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HP 40gs User Manual

Graphing calculator
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hp40g+.book Page i Friday, December 9, 2005 1:03 AM
HP 40gs graphing calculator
user's guide
Edition1
Part Number F2225AA-90001

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Summary of Contents for HP 40gs

  • Page 1 Page i Friday, December 9, 2005 1:03 AM HP 40gs graphing calculator user's guide Edition1 Part Number F2225AA-90001...
  • Page 2 Page ii Friday, February 17, 2006 9:48 AM Notice REGISTER YOUR PRODUCT AT: www.register.hp.com THIS MANUAL AND ANY EXAMPLES CONTAINED HEREIN ARE PROVIDED "AS IS" AND ARE SUBJECT TO CHANGE WITHOUT NOTICE. HEWLETT-PACKARD COMPANY MAKES NO WAR- RANTY OF ANY KIND WITH REGARD TO THIS MANUAL,...

  • Page 3: Table Of Contents

    hp40g+.book Page iii Friday, December 9, 2005 1:03 AM Contents Preface Manual conventions ... P-1 Notice ... P-2 1 Getting started On/off, cancel operations...1-1 The display ...1-2 The keyboard ...1-3 Menus ...1-8 Input forms ...1-9 Mode settings ...1-10 Setting a mode...1-11 Aplets (E-lessons)...1-12 Aplet library ...1-16 Aplet views...1-16...
  • Page 4 hp40g+.book Page iv Friday, December 9, 2005 1:03 AM Function aplet interactive analysis... 3-9 Plotting a piecewise-defined function ... 3-12 4 Parametric aplet About the Parametric aplet ... 4-1 Getting started with the Parametric aplet... 4-1 5 Polar aplet Getting started with the Polar aplet ... 5-1 6 Sequence aplet About the Sequence aplet...
  • 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 ...11-4 Hypothesis tests ...11-8 One-Sample Z-Test...11-8 Two-Sample Z-Test ...11-9 One-Proportion Z-Test...11-10 Two-Proportion Z-Test ...11-11 One-Sample T-Test ...11-12 Two-Sample T-Test ...11-14 Confidence intervals ...11-15...
  • 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 ...
  • Page 7 hp40g+.book Page vii Friday, December 9, 2005 1:03 AM Accessing CAS functions...15-12 Equation Writer variables ...15-16 Predefined CAS variables ...15-16 The keyboard in the Equation Writer ...15-17 16 Step-by-Step Examples Introduction ...16-1 17 Variables and memory management Introduction ...17-1 Storing and recalling variables ...17-2 The VARS menu ...17-4 Memory Manager ...17-9 18 Matrices...
  • Page 8 Sorting items in the aplet library menu list ... 22-6 Reference information Glossary... R-1 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 ...
  • 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...
  • Page 10 hp40g+.book Page x Friday, December 9, 2005 1:03 AM...

  • Page 11: Manual Conventions

    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 properties.

  • Page 12: Notice

    © 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 reserved. Reproduction, adaptation, or translation of those programs without prior written permission from Hewlett-Packard Company is also...

  • Page 13: Getting Started

    HOME HOME is the calculator’s home view and is common to all aplets. If you want to perform calculations, or you want to quit the current activity (such as an aplet, a program, or an editor), press available in the HOME.

  • Page 14: The Display

    “Press 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 ( lines of history: the most recent input and output. Older lines scroll off the top of the display but are retained in memory.

  • Page 15: The Keyboard

    Shift in effect for next keystroke. To cancel, press α Alpha in effect for next keystroke. To cancel, press ((•)) Low battery power. Busy. Data is being transferred. P 40gs Graphing Calculator Menu Keys Shift Key again. again. Cursor Keys Enter...
  • Page 16 Page 4 Friday, December 9, 2005 1:03 AM Menu 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 sometimes called “soft keys”.
  • Page 17 Entry/Edit keys The entry and edit keys are: Getting started Meaning Cancels the current operation if the CANCEL calculator is on by pressing Pressing , then calculator off. Accesses the function printed in blue above a key. Returns to the HOME view, for performing calculations.
  • Page 18 hp40g+.book Page 6 Friday, December 9, 2005 1:03 AM Shifted keystrokes There are two shift keys that you use to access the operations and characters printed above the keys: Meaning (Continued) Displays a menu of all available CHARS characters. To type one, use the arrow keys to highlight it, and press .
  • Page 19 Page 7 Friday, December 16, 2005 2:20 PM HELPWITH The HP 40gs built-in help is available in HOME only. It provides syntax help for built-in math functions. Access the HELPWITH command by pressing SYNTAX syntax help. Example Math keys HOME ( calculations.

  • Page 20: Menus

    H I N T When using the MATH menu, or any menu on the HP 40gs, pressing an alpha key takes you straight to the first menu option beginning with that alpha character. With this method, you do not need to press Just press the key that corresponds to the command’s...

  • Page 21: Input Forms

    hp40g+.book Page 9 Friday, December 9, 2005 1:03 AM To search a menu • • • • To cancel a menu Press current operation. Input forms An input form shows several fields of information for you to examine and specify. After highlighting the field to edit, you can enter or edit a number (or expression).

  • Page 22: Mode Settings

    hp40g+.book Page 10 Friday, December 9, 2005 1:03 AM Mode settings You use the Modes input form to set the modes for HOME. H I N T Although the numeric setting in Modes affects only HOME, the angle setting controls HOME and the current aplet.

  • Page 23: Setting A Mode

    hp40g+.book Page 11 Friday, December 9, 2005 1:03 AM Setting Decimal Mark Setting a mode This example demonstrates how to change the angle measure from the default mode, radians, to degrees for the current aplet. The procedure is the same for changing number format and decimal mark modes.

  • Page 24: Aplets (E-Lessons)

    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 configurations. See “Creating new aplets based on existing aplets”...
  • Page 25 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, together with accompanying documentation, often with student work sheets.
  • Page 26 Page 14 Friday, December 9, 2005 1:03 AM charge and transferred to the HP 40gs using the provided Connectivity Kit. Quad Explorer The Quad Explorer aplet is used to investigate the aplet behaviour of v change, both by manipulating the equation and seeing the change in the graph, and by manipulating the graph and seeing the change in the equation.
  • 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 values of a, b, c and d change, both by manipulating the equation and seeing the change in the graph, or by manipulating the graph and seeing the change in the equation.

  • Page 28: Aplet Library

    hp40g+.book Page 16 Friday, December 9, 2005 1:03 AM Aplet library Aplets are stored in the Aplet library. To open an aplet Press aplet and press From within an aplet, you can return to HOME any time by pressing Aplet views When you have configured an aplet to define the relation or data that you want to explore, you can display it in different views.

  • Page 29: Overlay Plot

    hp40g+.book Page 17 Friday, December 9, 2005 1:03 AM Numeric view Press In this view, the functions that you have defined are displayed in tabular format. See “About the numeric view” on page 2-16 for further information. Plot-Table view The VIEWS menu contains the Plot-Table view. Select Plot-Table Splits the screen into the plot and the data table.

  • Page 30: Aplet View Configuration

    Note view Press 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 for further information.

  • Page 31: Mathematical Calculations

    To save aplet You can save an aplet configuration that you have used, configuration and transfer the aplet to 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.
  • Page 32 hp40g+.book Page 20 Friday, December 9, 2005 1:03 AM Example Calculate Long results If the result is too long to fit on the display line, or if you want to see an expression in textbook format, press to highlight it and then press Negative Type numbers...
  • Page 33 The calculator inserts it automatically. Parentheses are also important in specifying the order of operation. Without parentheses, the HP 40gs calculates according to the order of algebraic precedence (the next topic). Following are some examples using parentheses.

  • Page 34: Clearing Numbers

    7. AND and NOT. 8. OR and XOR. 9. Left argument of | (where). 10.Equals, =. Largest and The smallest number the HP 40gs can represent is 1 × 10 smallest zero. The largest number is 9.99999999999 × 10 numbers (1E499).
  • Page 35 hp40g+.book Page 23 Friday, December 9, 2005 1:03 AM When you highlight a previous input or result (by pressing To copy a previous Highlight the line (press line number (or expression) is copied into the edit line. To reuse the last Press result HOME display into an expression.

  • Page 36: Storing A Value In A Variable

    hp40g+.book Page 24 Friday, December 9, 2005 1:03 AM H I N T When you retrieve a number from result to its full precision. When you retrieve a number from the HOME’s display history, you obtain exactly what was displayed. Pressing whereas pressing into the edit line.

  • Page 37: Using Fractions

    Clearing the It’s a good habit to clear the display history ( display history CLEAR saves calculator memory to clear the display history. Remember that all your previous inputs and results are saved until you clear them. Using fractions To work with fractions in HOME, you set the number...
  • Page 38 Setting fraction The fraction precision setting determines the precision in which the HP 40gs converts a decimal value to a fraction. precision The greater the precision value that is set, the closer the fraction is to the decimal value.

  • Page 39: Fraction Calculations

    hp40g+.book Page 27 Friday, December 9, 2005 1:03 AM • • • • Fraction When entering fractions: calculations • • For example, to perform the following calculation: 1. Set the Number format mode to Fraction or Getting started Precision set to 1: Precision set to 2: Precision set to 3: Precision set to 4...
  • Page 40 hp40g+.book Page 28 Friday, December 9, 2005 1:03 AM 2. Enter the calculation. 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 would have been expressed as 25+7/8.

  • Page 41: Complex Numbers

    Page 29 Friday, December 9, 2005 1:03 AM Complex numbers Complex results The HP 40gs can return a complex number as a result for some math functions. A complex number appears as an ordered pair (x, y), where x is the real part and y is the imaginary part.

  • Page 42: Catalogs And Editors

    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.

  • Page 43: Aplets And Their Views

    hp40g+.book Page 1 Friday, December 9, 2005 1:03 AM Aplets and their views Aplet views This section examines the options and functionality of the three main views for the Function, Polar, Parametric, and Sequence aplets: Symbolic, Plot, and Numeric views. About the Symbolic view The Symbolic view is the defining view for the Function, Parametric, Polar, and Sequence aplets.
  • Page 44 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 it automatically.

  • Page 45: Evaluating Expressions

    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 another function, then other functions in terms of their independent variable.
  • Page 46 hp40g+.book Page 4 Friday, December 9, 2005 1:03 AM In HOME You can also evaluate any expression in HOME by entering it into the edit line and pressing For example, define F4 as below. In HOME, type F4(9)and press substituting 9 in place of X into F4. SYMB view keys The following table details the menu keys that you use to work with the Symbolic view.

  • Page 47: About The Plot View

    hp40g+.book Page 5 Friday, December 9, 2005 1:03 AM About the Plot view After entering and selecting (check marking) the expression in the Symbolic view, press the appearance of the graph or the interval that is displayed, you can change the Plot view settings. You can plot up to ten expressions at the same time.
  • Page 48 hp40g+.book Page 6 Friday, December 9, 2005 1:03 AM Plot view The plot view settings are: settings Field XRNG, YRNG TRNG θRNG NRNG TSTEP θSTEP SEQPLOT XTICK YTICK Those items with space for a checkmark are settings you can turn on or off. Press page.

  • Page 49: Exploring The Graph

    hp40g+.book Page 7 Friday, December 9, 2005 1:03 AM Field CONNECT LABELS AXES GRID Reset plot To reset the default values for all plot settings, press settings value for a field, highlight the field, and press Exploring the graph Plot view gives you a selection of keys and menu keys to explore a graph further.
  • Page 50 hp40g+.book Page 8 Friday, December 9, 2005 1:03 AM Trace a graph You can trace along a function using the which moves the cursor along the graph. The display also shows the current coordinate position (x, y) of the cursor. Trace mode and the coordinate display are automatically set when a plot is drawn.
  • Page 51 hp40g+.book Page 9 Friday, December 9, 2005 1:03 AM To jump directly to To jump straight to a value rather than using the Trace a value function, use the a value. Press To turn trace on/off If the menu labels are not displayed, press •...
  • Page 52 hp40g+.book Page 10 Friday, December 9, 2005 1:03 AM Option Y-Zoom In Y-Zoom Out Square Factors... Auto Scale Decimal Integer Trig 2-10 Meaning (Continued) Divides vertical scale only, using Y-factor. Multiplies vertical scale only, using Y-factor. Changes the vertical scale to match the horizontal scale.
  • Page 53 hp40g+.book Page 11 Friday, December 9, 2005 1:03 AM Option Un-zoom ZOOM examples The following screens show the effects of zooming options on a plot of Plot of Zoom In: Un-zoom: Note: Press the bottom of the Zoom list. Zoom Out: Now un-zoom.
  • Page 54 hp40g+.book Page 12 Friday, December 9, 2005 1:03 AM Y-Zoom In: Now un-zoom. Y-Zoom Out: Y-Zoom Out Zoom Square: To box zoom The Box Zoom option lets you draw a box around the area you want to zoom in on by selecting the endpoints of one diagonal of the zoom rectangle.

  • Page 55: Other Views For Scaling And Splitting The Graph

    hp40g+.book Page 13 Friday, December 9, 2005 1:03 AM To set zoom factors 1. In the Plot view, press 2. Press 3. Select Set Factors... and press 4. Enter the zoom factors. There is one zoom factor for Other views for scaling and splitting the graph The preset viewing options menu ( options for drawing the plot using certain pre-defined configurations.
  • Page 56 hp40g+.book Page 14 Friday, December 9, 2005 1:03 AM Option Auto Scale Decimal Integer Trig Split the screen The Plot-Detail view can give you two simultaneous views of the plot. 1. Press The graph is plotted twice. You can now zoom in on the right side.
  • Page 57 hp40g+.book Page 15 Friday, December 9, 2005 1:03 AM 3. To un-split the screen, press The Plot-Table view gives you two simultaneous views of the plot. 1. Press 2. To move up and down the table, use the 3. To move between functions, use the 4.

  • Page 58: About The Numeric View

    hp40g+.book Page 16 Friday, December 9, 2005 1:03 AM About the numeric view After entering and selecting (check marking) the expression or expressions that you want to explore in the Symbolic view, press data values for the independent variable (X, T, θ, or N) and dependent variables.

