEVAL SIGMA 14-68 gives: - 5-- + 1-- ⋅ π2 46 Returns the value of the relation G(x + 1) - G(x) = f(x). It has two arguments: the first is a function f(x) of a variable x given as the second argument. Computer Algebra System (CAS) - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 251
hp40g+.book Page 69 Friday, December 9, 2005 1:03 AM SIGMAVX STURMAB Example Typing: SIGMA(X · X!, X) gives: X! because (X + 1)! - X! are numbers. Example 1 Typing: STURMAB(X2 · (X3 + 2), -2, 0) gives: 1 Example 2 Typing: STURMAB(X2 · (X3 + 2), -2, 1) gives: 3 Computer Algebra System (CAS) 14-69 - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 252
hp40g+.book Page 70 Friday, December 9, 2005 1:03 AM TSIMP VER Simplifies CAS. Example Typing: VER might give: 4.20050219 This particular result means that you have a version 4 CAS, dated 19 February 2005. Note that this is not the same as VERSION (which returns the version of the calculator's ROM - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 253
hp40g+.book Page 1 Friday, December 9, 2005 1:03 AM 15 Equation Writer Using CAS in the Equation Writer The Equation apply CAS functions to an expression or subexpression and how to store values in the Equation Writer variables. Chapter 14 explains all the symbolic calculation functions - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 254
hp40g+.book Page 2 Friday, December 9, 2005 1:03 AM ALGB menu DIFF menu selected the last time you used these commands, or the highlighted level when you selected COPY in CAS history. The menu contains functions that enable you to perform algebra, such as factoring, expansion, simplification - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 255
hp40g+.book Page 3 Friday, December 9, 2005 1:03 AM REWRI menu The menu contains functions functions that enable you to transform trigonometric expressions. NOTE You can get online help about any CAS function by pressing 2 and selecting that function (as explained in "Online Help" on page - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 256
hp40g+.book Page 4 Friday, December 9, 2005 1:03 AM NOTE • The fourth symbol, S, will appear on the menu. If you choose Sloppy, then Rigorous appears in its place. To return your CAS modes to their default settings, select Default cfg and press . To close the configuration menu, select Quit config - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 257
hp40g+.book Page 5 Friday, December 9, 2005 1:03 AM Entering expressions and they are automatically entered for you. It will help you understand how the Equation Writer works if you view a mathematical expression as a tree, with the four arrow keys enabling you to move through the tree: • the and - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 258
hp40g+.book Page 6 Friday, December 9, 2005 1:03 AM this case, you have to press expression. to select elements in the The following illustration shows how an - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 259
hp40g+.book Page 7 Friday, December 9, 2005 1:03 AM More Examples Equation Writer • Press again and again to progressively select more of the top-most branch, and - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 260
hp40g+.book Page 8 Friday, December 9, 2005 1:03 AM (- X) apply to it. As a result, the entered expression is interpreted, and displayed, as (2 + X)(3 - X). Select the entire expression by - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 261
hp40g+.book Page 9 Friday, December 9, 2005 1:03 AM Select the fifth branch by is shown at the right. Suppose now you want to perform the partial calculation: 1-2 + 1-5 Because the two terms in this partial calculation are not contiguous (that is, side by side), you must first perform - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 262
hp40g+.book Page 10 Friday, December 9, 2005 1:03 AM Cursor mode 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 - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 263
hp40g+.book Page 11 Friday, December 9, 2005 1:03 AM How to modify an expression by typing the desired expression. • Transform the selected expression by applying a CAS function to it (which you can invoke from one of CAS menus along the bottom of the screen). • Delete the selected expression by - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 264
hp40g+.book Page 12 Friday, December 9, 2005 1:03 AM Accessing CAS functions While you are in the Equation Writer, you can access all CAS + -1--- = 6---5-1! 2! 3! 4! 24 Note that Σ can symbolically calculate summations of rational fractions and hypergeometric series that allow a discrete primitive. - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 265
hp40g+.book Page 13 Friday, December 9, 2005 1:03 AM select the entire expression and press obtain: and MOD are infix functions.You can either: • type them in Alpha mode and then enter their arguments, or • select them from a CAS menu or by pressing an appropriate key, provided that you have already - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 266
hp40g+.book Page 14 Friday, December 9, 2005 1:03 AM First option: function first, then arguments In the Equation Writer, press , select FACTOR and then press or . - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 267
hp40g+.book Page 15 Friday, December 9, 2005 1:03 AM Press to obtain the an intermediate result (42 - 4) and again to evaluate the intermediate result. The final - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 268
used in CAS cannot be used in HOME, and vice versa. • In HOME or in the program editor, use an object in a variable. to store • In CAS, use the Aplets. Pressing while you are in the Equation Writer displays the names of the variables defined in CAS (as explained on page 15-18). Predefined CAS - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 269
hp40g+.book Page 17 Friday, December 9, 2005 1:03 AM • MODULO contains the value of p for performing symbolic calculations in Z/pZ or in Z/pZ[X]. You can change the value of p either with the MODSTO command on the MODULAR menu, (by typing, for example, MODSTO(n) to give p a value of n), or from CAS - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 270
hp40g+.book Page 18 Friday, December 9, calculations with polynomials. • The Real menu, containing functions specific to common real-number calculations to type it in ALPHA mode. Pressing while you're in the Equation Writer displays the names of the variables defined in CAS. Take special note - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 271
hp40g in the Equation Writer gives you access to CAS history. As in the HOME screen history, the calculations are written on the left and the graph a function, a parametric curve, or a polar curve. Depending on what you choose, the highlighted expression is copied into the appropriate aplet - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 272
hp40g+.book Page 20 Friday, December 9, 2005 1:03 AM NOTE NUM key SHIFT NUM key VIEWS key This operation supposes that the current variable is also the variable of the function or curve you want to graph Function, Aplet or Polar Aplet can be chosen, and the graph will be puts the calculator into - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 273
hp40g+.book Page 21 Friday, December 9, 2005 1:03 AM 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 ≥ Equation Writer 15-21 - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 274