  • Page 59: Exploring The Table Of Numbers

    hp40g+.book Page 17 Friday, December 9, 2005 1:03 AM Field NUMTYPE NUMZOOM Reset numeric To reset the default values for all table settings, press settings Exploring the table of numbers NUM view The following table details the menu keys that you use to work with the table of numbers.
  • Page 60 hp40g+.book Page 18 Friday, December 9, 2005 1:03 AM Zoom within a Zooming redraws the table of numbers in greater or lesser detail. table ZOOM options The following table lists the zoom options: Option Decimal Integer Trig Un-zoom The display on the right is a Zoom In of the display on the left.

  • Page 61: Building Your Own Table Of Numbers

    hp40g+.book Page 19 Friday, December 9, 2005 1:03 AM Automatic You can enter any new value in the X column. When you recalculation press recalculated, and the entire table is regenerated with the same interval between X values. Building your own table of numbers The default NUMTYPE is “Automatic”, which fills the table with data for regular intervals of the independent (X, T, θ, or N) variable.

  • Page 62: Build Your Own" Menu Keys

    hp40g+.book Page 20 Friday, December 9, 2005 1:03 AM “Build Your Own” menu keys Example: plotting a circle Plot the circle, x ± To plot both the positive and negative y values, you need to define two equations as follows: 1.
  • Page 63 hp40g+.book Page 21 Friday, December 9, 2005 1:03 AM 2. Reset the graph setup to the default settings. 3. Plot the two functions 4. Reset the numeric setup to the default settings. 5. Display the functions in numeric form. Aplets and their views Select Function SETUP...
  • Page 64 hp40g+.book Page 22 Friday, December 9, 2005 1:03 AM...

  • Page 65: Function Aplet

    hp40g+.book Page 1 Friday, December 9, 2005 1:03 AM 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 Once you have defined a function you can: •...
  • Page 66 hp40g+.book Page 2 Friday, December 9, 2005 1:03 AM Define the 2. There are 10 function definition fields on the Function aplet’s Symbolic view screen. They are labeled F1(X) expressions to F0(X). Highlight the function definition field you want to use, and enter an expression. (You can press clear all lines.) Set up the plot You can change the scales of the x and y axes, graph...
  • Page 67 hp40g+.book Page 3 Friday, December 9, 2005 1:03 AM Change the 6. You can change the scale to see more or less of your scale Trace a graph 7. Trace the linear function. 8. Jump from the linear function to the quadratic Function aplet graphs.
  • Page 68 hp40g+.book Page 4 Friday, December 9, 2005 1:03 AM Analyse graph 9. Display the Plot view menu. with FCN functions From the Plot view menu, you can use the functions on the FCN menu to find roots, intersections, slopes, and areas for a function defined in the Function aplet (and any Function-based aplets).
  • Page 69 hp40g+.book Page 5 Friday, December 9, 2005 1:03 AM 12.Choose the linear function whose intersection with the To find the slope of 13.Find the slope of the quadratic function at the the quadratic function To find the signed 14.To find the area between the two functions in the area of the two functions 15.Move the cursor to x = –2 by pressing the...
  • Page 70 hp40g+.book Page 6 Friday, December 9, 2005 1:03 AM 16.Press other boundary for the integral. 17. Choose the end value for x. The cursor jumps to x = –1 on the linear function. 18.Display the numerical value of the integral. Note: See “Shading area”...
  • Page 71 hp40g+.book Page 7 Friday, December 9, 2005 1:03 AM H I N T The Root and Extremum functions return one value only even if the function has more than one root or extremum. The function finds the value closest to the position of the cursor.
  • Page 72 hp40g+.book Page 8 Friday, December 9, 2005 1:03 AM To navigate around 24.Move to X = –5.9. a table To go directly to a 25. Move directly to X = 10. value To access the zoom 26. Zoom in on X = 10 by a factor of 4. Note: NUMZOOM options has a setting of 4.

  • Page 73: Function Aplet Interactive Analysis

    hp40g+.book Page 9 Friday, December 9, 2005 1:03 AM Function aplet interactive analysis From the Plot view ( the FCN menu to find roots, intersections, slopes, and areas for a function defined in the Function aplet (and any Function-based aplets). See “FCN functions” on page 3- 10.

  • Page 74: Signed Area

    hp40g+.book Page 10 Friday, December 9, 2005 1:03 AM FCN functions The FCN functions are: Function Root Extremum Slope Signed area 3-10 Description Select Root to find the root of the current function nearest the cursor. If no root is found, but only an extremum, then the result is labeled EXTR: instead of ROOT:.
  • Page 75 hp40g+.book Page 11 Friday, December 9, 2005 1:03 AM Function Intersection Shading area You can shade a selected area between functions. This process also gives you an approximate measurement of the area shaded. 1. Open the Function aplet. The Function aplet opens in 2.

  • Page 76: Plotting A Piecewise-Defined Function

    hp40g+.book Page 12 Friday, December 9, 2005 1:03 AM Plotting a piecewise-defined function Suppose you wanted to plot the following piecewise- defined function. f x ( ) 1. Open the Function aplet. Function 2. Highlight the line you want to use, and enter the expression.

  • Page 77: Parametric Aplet

    hp40g+.book Page 1 Friday, December 9, 2005 1:03 AM 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 Getting started with the Parametric aplet The following example uses the parametric equations x t ( )
  • Page 78 hp40g+.book Page 2 Friday, December 9, 2005 1:03 AM Set angle 3. Set the angle measure to degrees. measure Select Degrees Set up the plot 4. Display the graphing options. The Plot Setup input form has two fields not included in the Function aplet, TRNG and TSTEP.
  • 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. Display the 9. Display the table of values. numbers Parametric aplet PLOT Select Overlay Plot A triangle is displayed rather than a circle (without changing the equation) because the changed value of TSTEP ensures that points being plotted are 120°...
  • Page 80 hp40g+.book Page 4 Friday, December 9, 2005 1:03 AM...

  • Page 81: Polar Aplet

    hp40g+.book Page 1 Friday, December 9, 2005 1:03 AM Polar aplet Getting started with the Polar aplet Open the Polar 1. Open the Polar aplet. aplet Define the 2. Define the polar equation expression Specify plot 3. Specify the plot settings. In this example, we will use settings Plot the 4.
  • Page 82 hp40g+.book Page 2 Friday, December 9, 2005 1:03 AM Explore the 5. Display the Plot view menu key labels. graph 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. Display the 6.

  • Page 83: Sequence Aplet

    hp40g+.book Page 1 Friday, December 9, 2005 1:03 AM Sequence aplet About the Sequence aplet The Sequence aplet allows you to explore sequences. You can define a sequence named, for example, U1: • • • • • The Sequence aplet allows you to create two types of graphs: Getting started with the Sequence aplet The following example defines and then plots an...
  • Page 84 hp40g+.book Page 2 Friday, December 9, 2005 1:03 AM Open the 1. Open the Sequence aplet. Sequence aplet Sequence The Sequence aplet starts in the Symbolic view. Define the 2. Define the Fibonacci sequence, in which each term expression (after the first two) is the sum of the preceding two terms: In the Symbolic view of the Sequence aplet, highlight the U...
  • Page 85 hp40g+.book Page 3 Friday, December 9, 2005 1:03 AM Plot the 4. Plot the Fibonacci sequence 5. In Plot Setup, set the SEQPLOT option to Cobweb. Display the table 6. Display the table of values for this example. Sequence aplet sequence.
  • Page 86 hp40g+.book Page 4 Friday, December 9, 2005 1:03 AM...

  • Page 87: Solve Aplet

    hp40g+.book Page 1 Friday, December 9, 2005 1:03 AM Solve aplet About the Solve aplet The Solve aplet solves an equation or an expression for its unknown variable. You define an equation or expression in the symbolic view, then supply values for all the variables except one in the numeric view.

  • Page 88: Getting Started With The Solve Aplet

    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 kph) in a distance of 100 m. The equation to solve is: Open the Solve 1.
  • Page 89 hp40g+.book Page 3 Friday, December 9, 2005 1:03 AM 4. Enter the values for the known variables. H I N T If the Decimal Mark setting in the Modes input form Solve the 5. Solve for the unknown variable (A). unknown variable Plot the...
  • Page 90 hp40g+.book Page 4 Friday, December 9, 2005 1:03 AM 6. Plot the equation for variable A. Scale 7. Trace along the graph representing the left side of the equation until the cursor nears the intersection. Note the value of A displayed near the bottom left corner of the screen.

  • Page 91: Use An Initial Guess

    hp40g+.book Page 5 Friday, December 9, 2005 1:03 AM Use an initial guess You can usually obtain a faster and more accurate solution if you supply an estimated value for the unknown variable before pressing a solution at the initial guess. Before plotting, make sure the unknown variable is highlighted in the numeric view.

  • Page 92: Interpreting Results

    Condition The Solve aplet found a point where both sides of the equation were equal, or where the expression was zero (a root), within the calculator's 12-digit accuracy. Solve found two points where the difference between the two sides of...

  • Page 93: Plotting To Find Guesses

    hp40g+.book Page 7 Friday, December 9, 2005 1:03 AM If Solve could not find a solution, you will see one of the following two messages. Message Bad Guess(es) Constant? H I N T It is important to check the information relating to the solve process.
  • Page 94 hp40g+.book Page 8 Friday, December 9, 2005 1:03 AM where X is distance, V is acceleration. This is actually two equations, Y = X and Y = V T + (AT Since this equation is quadratic for T, there can be both a positive and a negative solution.
  • Page 95 hp40g+.book Page 9 Friday, December 9, 2005 1:03 AM 5. Move the cursor near the positive (right-side) 6. Return to the Numeric 7. Ensure that the T value is highlighted, and solve the Use this equation to solve for another variable, such as velocity.

  • Page 96: Using Variables In Equations

    All home variables (other than those for aplet settings, like Xmin and Ytick) are global, which means they are shared throughout the different aplets of the calculator. A value that is assigned to a home variable anywhere remains with that variable wherever its name is used.

  • Page 97: Linear Solver Aplet

    hp40g+.book Page 1 Friday, December 9, 2005 1:03 AM Linear Solver aplet About the Linear Solver aplet The Linear Solver aplet allows you to solve a set of linear equations. The set can contain two or three linear equations. In a two-equation set, each equation must be in the form be in the form You provide values for a, b, and k (and c in three- equation sets) for each equation, and the Linear Solver...
  • Page 98 hp40g+.book Page 2 Friday, December 9, 2005 1:03 AM example in the previous step). To solve a three- equation set, press displays three equations. If the three-equation input form is displayed and you want to solve a two-equation set, press In this example, we are going to solve the following equation set: Hence we need the three-equation input form.
  • 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.
  • Page 100 hp40g+.book Page 4 Friday, December 9, 2005 1:03 AM...

  • Page 101: Triangle Solve Aplet

    In each case, the solver will calculate the remaining lengths or angles. The HP 40gs will alert you if no solution can be found, or if you have provided insufficient data. If you are determining the properties of a right-angled...
  • Page 102 hp40g+.book Page 2 Friday, December 9, 2005 1:03 AM Open the 1. Open the Triangle Solver aplet. Triangle Solver aplet Triangle Solver The Triangle Solver aplet opens. Note: if you have already used the Triangle Solver, the entries and results from the previous use will still be displayed.
  • Page 103 hp40g+.book Page 3 Friday, December 9, 2005 1:03 AM 4. Press Errors No solution with given data If you are using the general input form and you enter more than 3 values, the values might not be consistent, that is, no triangle could possibly have all the values you specified.
  • 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.

  • Page 105: Statistics Aplet

    hp40g+.book Page 1 Friday, December 9, 2005 1:03 AM 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 Numeric view which is used to enter data.
  • Page 106 hp40g+.book Page 2 Friday, December 9, 2005 1:03 AM Open the 1. Open the Statistics aplet and clear existing data by Statistics aplet pressing Select Statistics The Statistics aplet starts in the Numerical view. At any time the Statistics aplet is configured for only one of two types of statistical explorations: one- variable ( menu key label in the Numeric view toggles between...
  • Page 107 hp40g+.book Page 3 Friday, December 9, 2005 1:03 AM Choose fit and 4. Select a fit in the Symbolic setup view. data columns 5. Specify the columns that hold the data you want to Explore statistics 6. Find the mean advertising time (MEANX) and the 7.
  • Page 108 hp40g+.book Page 4 Friday, December 9, 2005 1:03 AM Setup plot 8. Change the plotting range to ensure all the data points are plotted (and select a different point mark, if you wish). 4000 Plot the graph 9. Plot the graph. Draw the 10.Draw the regression curve (a curve to fit the data points).
  • 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 14.Return to the Plot view. 15.Jump to the indicated point on the regression line. Statistics aplet to go up to 6 minutes: S (to highlight Stat-Two) (to highlight...

  • Page 110: Entering And Editing Statistical Data

    hp40g+.book Page 6 Friday, December 9, 2005 1:03 AM Entering and editing statistical data The Numeric view ( Statistics aplet. Each column represents a variable named C0 to C9. After entering the data, you must define the data set in the Symbolic view ( H I N T A data column must have at least four data points to provide valid two-variable statistics, or two data points...
  • Page 111 hp40g+.book Page 7 Friday, December 9, 2005 1:03 AM cursor key Example You are measuring the height of students in a classroom to find the mean height. The first five students have the following measurements 160cm, 165cm, 170cm, 175cm, 180cm. 1.
  • Page 112 hp40g+.book Page 8 Friday, December 9, 2005 1:03 AM 3. Find the mean of the sample. Ensure the reads statistics calculated from the sample data in C1. Note that the title of the column of statistics is H1. There are 5 data set definitions available for one-variable statistics: H1–H5.
  • Page 113 hp40g+.book Page 9 Friday, December 9, 2005 1:03 AM To continue our example, suppose that the heights of the rest of the students in the class are measured, but each one is rounded to the nearest of the five values first recorded.
  • 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 the frequency value of 1 with the name C2. 6. Return to the numeric view. 7. Enter the frequency data shown in the above table. 8.
  • Page 115 hp40g+.book Page 11 Friday, December 9, 2005 1:03 AM Edit a data set In the Numeric view of the Statistics aplet, highlight the data value to change. Type a new value and press line for modification. Press value on the edit line. Delete data •...