hp40g+.book Page 22 Friday, December 9, 2005 1:03 AM - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 275
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. The examples are given in order of increasing difficulty. If A is: 3-- - 1 -2----------1-- + 1 2 calculate the result of - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 276
hp40g+.book Page 2 Friday, December 9, 2005 1:03 AM Press to simplify the numerator. Press to select the entire fraction. Example 2 16-2 Press to simplify the selected - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 277
hp40g+.book Page 3 Friday, December 9, 2005 1:03 AM Press to factor 20 into 22 ⋅ 5 . Press to select 22 ⋅ 5 and to simplify it. Press to select -2 5 and - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 278
hp40g+.book Page 4 Friday, December 9, 2005 1:03 AM Press to evaluate the selection. It remains to transform 3 12 and combine it with -6 3 . Follow the same procedure - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 279
hp40g+.book and press . The result is shown at the right. Press to display CAS history, select D or a version of it, and press . Press Calculate the price of one biscuit, and the price of one macaroon. Solution: Let x be the price of one biscuit, and y the price of one macaroon. The problem - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 280
hp40g+.book Page 6 Friday, December 9, 2005 1:03 AM Exercise 5 16-6 17x + 20y = 90 10x + 25y = , and press 5 you get X = 2 and Y = 2.8. In other words, the price of one biscuit is 2 cents, and the price of one macaroon is 2.8 cents. Suppose that A and B are points having the coordinates (-1, - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 281
hp40g+.book Page 7 Friday, December 9, 2005 1:03 AM First method 1. Find the exact length of AB in centimetres. 2. Determine the equation of the line AB. Type: - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 282
hp40g+.book Page 8 Friday, December 9, 2005 1:03 AM Press again to simplify the result to Y = 2X+5. Second method Type: (-3,-1 )-(-1,3) The answer is -(2+4i). Exercise 6 16-8 With - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 283
hp40g+.book Page 9 Friday, December 9, 2005 1:03 AM 4. Show that for every integer n > 0, bn 1 A = 4 N Finally press . Do likewise to define the other two expressions. You can now calculate various values of A(N), B(N) and C(N) simply by typing the defined variable and a value for N, and then - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 284
hp40g+.book Page 10 Friday, December 9, 2005 1:03 AM 16-10 Show that the whole numbers k such words, B(3) is a prime. Note: ISPRIME? is not available from a CAS soft menu, but you can select it from from CAS FUNCTIONS menu while you are in the Equation Writer by pressing , choosing the - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 285
hp40g+.book Page 11 Friday, December 9, 2005 1:03 AM Now consider the product of two of the 3, 23, 29 and 1999. Now let's consider whether bn and cn are relatively prime. Here, the calculator is useful only for trying out different values of n. To show that bn and cn are relatively prime, - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 286
hp40g+.book Page 12 Friday, December 9, 2005 1:03 AM 16-12 GCD(cn,bn) = GCD(cn,2) = GCD(bn,2) = 1 Part 2 Given the equation: b3 ⋅ x + c3 ⋅ y = 1 [1] where the - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 287
hp40g+.book Page 13 Friday, December 9, 2005 1:03 AM Exercise 7 Step-by-Step Examples so, b3 = 999 × (c3 - b3) + 1 , or b3 × 1000 + c3 × (-999) = 1 The calculator is not needed for finding the general solution to equation [1]. We started with b3 ⋅ x + c3 ⋅ y = 1 and have established that b3 × 1000 - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 288
hp40g+.book Page 14 Friday, December 9, 2005 1:03 AM Part 1 16-14 the circle C, M corresponding to t = 0, π/3, 2π/3 and π, and draw the tangent to Γ at these points. First go to CAS MODES screen and make t the VX variable. To do this, press to open the Equation Writer, and then press . This opens - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 289
hp40g+.book Page 15 Friday, December 9, 2005 1:03 AM Selecting the entire expression is shown at the right: Now store the result in variable M. Note that STORE is on the menu. To calculate the real part of the expression, apply the RE command (available on the COMPLEX submenu of the MATH menu). - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 290
hp40g+.book Page 16 Friday, December 9, 2005 1:03 AM Part 2 16-16 DEF command to it. Press definition. To calculate the real the coordinates of M in terms of t. To find an axis of symmetry for Γ, calculate x(-t) and y(-t) by typing: X t Press to highlight the expression. Then press to - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 291
hp40g+.book Page 17 Friday, December 9, 2005 1:03 AM Part 3 Then press to produce with respect to the xaxis, we can deduce that the x-axis is an axis of symmetry for Γ . Calculate x′(t) by typing: DERVX X t. Press to highlight the expression. Pressing returns the result at the right: Press - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 292
hp40g+.book Page 18 Friday, December 9, 2005 1:03 AM Part 4 Part 5 16-18 To calculate y′(t) , begin by typing: DERVX(Y(t)). Pressing thing with Y(t), making F2 the destination. To graph the functions, quit CAS (by pressing ), choose the Function aplet, and check F1 and F2. Step-by-Step - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 293
hp40g+.book Page 19 Friday, December 9, 2005 1:03 AM Now press the graphs. to see Part 6 Step-by-Step Examples To find the values of x(t) and y(t) for t = 0, π--, 2 33 return to CAS, type each function in turn and press . (You may need to press twice for further simplification). For example - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 294
hp40g+.book Page 20 Friday, December 9, 2005 1:03 AM The example at the right shows the case for t = 0. Select the entire expression and press to get - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 295
+ i × Y(t). Select the entire expression and press . Now press , select Parametric and press . Select X1,Y1 as the destination and press . To make the graph of Γ, quit CAS and choose the Parametric aplet. Check X1(T) and Y1(T). Now press the graph. to see Step-by-Step Examples 16-21 - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 296
hp40g+.book Page 22 Friday, December 9, 2005 1:03 AM Exercise 8 Part 1 For this exercise, make sure that the calculator is in exact real mode with X as the current variable. For an integer, n, define the following: ∫ un = 2 2----x----+-----3- e -xn dx 0 x+2 Define g over [0,2] where: - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 297
hp40g+.book Page 23 Friday, December 9, 2005 1:03 AM 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 - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 298
hp40g+.book Page 24 Friday, December 9, 2005 1:03 AM 16-24 Now press and scroll down the screen to: 1--------(x + 2)2 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 - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 299
hp40g+.book Page 25 Friday, December 9, 2005 1:03 AM We can now see that: 3-- ⎛ ⎜n e 2-n 2⎝ - ⎞ n⎟ ⎠ ≤ un ≤ 7-4 ⎛ ⎜ ⎝ 2-- nen - ⎞ n⎟ ⎠ To justify the preceding calculation, we must assume that -x- -x- n ⋅ en is a primitive of en . If you are not sure, you can use the INTVX - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 300
hp40g+.book Page 26 Friday, December 9, 2005 1:03 AM Part 2 16-26 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 setting. To check the result, we can say that: lim e---x---------1-- = 1 x→0 x and that therefore: 2-- lim - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 301
hp40g+.book Page 27 Friday, December 9, 2005 1:03 AM Solution 1 Start by defining the following: g(x) = 2 - -----1-----x+2 Now type PROPFRAC(G(X)). Note that PROPFRAC can be found on the - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 302
hp40g+.book Page 28 Friday, December 9, 2005 1:03 AM 16-28 Solution 3 The calculator is not needed here. Simply stating that -x- en increases for x ∈ [0,2] is sufficient to yield the inequality: -x- 2-- 1 ≤ en ≤ en Solution 4 Since g(x) is positive over [0, 2], through multiplication - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 303
hp40g+.book Page 29 Friday, December 9, 2005 1:03 AM Step-by-Step Examples 16-29 - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 304
hp40g+.book Page 30 Friday, December 9, 2005 1:03 AM - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 305
Introduction The HP 40gs has approximately 200K of user memory. The calculator uses this memory to store variables, perform computations, and store history. A variable is an object that you create in memory to hold data. The HP 40gs has two types of variables, home variables and aplet variables - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 306
hp40g+.book Page 2 Friday, December 9, 2005 1:03 AM Storing and recalling in the HOME view display history, for example the results of a previous calculation, you need to copy it to the command line, then store it. 1. Perform the calculation for the result you want to store. 3 8 6 3 2. Press - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 307
hp40g+.book Page 3 Friday, December 9, 2005 1:03 AM 5. Enter a name for the variable. A 6. Press to store the result. 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 - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 308
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 column. You select a variable category and then select a variable in the category. 1. Open the VARS menu. 2. Use the arrow keys or press the alpha key - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 309
hp40g+.book Page 5 Friday, December 9, 2005 1:03 AM 5. Choose whether to place the variable . Example Note: The VARS menu can also be used to enter the names or values of variables into programs. This example demonstrates how to use the VARS menu to add the contents of two list variables, and - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 310
hp40g+.book Page 6 Friday, December 9, 2005 1:03 AM 4. Enter data for L2. 55 48 86 90 77 5. Press to access HOME. 6. Open the variable menu and - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 311
hp40g+.book Page 7 Friday, December 9, 2005 1:03 AM Home variables It is graphic objects via programming commands. See "To store into a graphics variable" on page 20-5 for more information on storing graphic object via the sketch view. Library Aplet library variables can store aplets that - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 312
for the Plot and Numeric views, and the results of some calculations such as roots and intersections. See the Reference Information chapter for more information about aplet variables. Category Function Parametric Polar Sequence Solve Statistics Available names F0 to F9 (Symbolic view). See - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 313
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. You can make deletions - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 314
hp40g+.book Page 10 Friday, December 9, 2005 1:03 AM - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 315
hp40g+.book Page 1 Friday, December 9, 2005 1:03 AM 18 Matrices Introduction Vectors Matrices Matrix Variables You can perform matrix calculations in HOME and in programs. The matrix and each row of a matrix appear in brackets, and the elements and rows are separated by commas. For example, the - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 316
hp40g+.book Page 2 Friday, December 9, 2005 1:03 AM Creating and storing matrices empty matrix with the highlighted name. Transmits the highlighted matrix to another HP 40gs or a disk drive. See. Receives a matrix from another HP 40gs or a disk drive. See . Clears the highlighted matrix. Clears all - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 317
hp40g+.book Page 3 Friday, December 9, 2005 1:03 AM 2. Highlight the matrix variable name you want to use and press . 3. Select the type of matrix to create. - - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 318
hp40g+.book Page 4 Friday, December 9, 2005 1:03 AM To transmit a matrix You can send matrices between calculators just as you can send aplets, programs, lists, and notes. 1. Connect the calculators using an appropriate cable. 2. Open the Matrix catalogs on both calculators. 3. Highlight the - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 319
hp40g+.book Page 5 Friday, December 9, 2005 1:03 AM Key Meaning (Continued) Moves to the first row, last row, first column, or last column respectively. To display a - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 320
hp40g+.book Page 6 Friday, December 9, 2005 1:03 AM To store one element In HOME, enter, value matrixname(row, column). For example, to change the element in - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 321
hp40g+.book Page 7 Friday, December 9, 2005 1:03 AM To multiply and divide by a scalar M1 M2 For division by a scalar, enter the matrix first, then the - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 322
hp40g+.book Page 8 Friday, December 9, 2005 1:03 AM To divide by a square matrix For 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 leftmultiplication by the inverse of the divisor. M1/M2 is equivalent to M2-1 * M1. - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 323
hp40g+.book Page 9 Friday, December 9, 2005 1:03 AM 3. Return to the Matrix 1 2 In this example, the matrix you created is listed as M2. 6. Return to HOME and enter the calculation to left-multiply the constants vector by the inverse of the coefficients matrix. M2 x -1 M1 The result is - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 324
About functions About commands • Functions can be used in any aplet or in HOME. They are listed in the MATH menu under the Matrix category. They can be used in mathematical expressions-primarily in HOME-as well as in programs. • Functions always produce and display a result. They do not change - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 325
hp40g+.book Page 11 Friday, December 9, 2005 1:03 AM COND CROSS DET DOT EIGENVAL EIGENVV IDENMAT INVERSE LQ LSQ Matrices Condition Number. Finds the 1-norm (column - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 326
hp40g+.book Page 12 Friday, December 9, 2005 1:03 AM LU MAKEMAT QR RANK Creates a matrix of dimension rows × columns, using expression to calculate each element. If expression contains the variables I and J, then the calculation for each element substitutes the current row number for I and the - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 327
hp40g+.book Page 13 Friday, December 9, 2005 1:03 AM SPECNORM SPECRAD SVD SVL TRACE TRN Examples Identity Matrix Transposing a Matrix Matrices Spectral Norm of matrix. SPECNORM ( - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 328