  • Page 116: Defining A Regression Model

    hp40g+.book Page 12 Friday, December 9, 2005 1:03 AM Defining a regression model The Symbolic view includes an expression (Fit1 through Fit5) that defines the regression model, or “fit”, to use for the regression analysis of each two-variable data set. There are three ways to select a regression model: •...
  • Page 117 hp40g+.book Page 13 Friday, December 9, 2005 1:03 AM Fit model Quadratic Cubic Logistic Exponent Trigonometric User Defined To define your 1. In Numeric view, make sure own fit 2. Display the Symbolic view. 3. Highlight the Fit expression (Fit1, etc.) for the 4.

  • Page 118: Computed Statistics

    hp40g+.book Page 14 Friday, December 9, 2005 1:03 AM Computed statistics One-variable Statistic NΣ TOTΣ MEANΣ PVARΣ SVARΣ PSDEV SSDEV MINΣ MEDIAN MAXΣ 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.

  • Page 119: Plotting

    hp40g+.book Page 15 Friday, December 9, 2005 1:03 AM Two-variable Statistic MEANX Σ Σ MEANY Σ Σ Σ SCOV PCOV CORR RELERR Plotting You can plot: • • • Once you have entered your data ( data set ( variable statistics ( data.

  • Page 120: Plot Types

    hp40g+.book Page 16 Friday, December 9, 2005 1:03 AM To plot statistical 1. In Symbolic view ( data sets you want to plot. 2. For one-variable data ( Plot Setup ( press BoxWhisker, and press 3. For any plot, but especially for a histogram, adjust the plotting scale and range in the Plot Setup view.

  • Page 121: Fitting A Curve To 2Var Data

    hp40g+.book Page 17 Friday, December 9, 2005 1:03 AM Scatter Plot Two-variable statistics. The numbers below the plot indicate that the cursor is at the first data point for S2, at (1, 6). Press the next data point and display information about it. To connect the data points as they are plotted, checkmark CONNECT in the second...

  • Page 122: Setting Up The Plot (Plot Setup View)

    hp40g+.book Page 18 Friday, December 9, 2005 1:03 AM Relative Error The relative error is a measure of the error between predicted values and actual values based on the specified Fit. A smaller number means a better fit. The relative error is stored in a variable named RELERR. The relative error provides a measure of fit accuracy for all fits, and it does depend on the Fit model you have chosen.

  • Page 123: Trouble-Shooting A Plot

    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 plotting, check that you have the following: •...

  • Page 124: Calculating Predicted Values

    hp40g+.book Page 20 Friday, December 9, 2005 1:03 AM statistics only) Calculating predicted values The functions PREDX and PREDY estimate (predict) values for X or Y given a hypothetical value for the other. The estimation is made based on the curve that has been calculated to fit the data according to the specified fit.
  • Page 125 hp40g+.book Page 21 Friday, December 9, 2005 1:03 AM • You can type PREDX and PREDY into the edit line, or you can copy these function names from the MATH menu under the Stat-Two category. H I N T In cases where more than one fit curve is displayed, the PREDY function uses the most recently calculated curve.
  • Page 126 hp40g+.book Page 22 Friday, December 9, 2005 1:03 AM...

  • Page 127: Inference Aplet

    It is useful for gaining an understanding of what the test does, and for demonstrating the test. The calculator’s on-line help provides a description of what the example data represents. Getting started with the Inference aplet This example describes the Inference aplet’s options and...
  • 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: μ Z-Test on the difference of two means Z: 1 π, the Z-Test on 1 proportion...
  • Page 129 hp40g+.book Page 3 Friday, December 9, 2005 1:03 AM Select the 2. Select the Hypothesis Test inferential method. inferential method 3. Define the type of test. 4. Select an alternative hypothesis. Enter data 5. Enter the sample statistics and population The table below lists the fields in this view for our current Z-Test: 1 μ...

  • Page 130: Importing Sample Statistics From The Statistics Aplet

    hp40g+.book Page 4 Friday, December 9, 2005 1:03 AM By default, each field already contains a value. These values constitute the example database and are explained in the Display on-line 6. To display the on-line help help, press 7. To close the on-line help, press Display test 8.
  • Page 131 Page 5 Friday, December 9, 2005 1:03 AM A calculator produces the following 6 random numbers: 0.529, 0.295, 0.952, 0.259, 0.925, and 0.592 Open the 1. Open the Statistics aplet and reset the current Statistics aplet Enter data 2. In the C1 column, enter the random numbers...
  • Page 132 hp40g+.book Page 6 Friday, December 9, 2005 1:03 AM Open Inference 6. Open the Inference aplet and clear current settings. aplet Inference Select inference 7. Select an inference method. method and type Select CONF INTERVAL 8. Select a distribution statistic type. Select T-Int: 1 μ...
  • 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 11.Specify a 90% Display Numeric 12.Display the confidence interval in the Numeric view. view Display Plot 13.Display the confidence interval in the Plot view. view Inference aplet data from C1 is displayed by default.

  • Page 134: Hypothesis Tests

    You use hypothesis tests to test the validity of hypotheses that relate to the statistical parameters of one or two populations. The tests are 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 Z-Test: 1 μ...

  • Page 135: Two-Sample Z-Test

    hp40g+.book Page 9 Friday, December 9, 2005 1:03 AM Results The results are: Result Test Z Prob Critical Z Critical Two-Sample Z-Test Z-Test: μ1–μ2 Menu name On the basis of two samples, each from a separate population, this test measures the strength of the evidence for a selected hypothesis against the null hypothesis.

  • Page 136: One-Proportion Z-Test

    hp40g+.book Page 10 Friday, December 9, 2005 1:03 AM Field name σ2 α Results The results are: Result Test Z Prob Critical Z One-Proportion Z-Test Z-Test: 1π Menu name On the basis of statistics from a single sample, this test measures the strength of the evidence for a selected hypothesis against the null hypothesis.

  • Page 137: Two-Proportion Z-Test

    hp40g+.book Page 11 Friday, December 9, 2005 1:03 AM Inputs The inputs are: Field name π α Results The results are: Result Test P Test Z Prob Critical Z Two-Proportion Z-Test Z-Test: π1 – π2 Menu name On the basis of statistics from two samples, each from a different population, the Two-Proportion Z-Test measures the strength of the evidence for a selected hypothesis against the null hypothesis.

  • Page 138: One-Sample T-Test

    hp40g+.book Page 12 Friday, December 9, 2005 1:03 AM Inputs The inputs are: Field name α Results The results are: Result Test π1–π2 Test Z Prob Critical Z One-Sample T-Test T-Test: 1 μ Menu name The One-sample T-Test is used when the population standard deviation is not known.
  • Page 139 hp40g+.book Page 13 Friday, December 9, 2005 1:03 AM Inputs The inputs are: Field name μ0 α Results The results are: Result Test T Prob Critical T Critical Inference aplet Definition Sample mean. Sample standard deviation. Sample size. Hypothetical population mean. Significance level.

  • Page 140: Two-Sample T-Test

    hp40g+.book Page 14 Friday, December 9, 2005 1:03 AM Two-Sample T-Test T-Test: μ1 – μ2 Menu name The Two-sample T-Test is used when the population standard deviation is not known. On the basis of statistics from two samples, each sample from a different population, this test measures the strength of the evidence for a selected hypothesis against the null hypothesis.

  • Page 141: Confidence Intervals

    The results are: Result Test T Prob Critical T Confidence intervals The confidence interval calculations that the HP 40gs can perform are based on the Normal Z-distribution or Student’s t-distribution. One-Sample Z-Interval Z-INT: μ 1 Menu name This option uses the Normal Z-distribution to calculate a confidence interval for m, the true mean of a population, when the true population standard deviation, s, is known.

  • Page 142: Two-Sample Z-Interval

    hp40g+.book Page 16 Friday, December 9, 2005 1:03 AM Results The results are: Result Critical Z μ min μ max Two-Sample Z-Interval Z-INT: μ1– μ2 Menu name This option uses the Normal Z-distribution to calculate a confidence interval for the difference between the means of two populations, μ...

  • Page 143: One-Proportion Z-Interval

    hp40g+.book Page 17 Friday, December 9, 2005 1:03 AM One-Proportion Z-Interval Z-INT: 1 π Menu name This option uses the Normal Z-distribution to calculate a confidence interval for the proportion of successes in a population for the case in which a sample of size, n, has a number of successes, x.

  • Page 144: One-Sample T-Interval

    hp40g+.book Page 18 Friday, December 9, 2005 1:03 AM Field name Results The results are: Result Critical Z Δ π Min Δ π Max One-Sample T-Interval T-INT: 1 μ Menu name 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 true population standard deviation, s, is unknown.

  • Page 145: Two-Sample T-Interval

    hp40g+.book Page 19 Friday, December 9, 2005 1:03 AM Results The results are: Result Critical T μ Min μ Max Two-Sample T-Interval T-INT: μ1 – μ2 Menu name This option uses the Student’s t-distribution to calculate a confidence interval for the difference between the means of two populations, μ1 –...
  • 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 11-20 Description Critical value for T. Lower bound for μ 1 – μ 2 . Upper bound for μ 1 – μ 2 . Inference aplet...

  • Page 147: Using The Finance Solver

    Page 1 Friday, December 9, 2005 1:03 AM Using the Finance Solver The Finance Solver, or Finance aplet, is available by using the APLET key in your calculator. Use the up and down arrow keys to select the Finance aplet. Your screen should look as follows: Press the activate the aplet.
  • 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 of the notion that a dollar today will be worth more than a dollar sometime in the future.
  • Page 149 hp40g+.book Page 3 Friday, December 9, 2005 1:03 AM flow diagram shows lease payments at the beginning of each period. The following cash flow diagram shows deposits into an account at the end of each period. As these cash-flow diagrams imply, there are five TVM variables: I%YR Using the Finance Solver...

  • Page 150: Performing Tvm Calculations

    hp40g+.book Page 4 Friday, December 9, 2005 1:03 AM Performing TVM calculations 1. Launch the Financial Solver as indicated at the beginning of this section. 2. Use the arrow keys to highlight the different fields and enter the known variables in the TVM calculations, pressing the known value.
  • 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.
  • Page 152 hp40g+.book Page 6 Friday, December 9, 2005 1:03 AM Example 2 - Mortgage with balloon payment Suppose you have taken out a 30-year, $150,000 house mortgage at 6.5% annual interest. You expect to sell the house in 10 years, repaying the loan in a balloon payment.

  • Page 153: Calculating Amortizations

    The calculator will provide for you the amount applied to interest, to principal, and the remaining balance after this set of payments have been amortized.
  • Page 154 hp40g+.book Page 8 Friday, December 9, 2005 1:03 AM 3. Press the batch of payments. Repeat steps 1 through 3 as often as needed. Example 4 - Amortization for home mortgage For the results of Example 3, show the amortization of the next 10 years of the mortgage loan.

  • Page 155: Using Mathematical Functions

    Page 1 Friday, December 9, 2005 1:03 AM 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 Prob. on the MATH menu) contains functions for working with probability.

  • Page 156: Math Functions By Category

    hp40g+.book Page 2 Friday, December 9, 2005 1:03 AM To select a function 1. Press categories appear in alphabetical order. 2. Press jump directly to a category, press the first letter of the category’s name. Note: You do not need to press 3.

  • Page 157: Keyboard Functions

    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 MATH menu. Keyboard functions The most frequently used functions are available directly from the keyboard. Many of the keyboard functions also accept complex numbers as arguments.
  • Page 158 hp40g+.book Page 4 Friday, December 9, 2005 1:03 AM Add, Subtract, Multiply, Divide. Also accepts complex numbers, lists and matrices. value1+ value2, etc. Natural exponential. Also accepts complex numbers. e^value Example e^5 returns 148.413159103 Natural logarithm. Also accepts complex numbers. LN(value) Example LN(1) returns 0...
  • Page 159 hp40g+.book Page 5 Friday, December 9, 2005 1:03 AM Example Arc cosine: cos ACOS π, or 0 to 200 grads. Inputs and outputs depend on the current angle format. Also accepts complex numbers. Output will be complex for values outside the normal COS domain of Example Arc tangent: tan...

  • Page 160: Calculus Functions

    hp40g+.book Page 6 Friday, December 9, 2005 1:03 AM Example 2^8 returns 256 Absolute value. For a complex number, this is ABS(value) ABS((x,y)) Example ABS(–1) returns 1 ABS((1,2)) returns 2.2360679775 Takes the nth root of x. root NTHROOT value Example 3 NTHROOT 8 returns 2 Calculus functions The symbols for differentiation and integration are...

  • Page 161: Complex Number Functions

    hp40g+.book Page 7 Friday, December 9, 2005 1:03 AM Example TAYLOR Calculates the nth order Taylor polynomial of expression at the point where the given variable = 0. Example Complex number functions These functions are for complex numbers only. You can also use complex numbers with all trigonometric and hyperbolic functions, and with some real-number and keyboard functions.

  • Page 162: Constants

    Constants 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”...

  • Page 163: Hyperbolic Trigonometry

    hp40g+.book Page 9 Friday, December 9, 2005 1:03 AM →C Convert from Fahrenheit to Celcius. Example →F Convert from Celcius to Fahrenheit. Example →CM Convert from inches to centimeters. →IN Convert from centimeters to inches. →L Convert from US gallons to liters. →LGAL Convert from liters to US gallons.

  • Page 164: List Functions

    hp40g+.book Page 10 Friday, December 9, 2005 1:03 AM COSH Hyperbolic cosine COSH(value) SINH Hyperbolic sine. SINH(value) TANH Hyperbolic tangent. TANH(value) ALOG Antilogarithm (exponential). This is more accurate than 10^x due to limitations of the power function. ALOG(value) Natural exponential. This is more accurate than to limitations of the power function.

  • Page 165: Matrix Functions

    hp40g+.book Page 11 Friday, December 9, 2005 1:03 AM RECURSE Provides a method of defining a sequence without using the Symbolic view of the Sequence aplet. If used with | (“where”), RECURSE will step through the evaluation. Example Σ Summation. Finds the sum of expression with respect to variable from initialvalue to finalvalue.