hp40g+.book Page 14 Friday, December 9, 2005 1:03 AM Reduced-Row Echelon Form column 2) is swapped with element 2,1; element 2,3 is swapped with element 3,2; and so on. - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 329
hp40g+.book Page 15 Friday, December 9, 2005 1:03 AM The final row of zeros in the reduced-row echelon form of the augmented matrix indicates an inconsistent system with infinite solutions. Matrices 18-15 - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 330
hp40g+.book Page 16 Friday, December 9, 2005 1:03 AM - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 331
programs. A list consists of comma-separated real or complex numbers, expressions, or matrices, all enclosed in braces. A list may, for example, contain a sequence them in calculations or expressions in HOME or in a program. Retrieve the C1.C0 in the Statistics aplet. You can store a statistics - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 332
list for editing. Transmits the highlighted list to another HP 40gs or a PC. See "Sending and receiving aplets" on page 22-4 for further information. Receives a list from another HP 40gs or a PC. See "Sending and receiving aplets" on page 22-4 for further information. Clears the highlighted - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 333
hp40g+.book Page 3 Friday, December 9, 2005 1:03 AM List edit keys When you press to create or change a list, the following keys are available to you: - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 334
hp40g+.book Page 4 Friday, December 9, 2005 1:03 AM Displaying and editing lists To display a list To display one element To edit a list • In the List catalog, - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 335
hp40g+.book Page 5 Friday, December 9, 2005 1:03 AM To insert an element in a list 1. Open the List catalog. LIST. 2. Press or to highlight the name of - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 336
, press CLEAR. Transmitting lists You can send lists to calculators or PCs just as you can aplets, programs, matrices, and notes. 1. Connect the calculators using an appropriate cable). 2. Open the List catalogs on both calculators. 3. Highlight the list to send. 4. Press and choose the - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 337
hp40g+.book Page 7 Friday, December 9, 2005 1:03 AM CONCAT ΔLIST Lists variable name then the lists must have the same length, since the calculation pairs the elements. If there are two arguments and one is a real number, then the calculation pairs the number with each element of the list. Example - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 338
hp40g+.book Page 8 Friday, December 9, 2005 1:03 AM MAKELIST ΠLIST POS REVERSE Calculates a sequence of elements for a new list. a series of squares from 23 to 27. L Select MAKELIST A A 23 27 1 Calculates the product of all elements in list. ΠLIST(list) Example ΠLIST({2,3,4}) returns 24. Returns - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 339
hp40g+.book Page 9 Friday, December 9, 2005 1:03 AM SIZE ΣLIST SORT Calculates the number of elements in a list. SIZE(list) Also works with matrices. Calculates elements in a list, use the Statistics aplet. Example In this example, use the Statistics aplet to find the mean, median, maximum, and - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 340
the Statistics aplet, and select 1-variable mode (press , if necessary, to display ). Select Statistics Note: Your list values are now in column 1 (C1). 4. In the Symbolic view, define H1 (for example) as C1 (sample) and 1 (frequency). 5. Go to the Numeric view to display calculated statistics - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 341
Introduction The HP 40gs has text and picture editors for entering notes and sketches. • Each aplet has its own independent Note view and Sketch view. Notes and sketches that you create in these views are associated with the aplet. When you save the aplet, or send it to another calculator, the - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 342
. Lower-case alpha-lock for letter entry. Backspaces cursor and deletes character. Deletes current character. Starts a new line. Erases the entire note. Menu for entering variable names, and contents of variables. Menu for entering math operations, and constants. Menu for entering program commands - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 343
in its Sketch view ( SKETCH). Your work is automatically saved with the aplet. Press any other view key or to exit the Sketch view Sketch keys Key CLEAR Meaning Stores the specified portion of the current sketch to a graphics variable (G1 through G0). Adds a new, blank page to the current - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 344
hp40g+.book Page 4 Friday, December 9, 2005 1:03 AM To draw a box To draw a circle DRAW keys 1. In Sketch view, press and move the cursor to where - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 345
hp40g+.book Page 5 Friday, December 9, 2005 1:03 AM To label parts of a sketch 1. Press and type the text on the edit line. To lock the Alpha shift to exit the Sketch view. To create a set of sketches To store into a graphics variable You can create a set of up to ten sketches. This allows for - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 346
hp40g+.book Page 6 Friday, December 9, 2005 1:03 AM To import a graphics variable You can copy the contents of a graphics variable into the Sketch view of an aplet. 1. Open the Sketch view of the aplet ( The graphic will be copied here. 2. Press , . SKETCH). 3. Highlight Graphic, then press - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 347
you are finished, press or an aplet key to exit Notepad. Your work is automatically saved. Notepad Catalog keys Key CLEAR Meaning Opens the selected note for editing. Begins a new note, and asks for a name. Transmits the selected note to another HP 40gs or PC. Receives a note being transmitted - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 348
hp40g+.book Page 8 Friday, December 9, 2005 1:03 AM To import a note You can import a note from the Notepad into an aplet's Note view, and vice versa. Suppose you want to copy a note named "Assignments" from the Notepad into the Function Note view: 1. In the Function aplet, display the Note view - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 349
, including examples and special tools, can be found at HP's calculators web site: http://www.hp.com/calculators The Contents of a Program Structured Programming An HP 40gs program contains a sequence of numbers, mathematical expressions, and commands that execute automatically to perform a task - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 350
in an input form. (If you press from HOME without entering any data, the HP 40gs runs the contents of Editline.) Before starting to work with programs, you should take a few minutes to become familiar with the Program catalog menu keys. You can use any of the following keys (both menu and keyboard - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 351
hp40g+.book Page 3 Friday, December 9, 2005 1:03 AM Program catalog keys The program catalog keys are: Key or CLEAR Meaning 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 - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 352
commands Until you become familiar with the HP 40gs commands, the easiest way to enter commands is to select them from the Commands menu from the Program editor. You can also type in commands using alpha characters. 1. From the Program editor, press the Program Commands menu. CMDS to open CMDS - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 353
3. Press to paste the command into the program editor. Edit a program 1. Press PROGRM to open the Program catalog. 2. Use the arrow keys to highlight the program you want to edit, and press . The HP 40gs opens the Program Editor. The name of your program appears in the title bar of the display - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 354
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. Alpha-lock for letter entry. Press A...Z to lock lower case. Backspaces cursor and deletes - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 355
Ans (Home variable containing the last result), when the program has finished. If you start the program from the Program catalog, the HP 40gs returns you to the Program catalog when the program ends. If you run a program that contains errors, the program will stop and you will see an error message - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 356
calculator and on the receiving calculator. You can also send programs to, and receive programs from, a remote storage device (aplet disk drive or computer). This takes place via a cable connection and requires an aplet disk drive or specialized software running on a PC (such as a connectivity kit - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 357
or angle measures. 3. Develop the programs to work with your customized aplet. When you develop the aplet's programs, use the standard aplet naming convention. This allows you to keep track of the programs in the Program catalog that belong to each aplet. See "Aplet naming convention" on page 21-10 - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 358
Test the customized aplet and debug the associated programs. (Refer to "Debug a program" on page 16-7). Aplet naming convention To assist users in keeping track of aplets and associated programs, use the following naming convention when setting up an aplet's programs: • Start all program names with - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 359
hp40g+.book Page 11 Friday, December 9, 2005 1:03 AM Save the aplet 1. Open the Function aplet and save it as "EXPERIMENT". The new aplet appears in the Aplet library. Select Function EXPERIMENT 2. Create a program called EXP.ME1 with contents as shown. This program configures the plot ranges, - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 360
set the View menu (this program) is transferred with the aplet. The space character between the first set of quotes in the trio specifies that no menu option appears for the entry. You do not need to transfer this program with the aplet, but it allows users to modify the aplet's menu if they want to - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 361
that the name of the new aplet is highlighted in the Aplet view. 9. You can now return to the Aplet library and press to run your new aplet. Programming commands This section describes the commands for programming with HP 40gs. You can enter these commands in your program by typing them or by - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 362
that are called from the VIEWS menu are transferred when the aplet is transferred, for example to another calculator or to a PC. • As part of the VIEWS menu configuration, you can specify programs that you want transferred with the aplet, but are not called as menu options. For example, these can - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 363
, or you want to transfer a sub-program that other menu programs use. Auto-run programs If the Prompt item is "Start", then the ProgramName program runs whenever you start the aplet. This is useful for setting up a program to configure the aplet. Users can select the Start item from the VIEWS menu - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 364
hp40g+.book Page 16 Friday, December 9, 2005 1:03 AM 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 SETVIEWS command are transferred when the aplet is transmitted. ViewNumber ViewNumber is - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 365
Sketch view 10 Aplet Catalog 11 List Catalog 12 Matrix Catalog 13 Notepad Catalog 14 Program Catalog 15 Plot- programming commands, the branch commands work in logical groups. Therefore, the commands are described together rather than each independently. IF...THEN...END Executes a sequence - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 366
the CASE structure continues until a true-clause is executed (or until all the test-clauses evaluate to false). Many conditions are automatically recognized by the HP 40gs as error conditions and are automatically treated as errors in programs. Programming - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 367
Stops the current program. STOP : Drawing commands The drawing commands act on the display. The scale of the display depends on the current aplet's Xmin, Xmax, Ymin, and Ymax values. The following examples assume the HP 40gs default settings with the Function aplet as the current aplet. ARC Draws - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 368
hp40g+.book Page 20 Friday, December 9, 2005 1:03 AM BOX ERASE BOX -1;-1;1;1: FREEZE: Draws a box, lower corner at (-1,-1), upper corner at (1,1) Clears the display ERASE: Halts the program, freezing the current display. Execution resumes when any key is pressed. Draws a line from (x1, y1) to ( - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 369
current aplet's scale, which is specified by Xmin, Xmax, Ymin, and Ymax. The upper left corner of the target graphic ( graphic from expression, using font_size, and stores the resulting graphic in graphicname. Font sizes are 1, 2, or 3. If the fontsize argument is 0, the HP 40gs creates a graphic - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 370
hp40g+.book Page 22 Friday, December 9, 2005 1:03 AM GROBXOR MAKEGROB PLOT→ → Page: FREEZE: This program stores the current PLOT view to the first page in the sketch view of the current aplet and then displays the sketch as a graphic object until any key is pressed. Puts graph from graphicname into - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 371
hp40g+.book Page 23 Friday, December 9, 2005 1:03 AM Loop commands Loop hp allow a program to execute a routine repeatedly. The HP 40gs has three loop structures. The example programs that repeatedly evaluates test-clause and executes loop-clause sequence if the test is true. Because the test-clause - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 372
hp40g+.book Page 24 Friday, December 9, 2005 1:03 AM Matrix commands The matrix commands EDITMAT Starts the Matrix Editor and displays the specified matrix. If used in programming, returns to the program when user presses . EDITMAT name: RANDMAT Creates random matrix with a specified number of - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 373
hp40g Replace also works with lists and graphics. REPLACE name;start;object: Multiplies -object-a portion of a list, matrix, or graphic from object-and stores it into name. start or an ordered pair, (X,Y), for graphics. SUB name;object;start;end: Swaps an HP infrared printer, for example the HP 82240B - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 374