  • Page 166: Probability Functions

    hp40g+.book Page 12 Friday, December 9, 2005 1:03 AM Example For x POLYEVAL([1,2,-25,-26,120],8) returns 3432. POLYFORM Polynomial form. Creates a polynomial in variable1 from expression. POLYFORM(expression, variable1) Example POLYFORM((X+1)^2+1,X) returns X^2+2*X+2. POLYROOT Polynomial roots. Returns the roots for the nth-order polynomial with the specified n+1 coefficients.
  • Page 167 RANDOM to produce the numbers. H I N T The setting of Time will be different for each calculator, so using RANDSEED(Time) is guaranteed to produce a set of numbers which are as close to random as possible. You can set the seed using the command RANDSEED.

  • Page 168: Real-Number Functions

    hp40g+.book Page 14 Friday, December 9, 2005 1:03 AM UTPT Upper-Tail Student’s t-Probability given degrees of freedom, evaluated at value. Returns the probability that the Student's t- random variable is greater than value. UTPT(degrees, value) Real-number functions Some real-number functions can also take complex arguments.
  • Page 169 hp40g+.book Page 15 Friday, December 9, 2005 1:03 AM → Hours-minutes-seconds to decimal. Converts a number or expression in H.MMSSs format (time or angle that can include fractions of a second) to x.x format (number of hours or degrees with a decimal fraction). Example →...
  • Page 170 hp40g+.book Page 16 Friday, December 9, 2005 1:03 AM Example 9 MOD 4 returns 1 x percent of y; that is, x/100*y. %(x, y) Example %(20,50) returns 10 %CHANGE Percent change from x to y, that is, 100(y–x)/x. %CHANGE(x, y) Example %CHANGE(20,50) returns 150 %TOTAL...

  • Page 171: Two-Variable Statistics

    hp40g+.book Page 17 Friday, December 9, 2005 1:03 AM Examples TRUNCATE Truncates value to decimal places. Accepts complex numbers. Example XPON Exponent of value. Example Two-variable statistics These are functions for use with two-variable statistics. See “Two-variable” on page 10-15. Symbolic functions The symbolic functions are used for symbolic manipulations of expressions.
  • Page 172 hp40g+.book Page 18 Friday, December 9, 2005 1:03 AM Examples ISOLATE(2*X+8,X) returns -4 ISOLATE(A+B*X/C,X) returns -(A*C/B) LINEAR? Tests whether expression is linear for the specified variable. Returns 0 (false) or 1 (true). LINEAR?(expression, variable) Example LINEAR?((X^2-1)/(X+1),X) returns 0 QUAD Solves quadratic expression=0 for variable and returns a new expression, where variable=newexpression.

  • Page 173: Test Functions

    hp40g+.book Page 19 Friday, December 9, 2005 1:03 AM Test functions The test functions are logical operators that always return either a 1 (true) or a 0 (false). < Less than. Returns 1 if true, 0 if false. ≤ Less than or equal to. Returns 1 if true, 0 if false. Equals (logical test).

  • Page 174: Trigonometry Functions

    HOME” on page 14-7. In HOME When you perform calculations that contain normal variables, the calculator substitutes values for any variables. For example, if you enter A+B on the command line and press for A and B from memory and substitutes them in the calculation.

  • Page 175: Finding Derivatives

    See “To find derivatives in the Function aplet’s Symbolic view” on page 13-22 for an example. Finding derivatives The HP 40gs can perform symbolic differentiation on some functions. There are two ways of using the HP 40gs to find derivatives. • •...
  • Page 176 hp40g+.book Page 22 Friday, December 9, 2005 1:03 AM differentiation function substitutes the value that X holds, and returns a numeric result. For example, consider the function: 1. Enter the differentiation function onto the command line, substituting S1 in place of X. 2.
  • Page 177 hp40g+.book Page 23 Friday, December 9, 2005 1:03 AM 3. Select F2(X) and 4. Press To find the indefinite integral using formal variables 1. Enter the function. 2. Show the result format. 3. Press Using mathematical functions evaluate it. to display the result.

  • Page 178: Program Constants And Physical Constants

    hp40g+.book Page 24 Friday, December 9, 2005 1:03 AM 4. Copy the result and evaluate. Thus, substituting X for S1, it can be seen that: ∫ This result is derived from substituting X=S1 and X=0 into the original expression found in step 1. However, substituting X=0 will not always evaluate to zero and may result in an unwanted constant.

  • Page 179: Program Constants

    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...
  • Page 180 hp40g+.book Page 26 Friday, December 9, 2005 1:03 AM 3. Use the arrow keys to navigate through the options. 4. To see the symbol and value of a selected constant, press window that appears.) The following example shows the information available about the speed of light (one of the physics constants).
  • Page 181 hp40g+.book Page 27 Friday, December 9, 2005 1:03 AM 3. Select light s...from the Physics menu. 4. Press 5. Complete the equation as you would normally and Using mathematical functions . The menu closes and the value of the selected constant is copied to the edit line. press to get the result.
  • Page 182 hp40g+.book Page 28 Friday, December 9, 2005 1:03 AM...

  • Page 183: Computer Algebra System (Cas)

    HOME view or by an aplet, are numerical calculations and are limited by the precision of the calculator (to 10 HP 40gs). For example, with Standard as your numerical format, 1/2 + 1/6 returns 0.6666666666667 if you are working in the HOME screen;...

  • Page 184: An Example

    hp40g+.book Page 2 Friday, December 9, 2005 1:03 AM using vectors and matrices. (Vectors and matrices cannot be entered using the Equation Writer). To open the Equation Writer, press the key on the menu bar of the HOME screen. The illustration at the right shows an expression being written in the Equation Writer.
  • Page 185 hp40g+.book Page 3 Friday, December 9, 2005 1:03 AM 3. Press 4. Press the 5. Press 6. Press 7. Press 8. As you did earlier, press 9. Press Computer Algebra System (CAS) select just the 20 in the term. menu key and choose FACTOR.

  • Page 186: Cas Variables

    hp40g+.book Page 4 Friday, December 9, 2005 1:03 AM 10.Press select the entire expression and then press 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 permanent value).

  • Page 187: Cas Modes

    To change the setting, press 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 preferred independent variable for algebraic and calculus applications.
  • Page 188 (a,b). If is not selected and an operation results in a complex number, you will be asked to switch to you decline, the calculator will report an error. [Default: unselected.] When in range of operations than in non-complex (or real) mode, but it will also be considerably slower.

  • Page 189: Using Cas Functions In Home

    hp40g+.book Page 7 Friday, December 9, 2005 1:03 AM Using CAS functions in HOME You can use many computer algebra functions directly in the HOME screen, as long as you take certain precautions. CAS functions that take matrices as an argument work only from HOME.

  • Page 190: Online Help

    hp40g+.book Page 8 Friday, December 9, 2005 1:03 AM Symbolic matrices 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}, { then you have:...

  • Page 191: Cas Functions In The Equation Writer

    hp40g+.book Page 9 Friday, December 9, 2005 1:03 AM HELP and press appears. Each help topic includes the required syntax, along with real sample values. You can copy the syntax, with the sample values, to the HOME screen or to the Equation Writer, by pressing T I P If you highlight a CAS command and then press...

  • Page 192: Algb Menu

    hp40g+.book Page 10 Friday, December 9, 2005 1:03 AM For example, suppose you have stored the expression x in G, and have defined the function F(x) as x now you want to calculate INTVX(X • enter INTVX(X • enter INTVX(G), or •...
  • Page 193 hp40g+.book Page 11 Friday, December 9, 2005 1:03 AM Typing: produces the result: Typing: then returns: Example Calculate the first six Fermat numbers F1...F6 and determine whether they are prime. So, you want to calculate: Typing the formula: gives a result of 17. You can then invoke the ISPRIME?() command, which is found in the MATH key’s Integer menu.
  • Page 194 hp40g+.book Page 12 Friday, December 9, 2005 1:03 AM which gives 4294967297 You can factor F(5) with FACTOR, which you’ll find in the ALGB menu on the menu bar. Typing: FACTOR(F(5)) gives: 641·6700417 Typing: F(6) gives: 18446744073709551617 Using FACTOR to factor it, then yields: 274177·67280421310721 EXPAND Distributivity...
  • Page 195 hp40g+.book Page 13 Friday, December 9, 2005 1:03 AM In real mode, the result is: In complex mode (using CFG), the result is: ----- - ⋅ PARTFRAC Partial fraction expansion PARTFRAC has a rational fraction as an argument. PARTFRAC returns the partial fraction decomposition of this rational fraction.
  • Page 196 hp40g+.book Page 14 Friday, December 9, 2005 1:03 AM Example 2 Typing: SUBST(QUOTE(CONJ(Z)),Z=1+i) gives: CONJ(1+i) STORE Store an object in a variable STORE stores an object in a variable. STORE is found in the ALGB menu or the Equation Writer menu bar.
  • Page 197 hp40g+.book Page 15 Friday, December 9, 2005 1:03 AM SUBST Substitute a value for a variable SUBST has two parameters: an expression dependent on a parameter, and an equality (parameter=substitute value). SUBST substitutes the specified value for the variable in the expression.

  • Page 198: Diff Menu

    hp40g+.book Page 16 Friday, December 9, 2005 1:03 AM DIFF menu DERIV Derivative and partial derivative DERIV has two arguments: an expression (or a function) and a variable. DERIV returns the derivative of the expression (or the function) with respect to the variable given as the second parameter (used for calculating partial derivatives).
  • Page 199 Q[X] is then the limited nth-order expansion of: in the vicinity of X= 0. Typing: gives: N O T E : When the calculator displays a request to change to increasing powers mode, respond yes. FOURIER Fourier coefficients FOURIER has two parameters: an expression f(x) and a whole number N.
  • Page 200 2π and defined over interval [0, 2π] by f(x)=x Typing: STORE(2π,PERIOD) FOURIER(X The calculator does not know that N is a whole number, so you have to replace EXP(2∗ i∗N∗π) with 1 and then simplify the expression. We get 2 i N π ⋅ ⋅...
  • Page 201 hp40g+.book Page 19 Friday, December 9, 2005 1:03 AM IBP returns the AND of that is, the terms that are calculated when performing a partial integration. It remains then to calculate the integral of the second term of the AND, then add it to the first term of the AND to obtain a primitive of Typing: gives:...
  • Page 202 hp40g+.book Page 20 Friday, December 9, 2005 1:03 AM Example Given: f x ( ) calculate a primitive of f. Type: NTVX Or, if you have stored f(x) in F, that is, if you have already typed: TORE then type: INTVX(F) Or, if you have used DEF to define f(x), that is, if you have already typed:...
  • Page 203 hp40g+.book Page 21 Friday, December 9, 2005 1:03 AM gives a primitive: N o t e You can also type primitive which is zero for x = 1 Example Calculate: Typing: gives the result: N O T E : If the argument to INTVX is the AND of two elements, INTVX concerns itself only with the second element of the AND, and adds the result to the first argument.
  • Page 204 hp40g+.book Page 22 Friday, December 9, 2005 1:03 AM QUOTE(expression), to avoid rewriting the expression in normal form (i.e., not to have a rational simplification of the arguments) during the execution of the LIMIT command. Example Typing: lim QUOTE 2X 1 gives: +∞...
  • Page 205 hp40g+.book Page 23 Friday, December 9, 2005 1:03 AM Typing: gives: NOTE: To find the limit as x approaches a second argument is written: For the following expression, find the limit as x approaches +∞: Typing: produces (after a short wait): NOTE: the symbol ∞...
  • Page 206 hp40g+.book Page 24 Friday, December 9, 2005 1:03 AM PREVAL is used for calculating an integral defined from a primitive: it evaluates this primitive between the two limits of the integral. Typing: PREVAL(X gives: RISCH Primitive and defined integral RISCH has two parameters: an expression and the name of a variable.
  • Page 207 hp40g+.book Page 25 Friday, December 9, 2005 1:03 AM Typing: gives: • Example 1 Give a 5th-order expansion of arctan(x) in the vicinity of x=+∞, taking as infinitely small Typing: gives: Example 2 Give a 2nd-order expansion of vicinity of x=+∞, taking as infinitely small gives: •...
  • Page 208 hp40g+.book Page 26 Friday, December 9, 2005 1:03 AM You must be in Rigorous (not Sloppy) mode to apply SERIES with unidirectional expansion. (See “CAS modes” on page 14-5 for instructions on setting and changing modes. Example 1 Give a 3rd-order expansion of x = 0 Typing: SERIES...
  • Page 209 hp40g+.book Page 27 Friday, December 9, 2005 1:03 AM TABVAR Variation table TABVAR has as a parameter an expression with a rational derivative. TABVAR returns the variation table for the expression in terms of the current variable. Typing: gives, in step-by-step mode: –∞...

  • Page 210: Rewri Menu

    hp40g+.book Page 28 Friday, December 9, 2005 1:03 AM Typing: TAYLOR0 gives: ------ N o t e ‘th-order’ means that the numerator and the denominator are expanded to the 4th relative order (here, the 5th absolute order for the numerator, and for the denominator, which is given in the end, the 2nd order (5−...
  • Page 211 Transform a trigonometric expression into complex exponentials EXPLN takes as an argument a trigonometric expression. It transforms the trigonometric function into exponentials and logarithms without linearizing it. EXPLN puts the calculator into complex mode. Typing: gives: EXP2POW Transform exp(n EXP2POW transforms an expression of the form exp(n ×...
  • Page 212 LIN does not linearize trigonometric expressions (as does TLIN) 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:...
  • Page 213 hp40g+.book Page 31 Friday, December 9, 2005 1:03 AM Example 3 Typing: gives: LNCOLLECT Regroup the logarithms LNCOLLECT has as an argument an expression containing logarithms. LNCOLLECT regroups the terms in the logarithms. It is therefore preferable to use an expression that has already been factored (using FACTOR).
  • Page 214 Typing: XNUM(√2) gives: 1.41421356237 Rational approximation XQ has a real numeric expression as a parameter. XQ puts the calculator into exact mode and gives a rational or real approximation of the expression. Typing: XQ(1.41421) gives: 66441 -------------- -...