the contents of a program or a note. PRVAR programname;PROG: PRVAR notename;NOTE: Prompt commands BEEP CHOOSE CLRVAR Beeps at the frequency and for the time you specify. BEEP frequency;seconds: Creates a choose box, which is a box containing a list of options from which the user chooses one. Each - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 375
hp40g+.book Page 27 Friday, December 9, 2005 1:03 AM DISP DISPXY DISPTIME Programming Example If you have stored {1,2,3,4} in variable L1, entering CLVAR L1 will clear L1. Displays textitem in a row of the display at the line_number. A text - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 376
to opening the matrix editor with matrixname. It can be used in a program to enter a matrix. This command prevents the display from being updated after the program runs. This allows you to view the graphics created by the program. Cancel FREEZE by pressing any key. FREEZE: Waits for a key, then - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 377
hp40g+.book Page 29 Friday, December 9, 2005 1:03 AM MSGBOX PROMPT WAIT Example INPUT R; can be a variable such as A...Z, θ, L1...L9, C1...C9 or Z1...Z9.. PROMPT name: Halts program execution for the specified number of seconds. WAIT seconds: Stat-One and Stat-Two commands The following commands - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 378
hp40g+.book Page 30 Friday, December 9, 2005 1:03 AM Stat-One commands DO1VSTATS SETFREQ Calculates STATS using datasetname and stores the results in the corresponding variables: NΣ, TotΣ, MeanΣ, PVarΣ, SVarΣ, S2,..., or S5 and column can be C0-C9. SETINDEP datasetname;column: 21-30 Programming - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 379
hp40g+.book Page 31 Friday, December 9, 2005 1:03 AM Storing and retrieving variables in programs The HP 40gs has both Home variables and Aplet variables. Home variables are used for real numbers, complex numbers, graphics, lists, and matrices. Home variables keep the same values in HOME and in - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 380
Function Parametric Polar Sequence Solve Statistics Extremum Function FastRes Function Solve Grid All Aplets Hmin/Hmax Statistics Turns the coordinate-display mode in Plot view on or off. From Plot view, use the Menu mean key to toggle coordinate display on an off. In a program, type 1 X Coord-to - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 381
hp40g+.book Page 33 Friday, December 9, 2005 1:03 AM Hwidth Statistics Indep All Aplets InvCross All Aplets Isect Function Labels All Aplets 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 Defines the value of the independent - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 382
AM Nmin / Nmax Sequence Recenter All Aplets Root Function S1mark-S5mark Statistics SeqPlot Sequence 21-34 Defines the minimum and maximum 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 n1 XNmin n2 - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 383
hp40g+.book Page 35 Friday, December 9, 2005 1:03 AM Simult Function Parametric Polar Sequence Slope Function StatPlot Statistics Umin/Umax Polar Ustep Polar Programming Enables you to choose between simultaneous and sequential graphing of all selected expressions. From Plot Setup, check (or - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 384
1:03 AM Tmin / Tmax Parametric Tracing All Aplets Tstep Parametric Xcross All Aplets Ycross All Aplets Sets the minimum and maximum independent variable values. Appears as the TRNG field in the Plot Setup input form. From Plot Setup, enter values for TRNG. or In a program, type n1 X Tmin n2 X Tmax - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 385
hp40g+.book Page 37 Friday, December 9, 2005 1:03 AM Xtick AAll Aplets Ytick All Aplets Xmin / Xmax All Aplets Ymin / Ymax All Aplets Sets the distance between tick marks for the horizontal axis. From the Plot Setup input form, enter a value for Xtick. or In a program, type n X Xtick where n > 0 - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 386
hp40g+.book Page 38 Friday, December 9, 2005 1:03 AM Xzoom All Aplets Yzoom 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 where n > 0 The default value is 4. Sets the vertical zoom factor. From Plot-ZOOM-Set - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 387
hp40g+.book Page 39 Friday, December 9, 2005 1:03 AM X1, Y1...X9,Y9 X0,Y0 Parametric R1...R9, R0 Polar U1...U9, U0 Sequence E1...E9, E0 Solve S1fit...S5fit Statistics Programming fit in the field for S1FIT, S2FIT, etc. or In a program, store one of the following constant numbers or names into a - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 388
hp40g+.book Page 40 Friday, December 9, 2005 1:03 AM Example Cubic X S2fit or 6 X S2fit Numeric-view variables The following aplet variables control the Numeric view. The value of the variable applies to the current aplet program, type LIST XCn where n = 0, 1, 2, 3 ... 9 Digits All Aplets Number - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 389
hp40g+.book Page 41 Friday, December 9, 2005 1:03 AM NumCol All Aplets except Statistics aplet NumFont Function Parametric Polar Sequence Statistics NumIndep Function Parametric Polar Sequence NumRow All Aplets except Statistics aplet Programming 1 Standard 2 Fixed 3 Sci 4 Eng 5 Fraction 6 - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 390
factor in the Numeric view. From Num Setup, type in a value for NUMZOOM. or In a program, type n X NumZoom where n > 0 Enables you to choose between 1-variable and 2-variable statistics in the Statistics aplet. Does not appear in the Plot Setup input form. Corresponds to the and menu keys in - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 391
in Sketch view. Page All Aplets Sets a page in a sketch set. The graphics can be viewed one at a time using the and keys. The Page variable refers to the currently displayed page of a sketch set. In a program, type graphicname X Page PageNum All Aplets Sets a number for referring to - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 392
hp40g+.book Page 44 Friday, December 9, 2005 1:03 AM - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 393
classes of mathematical operations. You can extend the capability of the HP 40gs in the following ways: • Create new aplets, based on existing aplets, with specific configurations such as angle measure, graphical or tabular settings, and annotations. • Transmit aplets between HP 40gs calculators via - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 394
the four formulas: θ O H θ A H θ O A C A B 3. Decide whether you want the aplet to operate in Degrees, Radians, or Grads. MODES Degrees 4. View the Aplet Library. The "TRIANGLES" aplet is listed in the Aplet Library. The Solve aplet can now be reset and used for other problems. 22-2 Extending - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 395
hp40g+.book Page 3 Friday, December 9, 2005 1:03 AM Using a customized aplet To use the "Triangles" aplet, simply select the an angle of 35o with the horizontal and extends 5 metres up the wall. 1. Select the aplet. TRIANGLES 2. Choose the sine formula in E1. 3. Change to the Numeric view and enter - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 396
certain mathematical concepts. Note that you need the Graphing Calculator Connectivity Kit in order to load aplets from a PC. Hewlett-Packard's Calculators web site can be found at: http://www.hp.com/calculators Sending and receiving aplets A convenient way to distribute or share problems in - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 397
you are using the hp40gs connectivity kit to transfer the aplet. Highlight your selection and press . - If transmitting to a disk drive, you have the options of sending to the current (default) directory or to another directory. 3. Receiving calculator: Open the aplet library and press . - The - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 398
hp40g+.book Page 6 Friday, December 9, 2005 1:03 AM If you are using the PC Connectivity Kit to download aplets from a PC, you will see a list of aplets in the PC's current directory. Check as many items as you would like to receive. Sorting items in the aplet library menu list Once you have - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 399
topic. The built-in aplet types are Function, Parametric, Polar, Sequence, Solve, Statistics, Inference, Finance, Trig Explorer, Quad Explorer, Linear Explorer and Triangle Solve. An aplet can be filled with the data and solutions for a specific problem. It is reusable (like a program, but easier to - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 400
hp40g+.book Page 2 Friday, December 9, 2005 1:03 AM list matrix menu menu keys note program sketch aplet. A reusable set of instructions that you record using the Program editor. A drawing that you make in the Sketch view for a specific aplet. The name of a number, list, matrix, note, or graphic - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 401
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 certain conditions, and clears temporary memory locations. However, it does not clear stored data (variables, aplet databases, programs) unless - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 402
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. 1. Press and - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 403
hp40g+.book Page 5 Friday, December 9, 2005 1:03 AM To install the main batteries a. Slide up the battery compartment cover as illustrated. b. Insert 4 new AAA (LR03) batteries - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 404
hp40g+.book Page 6 Friday, December 9, 2005 1:03 AM Variables Home variables The home variables are: Category Complex Graphic Library List Matrix Modes Notepad Program Real Available name Z1...Z9, Z0 G1...G9, G0 Function Parametric Polar Sequence Solve Statistics User-named L1...L9, L0 M1...M9, - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 405
hp40g+.book Page 7 Friday, December 9, 2005 1:03 AM Function aplet variables The function aplet variables are: Category Plot Plot-FCN Symbolic Numeric Note Sketch Available name Axes Connect Coord FastRes Grid Indep InvCross Labels Recenter Simult Tracing Area Extremum Isect Angle F1 F2 F3 F4 F5 - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 406
hp40g+.book Page 8 Friday, December 9, 2005 1:03 AM Parametric aplet variables The parametric aplet variables are: Category Plot Symbolic Numeric Note Sketch Available name Axes Connect Coord Grid Indep InvCross Labels Recenter Simult Tmin Tmax Angle X1 Y1 X2 Y2 X3 Y3 X4 Y4 X5 Digits Format - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 407
hp40g+.book Page 9 Friday, December 9, 2005 1:03 AM Polar aplet variables The polar aplet variables are: Category Plot Symbolic Numeric Note Sketch Available names Axes Connect Coord Grid Indep InvCross Labels Recenter Simult Umin Umax θstep Tracing Xcross Ycross Xtick Ytick Xmin Xmax Ymin Ymax - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 408
hp40g+.book Page 10 Friday, December 9, 2005 1:03 AM Sequence aplet variables The sequence aplet variables are: Category Plot Symbolic Numeric Note Sketch Available name Axes Coord Grid Indep InvCross Labels Nmin Nmax Recenter SeqPlot Simult Angle U1 U2 U3 - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 409
hp40g+.book Page 11 Friday, December 9, 2005 1:03 AM Solve aplet variables The solve aplet variables are: Category Plot Symbolic Numeric Note Sketch Available name Axes Connect Coord FastRes Grid Indep InvCross Labels Recenter Tracing Angle E1 E2 E3 E4 E5 Digits Format NoteText Page Xcross - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 410
hp40g+.book Page 12 Friday, December 9, 2005 1:03 AM Statistics aplet variables The statistics aplet variables are: Category Plot Symbolic Numeric Stat-One Stat-Two Note Sketch Available name Axes Connect Coord Grid Hmin Hmax Hwidth Indep InvCross Labels Recenter S1mark S2mark S3mark Angle S1fit - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 411
hp40g+.book Page 13 Friday, December 9, 2005 1:03 AM MATH menu categories Math functions The math functions are: Category Calculus Complex Constant Available name ∂ ∫ TAYLOR ARG - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 412
hp40g+.book Page 14 Friday, December 9, 2005 1:03 AM Category Matrix Polynom. Prob. Real Stat-Two Symbolic Available name (Continued) COLNORM COND CROSS DET DOT EIGENVAL - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 413
hp40g+.book Page 15 Friday, December 9, 2005 1:03 AM Category Tests Trig Available name (Continued) < AND ≤ IFTE NOT = = OR ≠ XOR > ≥ ACOT COT ACSC CSC ASEC SEC Program constants The program constants are: Category Angle Format SeqPlot S1...5fit StatMode StatPlot Available name - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 414
hp40g+.book Page 16 Friday, December 9, 2005 1:03 AM Physical Constants The physical constants are: Category Chemist Phyics Quantum Available Name • Avogadro (Avagadro's Number, NA) • Boltz. ( - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 415
hp40g+.book Page 17 Friday, December 9, 2005 1:03 AM CAS functions CAS functions are: Category Algebra Complex Constant Diff & Int Hyperb. Integer Modular Function COLLECT DEF EXPAND FACTOR PARTFRAC QUOTE i ABS ARG CONJ DROITE e i DERIV DERVX DIVPC - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 416
hp40g+.book Page 18 Friday, December 9, 2005 1:03 AM Category Polynom. Real Rewrite Solve Tests Trig Function (Continued) EGCD FACTOR GCD HERMITE LCM LEGENDRE PARTFRAC PROPFRAC - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 417
hp40g+.book Page 19 Friday, December 9, 2005 1:03 AM Program commands The program commands are: Category Aplet Branch Drawing Graphic Loop Matrix Command CHECK SELECT SETVIEWS UNCHECK IF THEN ELSE END ARC BOX ERASE FREEZE DISPLAY→ →DISPLAY →GROB GROBNOT GROBOR GROBXOR FOR = TO STEP END - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 418
hp40g+.book Page 20 Friday, December 9, 2005 1:03 AM Category Stat-Two Status Delete one or more matrices, lists, notes, or programs (using catalogs), or custom (not builtin) aplets (using MEMORY). Not enough data points for the calculation. For two-variable statistics there must be two columns of - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 419
. The global variable named does not exist. The calculation has a mathematically undefined result (such as 0/0). You must recover a lot of memory to continue operation. Delete one or more matrices, lists, notes, or programs (using catalogs), or custom (not builtin) aplets (using MEMORY). R-21 - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 420
hp40g+.book Page 22 Friday, December 9, 2005 1:03 AM - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 421
hp40g+.book Page 1 Friday, December 9, 2005 1:03 AM Limited Warranty HP 40gs Graphing Calculator; Warranty period: 12 months 1. HP warrants to you, the end-user customer, that HP like-new. 2. HP warrants to you that HP software will not fail to execute its programming instructions after the date of - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 422