  • Page 215: Solv Menu

    hp40g+.book Page 33 Friday, December 9, 2005 1:03 AM Typing: gives: SOLV menu The SOLV menu contains functions that enable you to solve equations, linear systems, and differential equations. DESOLVE Solve differential equations DESOLVE enables you to solve differential equations. (For linear differential equations having constant coefficients, it is better to use LDEC.) DESOLVE has two arguments:...
  • Page 216 hp40g+.book Page 34 Friday, December 9, 2005 1:03 AM To produce the solutions for y(0) = 1, type: SUBST Y X ( ) cC0 COS X ( ) which gives: y x ( ) Example 2 Solve: y” + y = cos(x) y(0) = 1 y’(0) = 1 It is possible to solve for the constants from the outset.
  • Page 217 hp40g+.book Page 35 Friday, December 9, 2005 1:03 AM LDEC Linear differential equations having constant coefficients LDEC enables you to directly solve linear differential equations having constant coefficients. The parameters are the second member and the characteristic equation. Solve: Typing: gives: cC0 and cC1 are integration constants (y(0) = cC0 and y’(0) = cC1).
  • Page 218 hp40g+.book Page 36 Friday, December 9, 2005 1:03 AM L1=2L1+L2 1 1 3 ENTER Reduction Result 2 0 4 then press ENTER. The following is then written to the Equation Writer: (x = −2) AND (y = −1) Example 2 Type: (2·X+Y+Z=1)AND(X+Y+2·Z=1)AND(X+2·Y+Z=4) Then, invoke LINSOLVE and type the unknowns:...
  • Page 219 hp40g+.book Page 37 Friday, December 9, 2005 1:03 AM then press ENTER. The following is then written to the Equation Writer: SOLVE Solve equations SOLVE has as two parameters: (1) either an equality between two expressions, or a single expression (in which case = 0 is implied), and (2) the name of a variable.

  • Page 220: Trig Menu

    hp40g+.book Page 38 Friday, December 9, 2005 1:03 AM SOLVEVX Solve equations SOLVEVX has as a parameter either: (1) an equality between two expressions in the variable contained in VX, or (2) a single such expression (in which case = 0 is implied).
  • Page 221 hp40g+.book Page 39 Friday, December 9, 2005 1:03 AM Typing: gives, when simplified: ASIN2C Transform the arcsin into arccos ASIN2C has as a trigonometric expression as an argument. ASIN2C transforms the expression by replacing arcsin(x) with Typing: gives, when simplified: ASIN2T Transform the arccos into arctan ASIN2T has a trigonometric expression as an argument.
  • Page 222 hp40g+.book Page 40 Friday, December 9, 2005 1:03 AM Typing: ATAN2S(ATAN(X)) gives: asin HALFTAN Transform in terms of tan(x/2) HALFTAN has a trigonometric expression as an argument. HALFTAN transforms sin(x), cos(x) and tan(x) in the expression, rewriting them in terms of tan(x/2). Typing: HALFTAN(SIN(X) gives (SQ(X) = X...
  • Page 223 hp40g+.book Page 41 Friday, December 9, 2005 1:03 AM TAN2CS2 transforms this expression by replacing tan(x) with Typing: gives: TAN2SC Replace tan(x) with sin(x)/cos(x) TAN2SC has a trigonometric expression as an argument. TAN2SC transforms this expression by replacing tan(x) with Typing: gives: TAN2SC2...
  • Page 224 hp40g+.book Page 42 Friday, December 9, 2005 1:03 AM TCOLLECT linearizes this expression in terms of sin(n x) and cos(n x), then (in Real mode) reconstructs the sine and cosine of the same angle. Typing: TCOLLECT(SIN(X) + COS(X)) gives: TEXPAND Develop transcendental expressions TEXPAND has as an argument a transcendental expression (that is, an expression with trigonometric,...
  • Page 225 hp40g+.book Page 43 Friday, December 9, 2005 1:03 AM gives: TLIN Linearize a trigonometric expression TLIN has as an argument a trigonometric expression. TLIN linearizes this expression in terms of sin(n x) and cos(n x). Example 1 Typing: gives: Example 2 Typing: gives: Example 3...
  • Page 226 hp40g+.book Page 44 Friday, December 9, 2005 1:03 AM Typing: TRIG(SIN(X) gives: TRIGCOS Simplify using the cosines TRIGCOS has as an argument a trigonometric expression. TRIGCOS simplifies this expression, using the identity sin(x) +cos(x) Typing: TRIGCOS(SIN(X) gives: TRIGSIN Simplify using the sines TRIGSIN has as an argument a trigonometric expression.

  • Page 227: Cas Functions On The Math Menu

    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 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 the Equation Writer;...

  • Page 228: Constant Menu

    hp40g+.book Page 46 Friday, December 9, 2005 1:03 AM returns: Y = X –1 + 2 Pressing Y = X + 1 See “IM” on page 13-7. – Specifies the negation of the argument. See “RE” on page 13-8. SIGN Determines the quotient of the argument divided by its modulus.
  • Page 229 hp40g+.book Page 47 Friday, December 9, 2005 1:03 AM DIVIS Gives the divisors of an integer. Example Typing: gives: Note: DIVIS(0) returns 0 OR 1. EULER Returns the Euler index of a whole number. The Euler index of n is the number of whole numbers less than n that are prime with n.
  • Page 230 Typing: IDIV2(148, 5) gives: 29 AND 3 In step-by-step mode, the calculator shows the division process in longhand. IEGCD Returns the value of Bézout’s Identity for two integers. For example, IEGCD(A,B) returns U AND V = D, with U, V, D such that AU+BV=D and D=GCD(A,B).
  • Page 231 hp40g+.book Page 49 Friday, December 9, 2005 1:03 AM Pressing written to the Equation Writer. The intermediate steps shown are the combination of lines. For example, to get line L(n + 2), take L(n) – q*L(n + 1) where q is the Euclidean quotient of the integers at the beginning of the vector, these integers being the sequence of remainders).
  • Page 232 hp40g+.book Page 50 Friday, December 9, 2005 1:03 AM IREMAINDER works with integers and with Gaussian integers. This is what distinguishes it from MOD. Example 2 Typing: IREMAINDER(2 + 3·i, 1 + i) gives: ISPRIME? Returns a value indicating whether an integer is a prime number.

  • Page 233: Modular Menu

    hp40g+.book Page 51 Friday, December 9, 2005 1:03 AM NEXTPRIME NEXTPRIME(n) returns the smallest prime or pseudo-prime greater than n. Example Typing: gives: PREVPRIME PREVPRIME(n) returns the greatest prime or pseudo-prime less than n. Example Typing: gives: Modular menu All the examples of this section assume that p =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).
  • Page 234 hp40g+.book Page 52 Friday, December 9, 2005 1:03 AM DIVMOD Division in Z/pZ or Z/pZ[X]. Example 1 In Z/pZ, the arguments are two integers: A and B. When B has an inverse in Z/pZ, the result is A/B simplified as Z/pZ.
  • Page 235 hp40g+.book Page 53 Friday, December 9, 2005 1:03 AM Factors a polynomial in Z/pZ[X], providing that p ≤ 97, FACTORMOD p is prime and the order of the multiple factors is less than the modulo. Example Typing: gives: GCDMOD Calculates the GCD of the two polynomials in Z/pZ[X]. Example Typing: gives:...
  • Page 236 hp40g+.book Page 54 Friday, December 9, 2005 1:03 AM MULTMOD 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: – POWMOD Calculates A to the power of N in Z/pZ[X], and A(X) to the power of N in Z/pZ[X].

  • Page 237: Polynomial Menu

    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: gives: Example 2 Typing: gives: Polynomial menu EGCD Returns Bézout’s Identity, the Extended Greatest Common Divisor (EGCD). EGCD(A(X), B(X)) returns U(X) AND V(X) = D(X), with D, U, V such that D(X) = U(X)·A(X) + V(X)·B(X).
  • Page 238 hp40g+.book Page 56 Friday, December 9, 2005 1:03 AM FACTOR Factors a polynomial. Example 1 Typing: FACTOR(X gives: Example 2 Typing: FACTOR(X gives: Returns the GCD (Greatest Common Divisor) of two polynomials. Example Typing: GCD(X gives: HERMITE Returns the Hermite polynomial of degree n (where n is a whole number).
  • Page 239 hp40g+.book Page 57 Friday, December 9, 2005 1:03 AM Returns the LCM (Least Common Multiple) of two polynomials. Example Typing: gives: LEGENDRE Returns the polynomial L differential equation: where n is a whole number. Example Typing: gives: PARTFRAC Returns the partial fraction decomposition of a rational fraction.
  • Page 240 hp40g+.book Page 58 Friday, December 9, 2005 1:03 AM PROPFRAC PROPFRAC rewrites a rational fraction so as to bring out its whole number part. PROPFRAC(A(X)/ B(X)) writes the rational fraction A(X)/ B(X) in the form: Q X ( ) where R”(X) = 0, or 0 ≤ deg (R(X) < deg (B(X). Example Typing: ROPFRAC...
  • Page 241 hp40g+.book Page 59 Friday, December 9, 2005 1:03 AM Note that in step-by-step mode, synthetic division is shown, with each polynomial represented as the list of its coefficients in descending order of power. REMAINDER Returns the remainder from the division of the two polynomials, A(X) and B(X), divided in decreasing order by exponent.

  • Page 242: Real Menu

    hp40g+.book Page 60 Friday, December 9, 2005 1:03 AM Example 1 Typing: TCHEBYCHEFF(4) gives: Example 2 Typing: TCHEBYCHEFF(–4) gives: Real menu CEILING See “CEILING” on page 13-14. FLOOR See “FLOOR” on page 13-14. FRAC See “FRAC” on page 13-14. See “INT” on page 13-15. See “MAX”...

  • Page 243: Tests Menu

    Example Typing: sets an assumption that X is greater than Y. In fact, the calculator works only with large not strict relations, and thus ASSUME(X>Y) will actually set the assumption that X ≥ ASSUME function.) Note that X REALASSUME variable.

  • Page 244: Cas Functions On The Cmds Menu

    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 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 in the Equation Writer;...
  • Page 245 hp40g+.book Page 63 Friday, December 9, 2005 1:03 AM Example Find the solutions P(X) of: Typing: gives: That is: CYCLOTOMIC Returns the cyclotomic polynomial of order n. This is a polynomial having the nth primitive roots of unity as zeros. CYCLOTOMIC has an integer n as its argument.
  • Page 246 hp40g+.book Page 64 Friday, December 9, 2005 1:03 AM Example 1 Typing: EXP2HYP(EXP(A)) gives: sinh(a) + cosh(a) Example 2 Typing: EXP2HYP(EXP(–A) + EXP(A)) gives: 2 · cosh(a) Returns the values of the Γ function at a given point. GAMMA The Γ function is defined as: Γ...
  • Page 247 hp40g+.book Page 65 Friday, December 9, 2005 1:03 AM Example Typing: gives: IBERNOULLI Returns the nth Bernoulli’s number B(n) where: Example Typing: gives: ICHINREM Chinese Remainders: ICHINREM(A AND P,B AND Q) returns C AND R, where A, B, P and Q are whole numbers.
  • Page 248 hp40g+.book Page 66 Friday, December 9, 2005 1:03 AM ILAP is the inverse Laplace transform of a given expression. Again, the expression is the value of a function of the variable stored in VX. Laplace transform (LAP) and inverse Laplace transform (ILAP) are useful in solving linear differential equations with constant coefficients, for example: y″...
  • Page 249 See ILAP above. PA2B2 Decomposes a prime integer p congruent to 1 modulo 4, as follows: p = a The calculator gives the result as a + b · i. Example 1 Typing: gives: that is, 17 = 4 Example 2...
  • Page 250 hp40g+.book Page 68 Friday, December 9, 2005 1:03 AM gives: -- - – Returns the value of the Digamma function at a. The Digamma function is defined as the derivative of ln(Γ(x)), so we have PSI(a,0) = Psi(a). Example Typing: Psi(3) and pressing gives:...
  • Page 251 hp40g+.book Page 69 Friday, December 9, 2005 1:03 AM Example Typing: gives: because (X + 1)! – X! = X · X!. SIGMAVX Returns the discrete antiderivative of the input function, that is a function, G, that satisfies the relation: G(x + 1) – G(x) = f(x).
  • Page 252 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). 14-70 SIN 3X SIN 7X ⎛...

  • Page 253: Equation Writer

    hp40g+.book Page 1 Friday, December 9, 2005 1:03 AM Equation Writer Using CAS in the Equation Writer The Equation Writer enables you to type expressions that you want to simplify, factor, differentiate, integrate, and so on, and then work them through as if on paper. screen menu bar opens the Equation Writer, and the This chapter explains how to...
  • Page 254 hp40g+.book Page 2 Friday, December 9, 2005 1:03 AM Cursor mode Edit expr. Change font Copy Paste ALGB menu functions that enable you to perform algebra, such as factoring, expansion, simplification, substitution, and so on. DIFF menu functions that enable you to perform differential calculus, such as differentiation, integration, series...

  • Page 255: Configuration Menus

    hp40g+.book Page 3 Friday, December 9, 2005 1:03 AM REWRI menu functions that enable you to rewrite an expression in another form. SOLV menu functions that enable you to solve equations, linear systems, and differential equations. TRIG menu functions that enable you to transform trigonometric expressions.
  • Page 256 hp40g+.book Page 4 Friday, December 9, 2005 1:03 AM • The fourth symbol, S, in the above example, indicates that you are in step-by-step mode. If you were not in step-by-step mode, this symbol would be D (which stands for Direct). The first line of an Equation Writer menu only indicates some of the mode settings.

  • Page 257: Entering Expressions And Subexpressions

    hp40g+.book Page 5 Friday, December 9, 2005 1:03 AM Entering expressions and subexpressions You type expressions in the Equation Writer is much the same way as you type them in the HOME screen, using the keys to directly enter numbers, letters and operators, and menus to select various functions and commands.
  • Page 258 hp40g+.book Page 6 Friday, December 9, 2005 1:03 AM this case, you have to press expression. The following illustration shows how an expression can be viewed as a tree in the Equation Writer. It illustrates a tree view of the expression: ---------------------------------------- - Suppose that the cursor is positioned to the right of 3: •...
  • Page 259 hp40g+.book Page 7 Friday, December 9, 2005 1:03 AM • More Examples Example1 If you enter: and press entire expression is selected. Pressing what is selected (that is, the entire expression) and returns: If you enter the same expression as earlier but press after the first X, as in: the 2 + X is selected and the next operation,...
  • 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 pressing evaluate it by pressing Example2 To enter X If, instead, you had to enter...
  • Page 261 hp40g+.book Page 9 Friday, December 9, 2005 1:03 AM Select the fifth branch by pressing the desired expression is in the Equation Writer, as shown at the right. Suppose that you want to select the second and third branches, that is: the second term.

  • Page 262: Cursor Mode

    hp40g+.book Page 10 Friday, December 9, 2005 1:03 AM Pressing the result of the partial calculation. Summing up Pressing element and its neighbour to the right. you to exchange the selected element with its neighbour to the left. The selected element remains selected after you move it.

  • Page 263: How To Modify An Expression

    hp40g+.book Page 11 Friday, December 9, 2005 1:03 AM How to modify an expression If you’re typing an expression, the to erase what you’ve typed. If you’re selecting, you can: • • • • • • • • Equation Writer Cancel the selection without deleting the expression by pressing .

  • Page 264: Accessing Cas Functions

    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 functions, and you can access them in various ways. General principle: When you have written an expression in the Equation Writer, all you have to do is press the entire expression, if nothing is selected).
  • Page 265 hp40g+.book Page 13 Friday, December 9, 2005 1:03 AM select the entire expression and press obtain: However, if you type: select the entire expression and press obtain 1. How to enter infix An infix function is one that is typed between its functions arguments.
  • 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 FACTOR() is displayed in the Equation Writer, with the cursor between the parentheses (as shown at the right). Enter your expression, using the rules of selection described earlier.
  • Page 267 hp40g+.book Page 15 Friday, December 9, 2005 1:03 AM Press to obtain the an intermediate result (4 – 4) again to evaluate the intermediate result. The final answer is 12. Second option: arguments first, then function Enter your expression, using the rules of selection described earlier.

  • Page 268: Equation Writer Variables

    hp40g+.book Page 16 Friday, December 9, 2005 1:03 AM Press intermediate result, (4– 2)(4 + 2), and evaluate the intermediate result. The final answer, as before, is 12. N o t e If you call a CAS function while you’re writing an expression, whatever is currently selected is copied to the function’s first or main argument.

  • Page 269: The Keyboard In The Equation Writer

    hp40g+.book Page 17 Friday, December 9, 2005 1:03 AM • • • • The keyboard in the Equation Writer The keys mentioned in this section have different functions when pressed in the Equation Writer than when used elsewhere. MATH key the Equation Writer, displays just those functions used in symbolic calculation.
  • Page 270 hp40g+.book Page 18 Friday, December 9, 2005 1:03 AM Diff&Int ( • The Complex menu, providing functions specific to manipulating with complex numbers. The Constant menu, containing e, i,∞ and π. • • The Hyperb. menu, containing hyperbolic functions. • The Integer menu, containing functions that enable you to perform integer arithmetic.
  • Page 271 hp40g+.book Page 19 Friday, December 9, 2005 1:03 AM SYMB key Pressing the the Equation Writer gives you access to CAS history. As in the HOME screen history, the calculations are written on the left and the results are written on the right. Using the arrow keys, you can scroll through the history.
  • Page 272 Equation Writer. 15-20 in the Equation Writer causes the puts the calculator into in the Equation Writer causes the puts the calculator into exact in the Equation Writer enables you to arrow keys to see to return in Equation Writer...
  • 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: Equation Writer 0 for ∞ 1 for i 3 for π 5 for < 6 for > 8 for ≤...
  • Page 274 hp40g+.book Page 22 Friday, December 9, 2005 1:03 AM...

  • Page 275: Step-By-Step Examples

    hp40g+.book Page 1 Friday, December 9, 2005 1:03 AM Step-by-Step Examples Introduction This chapter illustrates the power of CAS, and the Equation Writer, by working though a number of examples. Some of these examples are variations on questions from senior math examination papers. The examples are given in order of increasing difficulty.
  • Page 276 hp40g+.book Page 2 Friday, December 9, 2005 1:03 AM Press numerator. Press entire fraction. Press selected fraction, giving the result shown at the right. Example 2 Given that write C in the form Solution: In the Equation Writer, enter C by typing: Press select Press...
  • Page 277 hp40g+.book Page 3 Friday, December 9, 2005 1:03 AM Step-by-Step Examples Press to factor 5 ⋅ 20 into Press to select 5 ⋅ simplify it. Press to select – 3 12 to exchange with – Press to select 2 45 to select 45.
  • Page 278 hp40g+.book Page 4 Friday, December 9, 2005 1:03 AM Press evaluate the selection. It remains to transform 3 12 with same procedure as undertaken a number of times above. You will find that out. Hence the result is Example 3 Given the expression •...
  • Page 279 hp40g+.book Page 5 Friday, December 9, 2005 1:03 AM Press equation, then press Press FACTOR, press then as shown at the right. Now press SOLVEVX, press press shown at the right. Press CAS history, select D or a version of it, and press Press press complete the second...
  • Page 280 hp40g+.book Page 6 Friday, December 9, 2005 1:03 AM Press LINSOLVE and press Enter 17 If you are working in step by step mode, pressing at the right. Press produce the next step in the solution: Press produce the reduction result: Pressing produces the final result:...
  • Page 281 hp40g+.book Page 7 Friday, December 9, 2005 1:03 AM 1. Find the exact length of AB in centimetres. 2. Determine the equation of the line AB. Type: First method Accept the change to Complex mode, if necessary. Note that pressing returns the coordinates in complex form: –1+3i.
  • Page 282 hp40g+.book Page 8 Friday, December 9, 2005 1:03 AM Press simplify the result to Y = 2X+5. Type: Second method (-3,-1 )-(-1,3) The answer is –(2+4i). With the answer still selected, apply the ABS command by pressing Pressing method 1 above. You can also determi1ne the equation of the line typing: DROITE(( -1,3), (-3,-1))
  • Page 283 DEF(A(N) = 4 · 10 –1) DEF(B(N) = 2 · 10 –1) DEF(C(N) = 2 · 10 . For example: yields 39 yields 399 yields 3999 yields 19 yields 199 yields 1999 and c can have, the calculator is × c 16-9...
  • Page 284 hp40g+.book Page 10 Friday, December 9, 2005 1:03 AM Show that the whole numbers k such that: ≤ k 10 We have: Moreover, decimal notation can only end in 9. We also have: Let’s consider whether B(3) is a prime number. Type ISPRIME?(B(3)) and press result is 1, which means...
  • Page 285 In this case, the factors are 3, 23, 29 and 1999. Now let’s consider whether b Here, the calculator is useful only for trying out different values of n. To show that b to note that: That means that the common divisors of b...
  • Page 286 hp40g+.book Page 12 Friday, December 9, 2005 1:03 AM GCD c Part 2 Given the equation: ⋅ where the integers x and y are unknown and b are defined as in part 1 above: 1. Show that [1] has at least one solution. 2.
  • Page 287 Page 13 Friday, December 9, 2005 1:03 AM The calculator is not needed for finding the general solution to equation [1]. We started with and have established that So, by subtraction we have: According to Gauss’s Theorem, Hence there exists...
  • Page 288 hp40g+.book Page 14 Friday, December 9, 2005 1:03 AM the circle C, M will move on a curve Γ. In this exercise we will study and plot Γ. 1. Let 2. Compare x(–t) with x(t) and y(–t) with y(t). 3. Compute x′(t) and find the variations of x over [0, π]. 4.
  • Page 289 hp40g+.book Page 15 Friday, December 9, 2005 1:03 AM Selecting the entire expression and pressing gives the result at the right: Now linearize the result by applying the LIN command (which can be found on the menu). The result, after accepting the switch to complex mode, is shown at the right: Now store the result in...
  • Page 290 hp40g+.book Page 16 Friday, December 9, 2005 1:03 AM DEF command to it. Press definition. To calculate the real part of the expression, apply the IM command (available on the COMPLEX submenu of the MATH menu) to the stored variable M. Press result at the right: Finally, define the result as...
  • Page 291 hp40g+.book Page 17 Friday, December 9, 2005 1:03 AM Then press produce the result at the right: In other words, y t – part of Since axis, we can deduce that the x-axis is an axis of symmetry Part 3 Calculate Pressing result at the right:...
  • Page 292 hp40g+.book Page 18 Friday, December 9, 2005 1:03 AM Part 4 To calculate by typing: DERVX(Y(t)). Pressing Press simplify the result: Select FACTOR and press You can now define the function way that you defined x′ t ( ) Part 5 To show the variations of x t ( ) The independent variable must be t which it should be as...
  • Page 293 hp40g+.book Page 19 Friday, December 9, 2005 1:03 AM Now press the graphs. Part 6 To find the values of return to CAS, type each function in turn and press simplification). For example, pressing gives the result at the right: Likewise, pressing answer at the right: The other results are:...
  • 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 answer: The example at the right shows the case for t = π/3. Selecting the entire expression and pressing message shown at the right.
  • Page 295 hp40g+.book Page 21 Friday, December 9, 2005 1:03 AM Now we will graph Γ, which is a parametric curve. In the Equation Writer, type X(t) + i × Y(t). Select the entire expression and press Now press Parametric and press destination and press To make the graph of Γ, quit CAS and choose the Parametric aplet.
  • Page 296 Page 22 Friday, December 9, 2005 1:03 AM Exercise 8 For this exercise, make sure that the calculator is in exact real mode with X as the current variable. Part 1 For an integer, n, define the following: Define g over [0,2] where: g x ( ) 1.
  • Page 297 hp40g+.book Page 23 Friday, December 9, 2005 1:03 AM Solution 1 Start by defining G(X): Now press Press the numerator and denominator, and then press leaves G(X) displayed: Finally, apply the TABVAR function: The first line of the variation table gives the sign of g′...
  • Page 298 Now calculate g(2) by typing G(2) and pressing The answer is The two results prove that: ≤ -- - Solution 2 The calculator is not needed here. Simply stating that: -- - ≥ is sufficient to show that, for -- - -- - e...
  • Page 299 hp40g+.book Page 25 Friday, December 9, 2005 1:03 AM We can now see that: To justify the preceding calculation, we must assume that If you are not sure, you can use the INTVX function as illustrated at the right: Note that the INTVX command is on the menu.
  • Page 300 hp40g+.book Page 26 Friday, December 9, 2005 1:03 AM NOTE pressing and change the INDEP VAR setting. To check the result, we can say that: → and that therefore: → or, simplifying: → If the limit inequalities in solution 2 above, we get: -- - 2 ⋅...
  • Page 301 hp40g+.book Page 27 Friday, December 9, 2005 1:03 AM Solution 1 Start by defining the following: Now type PROPFRAC(G(X)). Note that PROPFRAC can be found on the POLYNOMIAL submenu of the MATH menu. Pressing result shown at the right. Solution 2 Enter the integral: Pressing result shown at the right:...
  • Page 302 Page 28 Friday, December 9, 2005 1:03 AM Solution 3 The calculator is not needed here. Simply stating that -- - increases for inequality: ≤ Solution 4 g x ( ) Since we get: g x ( ) g x ( )e and then, integrating: ≤...
  • Page 303 hp40g+.book Page 29 Friday, December 9, 2005 1:03 AM Step-by-Step Examples 16-29...
  • Page 304 hp40g+.book Page 30 Friday, December 9, 2005 1:03 AM...

  • Page 305: Variables And Memory Management

    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. •...

  • Page 306: Storing And Recalling Variables

    hp40g+.book Page 2 Friday, December 9, 2005 1:03 AM Storing and recalling variables You can store numbers or expressions from a previous input or result into variables. Numeric Precision A number stored in a variable is always stored as a 12- digit mantissa with a 3-digit exponent.
  • Page 307 To recall a value To recall a variable’s value, type the name of the variable and press To use variables in You can use variables in calculations. The calculator calculations substitutes the variable’s value in the calculation: To clear a variable...

  • Page 308: The Vars Menu

    The VARS menu You use the VARS menu to access all variables in the calculator. The VARS menu is organised by category. For each variable category in the left column, there is a list of variables in the right column. You select a variable category and then select a variable in the category.
  • Page 309 hp40g+.book Page 5 Friday, December 9, 2005 1:03 AM 5. Choose whether to place the variable name or the 6. Press Example This example demonstrates how to use the VARS menu to add the contents of two list variables, and to store the result in another list variable.
  • Page 310 hp40g+.book Page 6 Friday, December 9, 2005 1:03 AM 4. Enter data for L2. 5. Press 6. Open the variable menu and select L1. 7. Copy it to the command line. Note: Because the rather than its contents, is copied to the command line.

  • Page 311: Home Variables

    hp40g+.book Page 7 Friday, December 9, 2005 1:03 AM Home variables It is not possible to store data of one type in a variable of another type. For example, you use the Matrix catalog to create matrices. You can create up to ten matrices, and you can store these in variables M0 to M9.
  • Page 312 hp40g+.book Page 8 Friday, December 9, 2005 1:03 AM Aplet variables Most aplet variables store values that are unique to a particular aplet. These include symbolic expressions and equations (see below), settings for the Plot and Numeric views, and the results of some calculations such as roots and intersections.

  • Page 313: Memory Manager

    Page 9 Friday, December 9, 2005 1:03 AM Memory Manager You can use the Memory Manager to determine the amount of available memory on the calculator. You can also use Memory Manager to organize memory. For example, if the available memory is low, you can use the Memory Manager to determine which aplets or variables consume large amounts of memory.
  • Page 314 hp40g+.book Page 10 Friday, December 9, 2005 1:03 AM...

  • Page 315: Matrices

    hp40g+.book Page 1 Friday, December 9, 2005 1:03 AM Matrices Introduction 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.