hp40g+.book Page 2 Friday, December 9, 2005 1:03 AM 6. HP MAKES NO OTHER EXPRESS WARRANTY OR CONDITION WHETHER you. 8. The only warranties for HP products and services are set forth in the express warranty statements accompanying such products and services . HP shall not be liable for technical or - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 423
hp40g+.book Page 3 Friday, December 9, 2005 1:03 AM Service Europe Country : Telephone numbers Austria +43-1-3602771203 Belgium +32-2-7126219 Denmark +45-8-2332844 Eastern Europe +420-5-41422523 countries Finland +35-89640009 France +33-1-49939006 Germany + - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 424
hp40g+.book Page 4 Friday, December 9, 2005 1:03 AM L.America Country: -0524 N.America Country : Telephone numbers U.S. 1800-HP INVENT Canada (905) 206-4663 or 800- HP INVENT ROTC = Rest of the country Please logon to http://www.hp.com for the latest service and support information.h W-4 - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 425
hp40g+.book Page 5 Friday , if not installed and used in accordance with the instructions, may cause harmful interference to radio communications. However, there by Hewlett-Packard Company may void the user's authority to operate the equipment. Cables Connections to this device must be made with - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 426
hp40g+.book Page 6 Friday, December 9, 2005 1:03 AM Hewlett-Packard Company P. O. Box 692000, Mail Stop 530113 Houston, Texas 77269-2000 Or, call 1-800-474-6836 For - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 427
hp40g+.book Page 7 Friday, December 9, 2005 1:03 AM Japanese Notice VCCI B Korean Notice Disposal of Waste Equipment by Users in Private Household in the European Union This your local city office, your household waste disposal service or the shop where you purchased the product. W-7 - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 428
hp40g+.book Page 8 Friday, December 9, 2005 1:03 AM - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 429
13-20 arc sine 13-4 arc tangent 13-5 area graphical 3-10 interactive 3-10 variable 21-31 ARG 13-7 arguments with matrices 18-10 ASIN2C 14-39 ASIN2T 14-39 ASSUME 14-61 ATAN2S 14-39 attaching a note to an aplet 20-1 a sketch to an aplet 20-3 auto scale 2-14 axes plotting 2-7 variable 21 - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 430
-5 connectivity kit 22-4 constant? error message 7-7 constants e 13-8 i 13-8 maximum real number 13-8 minimum real number 13-8 physical 1-8, 13-25, R-16 program R-15, R-16 contrast decreasing display 1-2 increasing display 1-2 conversions 13-8 coordinate display 2-9 copying display 1-22 graphics 20 - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 431
hp40g+.book Page 3 Friday, December 9, 2005 1:03 AM 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) displayed 11-4 cross product vector 18-11 curve - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 432
1-11 full-precision display 1-10 function analyze graph with FCN tools 3-4 definition 2-2, R-1 entering 1-19 gamma 13-13 intersection point 3-5 math menu R-13, R-17 slope 3-5 syntax 13-2 tracing 2-8 Function aplet 2-20, 3-1 function variables area 21-31 axes 21-31 connect 21-31 fastres 21-32 grid 21 - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 433
graph analyzing statistical data in 10-19 auto scale 2-14 box-and-whisker 10-16 capture current display 21-21 cobweb 6-1 comparing 2-5 connected points 10-17 defining the independent variable 21-36 drawing axes 2-7 expressions 3-3 grid points 2-7 histogram 10-15 in Solve aplet graphics calculating in - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 434
hp40g+.book Page 6 Friday, December 9, 2005 1:03 AM using symbolic variables -30 linear fit 10-13 Linear Solver aplet 8-1 linear systems 14-35 linearize 14-30, 14-43 LINSOLVE 14-35 list arithmetic with 19-7 calculate sequence of elements 19-8 calculating product of 19-8 composed from differences 19 - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 435
hp40g+.book Page 7 Friday, December 9, 2005 1:03 AM finding statistical values in -4 extracting a portion 21-25 finding the trace of a square matrix 18-13 inverting 18-8 matrix calculations 18-1 multiplying and dividing by scalar 18-7 multiplying by vector 18-7 multiplying row by value and adding - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 436
hp40g+. real number 13-8 mixed fraction format 1-11 modes angle measure 1-10 CAS 14-5 decimal mark 1-11 number format 1-10 MODSTO 14-53 modular arithmetic 14-28 implied 1-20 MULTMOD 14-54 N name conflict R-21 naming programs 21-4 natural exponential 13-4, 13-10 natural log plus 1 13- Solve aplet 7-5 - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 437
hp40g+.book Page 9 π 13-8 PA2B2 14-67 paired columns 10-11 parametric variables axes 21-31 connect 21-31 grid 21-32 in menu map R-8 indep 21-33 labels 21-34 aplet 7-7 integer scaling 2-14 one-variable statistics 10-18 overlay plot 2-13 overlaying 2-15, 4-3 scaling 2-13 scatter 10-15, 10-17 sequence - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 438
hp40g+.book Page 10 Friday, December 9, 2005 1:03 AM labels 21-34 recenter 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 halt program execution 21-29 insert line breaks 21-29 prevent screen display being updated 21- - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 439
menu lists 1-9 speed searches 1-9 secant 13-20 Sending 22-5 sending aplets 22-4 lists 19-6 programs 21-8 sequence definition 2-2 sequence variables Axes 21-31 Grid 21-32 in menu map R-10 Indep 21-33 Labels 21-34 Recenter 21-34 Ycross 21-37 serial port connectivity 22-5 SERIES 14-24 setting I-11 - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 440
22-6 I-12 aplets in chronological order 22-6 elements in a list 19-9 spectral norm 18-13 spectral radius 18-13 square root 13-5 stack history printing 21-25 stairsteps graph 6-1 standard number format 1-10 statistics analysis 10-1 analyzing plots 10-19 angle mode 10-12 calculate one-variable 21 - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 441
14-55 subtract 13-4 summation function 13-11 symbolic calculations in Function aplet 13-21 defining expressions 2-1 differentiation 13-21 displaying 14-42 transmitting lists 19-6 matrices 18-4 programs 21-8 transposing a matrix 18-13 Triangle Solver aplet 9-1 TRIG 14-43 TRIGCOS 14-44 trigonometric - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 442
13-13 upper-tail Snedecor's F 13-13 upper-tail student's t-probability 13-14 USB connectivity 22-5 user defined regression fit 10-13 V value recall 17-3 storing 17-2 variables aplet 17-1 I-14 CAS 14-4 categories 17-7 clearing 17-3 definition 17-1, 17-7, R-2 in equations 7-10 in Symbolic view - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 443
hp40g+.book Page 15 Friday, December 9, 2005 1:03 AM in 2-9 options 2-9, 3-8 options within a table 2-18 out 2-9 redrawing table of numbers options 2-18 square 2-10 un-zoom 2-11 within Numeric view 2-18 X-zoom 2-9 Y-zoom 2-10 I-15 - HP 40gs | hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 444
hp40g+.book Page 16 Friday, December 9, 2005 1:03 AM
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HP
40gs graphing calculator
user's guide
Edition1
Part Number
F2225AA-90001
hp40g+.book
Page i
Friday, December 9, 2005
1:03 AM