  • Page 316: Creating And Storing Matrices

    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 matrices. CLEAR Moves to the end or the beginning of the catalog.
  • Page 317 hp40g+.book Page 3 Friday, December 9, 2005 1:03 AM 2. Highlight the matrix variable name you want to use 3. Select the type of matrix to create. 4. For each element in the matrix, type a number or an 5. Use the cursor keys to move to a different row or 6.

  • Page 318: Working With Matrices

    Matrix edit keys The following table lists the matrix edit key operations. 18-4 and choose the method of sending. on the receiving calculator and choose Meaning Copies the highlighted element to the edit line. Inserts a row of zeros above, or a column of zeros to the left, of the highlighted cell.
  • Page 319 hp40g+.book Page 5 Friday, December 9, 2005 1:03 AM To display a matrix • • To display one In HOME, enter matrixname(row,column). For example, element if M2 is [[3,4],[5,6]], then M2(1,2) To create a matrix 1. Enter the matrix in the edit line. Start and end the in HOME 2.

  • Page 320: Matrix Arithmetic

    hp40g+.book Page 6 Friday, December 9, 2005 1:03 AM To store one In HOME, enter, value element For example, to change the element in the first row and second column of M5 to 728, then display the resulting matrix: An attempt to store an element to a row or column beyond the size of the matrix results in an error message.
  • Page 321 hp40g+.book Page 7 Friday, December 9, 2005 1:03 AM To multiply and For division by a scalar, enter the matrix first, then the divide by a scalar operator, then the scalar. For multiplication, the order of the operands does not matter. The matrix and the scalar can be real or complex.

  • Page 322: Solving Systems Of Linear Equations

    hp40g+.book Page 8 Friday, December 9, 2005 1:03 AM To divide by a For division of a matrix or a vector by a square matrix, square matrix the number of rows of the dividend (or the number of elements, if it is a vector) must equal the number of rows in the divisor.
  • Page 323 hp40g+.book Page 9 Friday, December 9, 2005 1:03 AM 3. Return to the Matrix 4. Create a new matrix. 5. Enter the equation 6. Return to HOME and enter the calculation to The result is a vector of the solutions x = 2, y = 3 and z = –2. An alternative method, is to use the RREF function.

  • Page 324: Matrix Functions And Commands

    hp40g+.book Page 10 Friday, December 9, 2005 1:03 AM Matrix functions and commands About functions • 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.
  • Page 325 hp40g+.book Page 11 Friday, December 9, 2005 1:03 AM COND Condition Number. Finds the 1-norm (column norm) of a square matrix. CROSS Cross Product of vector1 with vector2. Determinant of a square matrix. Dot Product of two arrays, matrix1 matrix2. EIGENVAL Displays the eigenvalues in vector form for matrix.
  • Page 326 hp40g+.book Page 12 Friday, December 9, 2005 1:03 AM LU Decomposition. Factors a square matrix into three matrices: {[[lowertriangular]],[[uppertriangular]],[[permutation]]} The uppertriangular has ones on its diagonal. LU(matrix) MAKEMAT Make Matrix. 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 current column number for J.

  • Page 327: Examples

    hp40g+.book Page 13 Friday, December 9, 2005 1:03 AM SPECNORM Spectral Norm of matrix. SPECRAD Spectral Radius of a square matrix. Singular Value Decomposition. Factors an m × n matrix into two matrices and a vector: {[[m × m square orthogonal]],[[n × n square orthogonal]], [real]}.
  • Page 328 hp40g+.book Page 14 Friday, December 9, 2005 1:03 AM column 2) is swapped with element 2,1; element 2,3 is swapped with element 3,2; and so on. For example, TRN([[1,2],[3,4]]) creates the matrix [[1,3],[2,4]]. Reduced-Row The following set of equations Echelon Form can be written as the augmented matrix 1 2 –...
  • 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...
  • Page 330 hp40g+.book Page 16 Friday, December 9, 2005 1:03 AM...

  • Page 331: Lists

    hp40g+.book Page 1 Friday, December 9, 2005 1:03 AM Lists You can do list operations in HOME and in 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 of real numbers such as {1,2,3}.
  • Page 332 Meaning Opens the highlighted 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”...
  • Page 333 hp40g+.book Page 3 Friday, December 9, 2005 1:03 AM List edit keys When you press following keys are available to you: Create a list in 1. Enter the list on the edit line. Start and end the list HOME 2. Press Lists to create or change a list, the Meaning...

  • Page 334: Displaying And Editing Lists

    hp40g+.book Page 4 Friday, December 9, 2005 1:03 AM Displaying and editing lists To display a list • In the List catalog, highlight the list name and press • In HOME, enter the name of the list and press To display one In HOME, enter listname(element#).
  • Page 335 hp40g+.book Page 5 Friday, December 9, 2005 1:03 AM To insert an element 1. Open the List catalog. in a list 2. Press 3. Press 4. Press To store one In HOME, enter value element example, to store 148 as the second element in L1, type Lists LIST highlight the name of...

  • Page 336: Deleting Lists

    List functions have the following syntax: • Functions have arguments that are enclosed in parentheses and separated by commas. Example: CONCAT(L1,L2). An argument can be either a list 19-6 CLEAR and choose the method of sending. on the receiving calculator and choose (the Lists...
  • Page 337 hp40g+.book Page 7 Friday, December 9, 2005 1:03 AM • Common operators like +, –, ×, and / can take lists as arguments. If there are two arguments and both are lists, then the lists must have the same length, since the calculation pairs the elements.
  • Page 338 hp40g+.book Page 8 Friday, December 9, 2005 1:03 AM MAKELIST Calculates a sequence of elements for a new list. Evaluates expression with variable from begin to end values, taken at increment steps. MAKELIST(expression,variable,begin,end, increment) The MAKELIST function generates a series by automatically producing a list from the repeated evaluation of an expression.

  • Page 339: Finding Statistical Values For List Elements

    hp40g+.book Page 9 Friday, December 9, 2005 1:03 AM SIZE Calculates the number of elements in a list. Also works with matrices. ΣLIST Calculates the sum of all elements in list. Example SORT Sorts elements in ascending order. Finding statistical values for list elements To find values such as the mean, median, maximum, and minimum values of the elements in a list, use the Statistics aplet.
  • Page 340 hp40g+.book Page 10 Friday, December 9, 2005 1:03 AM 3. Start the Statistics aplet, and select 1-variable mode (press 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).

  • Page 341: Notes And Sketches

    Page 1 Friday, December 9, 2005 1:03 AM Notes and sketches Introduction The HP 40gs has text and picture editors for entering notes and sketches. • • Aplet note view You can attach text to an aplet in its Note view.
  • Page 342 hp40g+.book Page 2 Friday, December 9, 2005 1:03 AM Note edit keys 20-2 Meaning Space key for text entry. Displays next page of a multi-page note. Alpha-lock for letter entry. Lower-case alpha-lock for letter entry. Backspaces cursor and deletes character. Deletes current character.

  • Page 343: Aplet Sketch View

    hp40g+.book Page 3 Friday, December 9, 2005 1:03 AM Aplet sketch view You can attach pictures to an aplet in its Sketch view aplet. Press any other view key or Sketch view Sketch keys To draw a line 1. In an aplet, press 2.
  • Page 344 hp40g+.book Page 4 Friday, December 9, 2005 1:03 AM To draw a box 1. In Sketch view, press where you want any corner of the box to be. 2. Press 3. Move the cursor to mark the opposite corner for the box.
  • Page 345 hp40g+.book Page 5 Friday, December 9, 2005 1:03 AM To label parts of a 1. Press sketch 2. Press 3. Position the label where you want it by pressing the 4. Press 5. Press To create a set of You can create a set of up to ten sketches. This allows for sketches simple animation.

  • Page 346: The Notepad

    hp40g+.book Page 6 Friday, December 9, 2005 1:03 AM To import a You can copy the contents of a graphics variable into the graphics variable Sketch view of an aplet. 1. Open the Sketch view of the aplet ( The graphic will be copied here. 2.
  • Page 347 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 from another HP 40gs or PC. Deletes the selected note.
  • 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.

  • Page 349: Programming

    • • • H I N T More information on programming, including examples and special tools, can be found at HP’s calculators web site: http://www.hp.com/calculators The Contents of a An HP 40gs program contains a sequence of numbers, mathematical expressions, and commands that execute Program automatically to perform a task.

  • Page 350: Program Catalog

    HOME, or the last data you entered 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.
  • Page 351 Prompts for a new program name, then opens an empty program. Transmits the highlighted program to another HP 40gs or to a disk drive. Receives the highlighted program from another HP 40gs or from a disk drive. Runs the highlighted program.

  • Page 352: Creating And Editing Programs

    4. Enter your program. When done, start any other activity. Your work is saved automatically. Enter 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.
  • Page 353 PROGRM open the Program catalog. to edit, and press . The HP 40gs opens the Program Editor. The name of your program appears in the title bar of the display. You can use the following keys to edit your program.
  • Page 354 hp40g+.book Page 6 Friday, December 9, 2005 1:03 AM Editing keys The editing keys are: 21-6 Meaning Inserts the character at the editing point. Inserts space into text. Displays previous page of the program. Displays next page of the program. Moves up or down one line.

  • Page 355: Using Programs

    HOME, the HP 40gs displays the contents of Ans (Home variable containing the last result), when the program has finished. If you start the program from the Program catalog, the HP 40gs returns you to the Program catalog when the program ends. Debug a...
  • Page 356 PC (such as a connectivity kit). 21-8 to open the Program catalog. PROGRM to open the variables menu. to quickly scroll to Program. , then highlight the program you want to , then press on the receiving calculator. Programming on the...

  • Page 357: Customizing An Aplet

    hp40g+.book Page 9 Friday, December 9, 2005 1:03 AM Delete a To delete a program: program 1. Press 2. Highlight a program to delete, then press Delete all You can delete all programs at once. programs 1. In the Program catalog, press 2.

  • Page 358: Aplet Naming Convention

    hp40g+.book Page 10 Friday, December 9, 2005 1:03 AM 4. Develop a program that uses the SETVIEWS command to modify the aplet’s VIEWS menu. The menu options provide links to associated programs. You can specify any other programs that you want transferred with the aplet.
  • 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 2. Create a program 3. Create a program 4. Create a program 5. Create a program Configuring the Setviews menu option programs Programming...
  • Page 360 hp40g+.book Page 12 Friday, December 9, 2005 1:03 AM 6. Open the Program catalog and create a program named “EXP.SV”. Include the following code in the program. Each entry line after the command SETVIEWS is a trio that consists of a VIEWS menu text line (a space indicates none), a program name, and a number that defines the view to go to after the program has run its course.

  • Page 361: Programming Commands

    9. You can now return to the Aplet library and press 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 accessing them from the Commands menu.

  • Page 362: Aplet Commands

    • All the programs 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.
  • Page 363 hp40g+.book Page 15 Friday, December 9, 2005 1:03 AM • Command syntax The syntax for the command is as follows: Within each Prompt/ProgramName/ViewNumber trio, you separate each item with a semi-colon. Prompt Prompt is the text that is displayed for the corresponding entry in the Views menu.
  • 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 the number of a view to start after the program finishes running.

  • Page 365: Branch Commands

    hp40g+.book Page 17 Friday, December 9, 2005 1:03 AM View numbers The Function aplet views are numbered as follows: View numbers from 15 on will vary according to the parent aplet. The list shown above is for the Function aplet. Whatever the normal VIEWS menu for the parent aplet, the first entry will become number 15, the second number 16 and so on.
  • Page 366 (or until all the test-clauses evaluate to false). IFERR... Many conditions are automatically recognized by the HP THEN... 40gs as error conditions and are automatically treated as errors in programs. ELSE… END... 21-18 THEN true-clause...

  • Page 367: Drawing Commands

    Xmin, Xmax, Ymin, and Ymax values. The following examples assume the HP 40gs default settings with the Function aplet as the current aplet. Draws a circular arc, of given radius, whose centre is at (x,y) The arc is drawn from start_angle_measurement to end_angle_measurement.
  • Page 368 hp40g+.book Page 20 Friday, December 9, 2005 1:03 AM Example ARC 0;0;2;0;2π: FREEZE: Draws a circle centered at (0,0) of radius 2. The FREEZE command causes the circle to remain displayed on the screen until you press a key. Draws a box with diagonally opposite corners (x1,y1) and (x2,y2).

  • Page 369: Graphic Commands

    Creates a 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 display like that created by the SHOW operation.
  • Page 370 hp40g+.book Page 22 Friday, December 9, 2005 1:03 AM GROBXOR Using the logical XOR, superimposes graphicname2 onto graphicname1. The upper left corner of graphicname2 is placed at position. GROBXOR graphicname1;(position);graphicname2: MAKEGROB Creates graphic with given width, height, and hexadecimal data, and stores it in graphicname. MAKEGROB graphicname;width;height;hexdata: PLOT→...

  • Page 371: Loop Commands

    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 below illustrate each of these structures incrementing the variable A from 1 to 12.

  • Page 372: Matrix Commands

    hp40g+.book Page 24 Friday, December 9, 2005 1:03 AM Matrix commands The matrix commands take variables M0–M9 as arguments. ADDCOL Add Column. Inserts values into a column before column_number in the specified matrix. You enter the values as a vector. The values must be separated by commas and the number of values must be the same as the number of rows in the matrix name.

  • Page 373: Print Commands

    SWAPROW Swap Rows. Exchanges row1 and row2 in the specified matrix. Print commands These commands print to an HP infrared printer, for example the HP 82240B printer. PRDISPLAY Prints the contents of the display. PRHISTORY Prints all objects in the history.

  • Page 374: Prompt Commands

    hp40g+.book Page 26 Friday, December 9, 2005 1:03 AM PRVAR Prints name and contents of variablename. PRVAR variablename: You can also use the PRVAR command to print the contents of a program or a note. PRVAR programname;PROG: PRVAR notename;NOTE: Prompt commands BEEP Beeps at the frequency and for the time you specify.
  • Page 375 hp40g+.book Page 27 Friday, December 9, 2005 1:03 AM Example If you have stored {1,2,3,4} in variable L1, entering CLVAR L1 will clear L1. DISP Displays textitem in a row of the display at the line_number. A text item consists of any number of expressions and quoted strings of text.
  • Page 376 hp40g+.book Page 28 Friday, December 9, 2005 1:03 AM Examples 5.152000 10.1500 EDITMAT Matrix Editor. Opens the Matrix editor for the specified matrix. Returns to the program when user presses EDITMAT matrixname: The EDITMAT command can also be used to create matrices.

  • Page 377: Stat-One And Stat-Two Commands

    hp40g+.book Page 29 Friday, December 9, 2005 1:03 AM Example MSGBOX Displays a message box containing textitem. A text item consists of any number of expressions and quoted strings of text. The expressions are evaluated and turned into strings of text. For example, "AREA IS:"...

  • Page 378: Stat-Two Commands

    hp40g+.book Page 30 Friday, December 9, 2005 1:03 AM Stat-One commands DO1VSTATS Calculates STATS using datasetname and stores the results in the corresponding variables: NΣ, TotΣ, MeanΣ, PVarΣ, SVarΣ, PSDev, SSDev, MinΣ, Q1, Median, Q3, and MaxΣ. Datasetname can be H1, H2, ..., or H5. Datasetname must include at least two data points.

  • Page 379: Storing And Retrieving Variables In Programs

    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 aplets.
  • Page 380 hp40g+.book Page 32 Friday, December 9, 2005 1:03 AM Coord Turns the coordinate-display mode in Plot view on or off. Function From Plot view, use the Menu mean key to toggle Parametric coordinate display on an off. Polar In a program, type Sequence Solve Statistics...
  • Page 381 hp40g+.book Page 33 Friday, December 9, 2005 1:03 AM Hwidth Sets the width of histogram bars. Statistics From Plot Setup in 1VAR stats set a value for Hwidth In a program, type Indep Defines the value of the independent variable used in tracing mode.
  • Page 382 hp40g+.book Page 34 Friday, December 9, 2005 1:03 AM Nmin / Nmax Defines the minimum and maximum independent variable values. Appears as the NRNG fields in the Plot Setup input Sequence form. From Plot Setup, enter values for NRNG. In a program, type where Recenter Recenters at the crosshairs locations when zooming.
  • Page 383 hp40g+.book Page 35 Friday, December 9, 2005 1:03 AM Simult Enables you to choose between simultaneous and sequential graphing of all selected expressions. Function Parametric From Plot Setup, check (or uncheck) _SIMULT Polar Sequence In a program, type Slope Contains the last value found by the Slope function in the Plot-FCN menu.
  • Page 384 hp40g+.book Page 36 Friday, December 9, 2005 1:03 AM Tmin / Tmax Sets the minimum and maximum independent variable values. Appears as the TRNG field in the Plot Setup input Parametric form. From Plot Setup, enter values for TRNG. In a program, type where Tracing Turns the tracing mode on or off in Plot view.
  • Page 385 hp40g+.book Page 37 Friday, December 9, 2005 1:03 AM Xtick Sets the distance between tick marks for the horizontal AAll Aplets axis. From the Plot Setup input form, enter a value for Xtick. In a program, type Ytick Sets the distance between tick marks for the vertical axis. All Aplets From the Plot Setup input form, enter a value for Ytick.

  • Page 386: Symbolic-View Variables

    hp40g+.book Page 38 Friday, December 9, 2005 1:03 AM Xzoom Sets the horizontal zoom factor. All Aplets From Plot-ZOOM-Set Factors, enter the value for XZOOM. In a program, type where The default value is 4. Yzoom Sets the vertical zoom factor. All Aplets From Plot-ZOOM-Set Factors, enter the value for YZOOM.
  • Page 387 hp40g+.book Page 39 Friday, December 9, 2005 1:03 AM X1, Y1...X9,Y9 Can contain any expression. Independent variable is T. X0,Y0 Example Parametric Can contain any expression. Independent variable is θ. R1...R9, R0 Polar Example U1...U9, U0 Can contain any expression. Independent variable is N. Sequence Example E1...E9, E0...

  • Page 388: Numeric-View Variables

    hp40g+.book Page 40 Friday, December 9, 2005 1:03 AM Example Cubic Numeric-view variables The following aplet variables control the Numeric view. The value of the variable applies to the current aplet only. C1...C9, C0 C0 through C9, for columns of data. Can contain lists. Statistics Enter data in the Numeric view In a program, type...

  • Page 389: Scientific Format

    hp40g+.book Page 41 Friday, December 9, 2005 1:03 AM 1 Standard 2 Fixed 3 Sci 4 Eng 5 Fraction 6 MixFraction Note: if Fraction or Mixed Fraction is chosen, the setting will be disregarded when labeling axes in the Plot view.
  • Page 390 hp40g+.book Page 42 Friday, December 9, 2005 1:03 AM NumStart Sets the starting value for a table in Numeric view. Function From Num Setup, enter a value for NUMSTART. Parametric Polar Sequence In a program, type NumStep Sets the step size (increment value) for an independent variable in Numeric view.

  • Page 391: Note Variables

    hp40g+.book Page 43 Friday, December 9, 2005 1:03 AM Example Note variables The following aplet variable is available in Note view. NoteText Use NoteText to recall text previously entered in Note view. All Aplets Sketch variables The following aplet variables are available in Sketch view.
  • Page 392 hp40g+.book Page 44 Friday, December 9, 2005 1:03 AM...

  • Page 393: Extending Aplets

    Page 1 Friday, December 9, 2005 1:03 AM Extending aplets Aplets are the application environments where you explore different classes of mathematical operations. You can extend the capability of the HP 40gs in the following ways: • • •...
  • Page 394 hp40g+.book Page 2 Friday, December 9, 2005 1:03 AM 1. Open the Solve aplet and save it under the new name. T R I A N G L E S 2. Enter the four formulas: 3. Decide whether you want the aplet to operate in Degrees, Radians, or Grads.

  • Page 395: Using A Customized Aplet

    hp40g+.book Page 3 Friday, December 9, 2005 1:03 AM Using a customized aplet To use the “Triangles” aplet, simply select the appropriate formula, change to the Numeric view and solve for the missing variable. Find the length of a ladder leaning against a vertical wall if it forms an angle of 35 extends 5 metres up the wall.

  • Page 396: Annotating An Aplet With Notes

    A convenient way to distribute or share problems in class and to turn in homework is to transmit (copy) aplets directly from one HP 40gs to another. This can take place via a suitable cable. ( You can use a serial cable with a 4-pin mini-USB connector, which plugs into the RS232 port on the calculator.
  • Page 397 Page 5 Friday, December 9, 2005 1:03 AM To transmit 1. Connect the PC or aplet disk drive to the calculator by an aplet 2. Sending calculator: Open the Library, highlight the 3. Receiving calculator: Open the aplet library and Extending aplets an appropriate cable.

  • Page 398: Sorting Items In The Aplet Library Menu List

    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.

  • Page 399: Glossary

    (or periods in Comma mode), such as CROSS(matrix1,matrix2). The basic starting point of the calculator. Go to HOME to do calculations. For aplet management: to start, save, reset, send and receive aplets.
  • Page 400 hp40g+.book Page 2 Friday, December 9, 2005 1:03 AM list matrix menu menu keys note program sketch variable vector A set of values separated by commas (periods if the Decimal Mark mode is set to Comma) and enclosed in braces. Lists are commonly used to enter statistical data and to evaluate a function with multiple values.

  • Page 401: Resetting The Hp 40Gs

    ReferenceInfo.fm Page 3 Friday, December 16, 2005 11:26 AM views Resetting the HP 40gs If the calculator “locks up” and seems to be stuck, you must reset it. This is much like resetting a PC. It cancels certain operations, restores certain conditions, and clears temporary memory locations.

  • Page 402: If The Calculator Does Not Turn On

    Page 4 Friday, December 9, 2005 1:03 AM If the calculator does not turn on If the HP 40gs does not turn on follow the steps below until the calculator turns on. You may find that the calculator turns on before you have completed the procedure.
  • Page 403 hp40g+.book Page 5 Friday, December 9, 2005 1:03 AM To install the main a. Slide up the battery compartment cover as illustrated. batteries b. Insert 4 new AAA (LR03) batteries into the main To install the a. Press down the holder. Push the plate to the shown backup battery b.

  • Page 404: Variables

    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, M0 Date HAngle...

  • Page 405: Function Aplet Variables

    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 Xcross Connect Ycross Coord Xtick FastRes Ytick Grid Xmin Indep Xmax InvCross Ymin Labels Ymax Recenter...

  • Page 406: Parametric Aplet Variables

    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 Tracing Connect Tstep Coord Xcross Grid Ycross Indep Xtick InvCross Ytick Labels Xmin Recenter Xmax Simult Ymin...

  • Page 407: Polar Aplet Variables

    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 Xcross Coord Ycross Grid Xtick Indep Ytick InvCross Xmin Labels Xmax Recenter Ymin Simult Ymax Umin...

  • Page 408: Sequence Aplet Variables

    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 R-10 Available name Axes Tracing Coord Xcross Grid Ycross Indep Xtick InvCross Ytick Labels Xmin Nmin Xmax Nmax Ymin Recenter...

  • Page 409: Solve Aplet Variables

    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 Xcross Connect Ycross Coord Xtick FastRes Ytick Grid Xmin Indep Xmax InvCross Ymin Labels Ymax Recenter Xzoom...

  • Page 410: Statistics Aplet Variables

    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 R-12 Available name Axes S4mark Connect S5mark Coord StatPlot Grid Tracing Hmin Xcross Hmax Ycross Hwidth Xtick Indep...

  • Page 411: Math Menu Categories

    hp40g+.book Page 13 Friday, December 9, 2005 1:03 AM MATH menu categories Math functions The math functions are: Category Calculus Complex Constant Hyperb. List Loop Available name ∂ ∫ TAYLOR CONJ MAXREAL MINREAL π ACOSH TANH ASINH ALOG ATANH COSH EXPM1 SINH LNP1...
  • Page 412 hp40g+.book Page 14 Friday, December 9, 2005 1:03 AM Category Matrix Polynom. Prob. Real Stat-Two Symbolic R-14 Available name (Continued) COLNORM COND RANK CROSS ROWNORM RREF SCHUR EIGENVAL SIZE EIGENVV SPECNORM IDENMAT SPECRAD INVERSE TRACE MAKEMAT POLYCOEF POLYFORM POLYEVAL POLYROOT COMB UTPC UTPF...

  • Page 413: Program Constants

    hp40g+.book Page 15 Friday, December 9, 2005 1:03 AM Category Tests Trig Program constants The program constants are: Category Angle Format SeqPlot S1...5fit StatMode StatPlot Available name (Continued) < IFTE ≤ ≠ > ≥ ACOT ACSC ASEC Available name Degrees Grads Radians Standard...

  • Page 414: Physical Constants

    hp40g+.book Page 16 Friday, December 9, 2005 1:03 AM Physical Constants The physical constants are: Category Chemist Phyics Quantum R-16 Available Name • Avogadro (Avagadro’s Number, • Boltz. (Boltmann, k) • mol. vo... (molar volume, Vm) • univ gas (universal gas, R) •...

  • Page 415: Cas Functions

    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 STORE EXPAND SUBST FACTOR TEXPAND PARTFRAC UNASSIGN QUOTE – CONJ SIGN DROITE ∞ π DERIV PREVAL DERVX...
  • Page 416 hp40g+.book Page 18 Friday, December 9, 2005 1:03 AM Category Polynom. Real Rewrite Solve Tests Trig R-18 Function (Continued) EGCD PARTFRAC FACTOR PROPFRAC PTAYL HERMITE QUOT REMAINDER LEGENDRE TCHEBYCHEFF CEILING FLOOR FRAC DISTRIB POWEXPAND EPSX0 SINCOS EXPLN SIMPLIFY EXP2POW XNUM FDISTRIB LNCOLLECT DESOLVE...

  • Page 417: Program Commands

    hp40g+.book Page 19 Friday, December 9, 2005 1:03 AM Program commands The program commands are: Category Aplet Branch Drawing Graphic Loop Matrix Print Prompt Stat-One Command CHECK SELECT SETVIEWS UNCHECK CASE THEN IFERR ELSE STOP LINE PIXOFF ERASE PIXON FREEZE TLINE DISPLAY→...

  • Page 418: Status Messages

    hp40g+.book Page 20 Friday, December 9, 2005 1:03 AM Category Stat-Two Status messages Message Bad Argument Type Bad Argument Value Infinite Result Insufficient Memory Insufficient Statistics Data Invalid Dimension Invalid Statistics Data Command (Continued) DO2VSTATS SETDEPEND SETINDEP Meaning Incorrect input for this operation.
  • Page 419 Function value, root, extremum, or intersection is not visible in the current screen. Problem with data reception from another calculator. Re- send the data. The command requires more arguments than you supplied. The global variable named does not exist.
  • Page 420 hp40g+.book Page 22 Friday, December 9, 2005 1:03 AM...

  • Page 421: Limited Warranty

    1. HP warrants to you, the end-user customer, that HP 2. HP warrants to you that HP software will not fail to 3. HP does not warrant that the operation of HP 4. HP products may contain remanufactured parts 5.
  • Page 422 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 editorial errors or omissions contained herein.

  • Page 423: Service

    hp40g+.book Page 3 Friday, December 9, 2005 1:03 AM Service Europe Asia Pacific Country : 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 +49-69-95307103 Greece +420-5-41422523 Holland +31-2-06545301 Italy +39-02-75419782 Norway +47-63849309...
  • Page 424 Columbia 9-800-114726 Peru 0-800-10111 Central 1-800-711-2884 America & Caribbean Guatemala 1-800-999-5105 Puerto Rico 1-877-232-0589 Costa Rica 0-800-011-0524 Telephone numbers U.S. 1800-HP INVENT Canada (905) 206-4663 or 800- HP INVENT ROTC = Rest of the country http://www.hp.com for the latest service...

  • Page 425: Regulatory Notices

    hp40g+.book Page 5 Friday, December 9, 2005 1:03 AM Regulatory Notices Federal Commu- This equipment has been tested and found to comply with the limits for a Class B digital device, pursuant to Part 15 nications of the FCC Rules. These limits are designed to provide Commission reasonable protection against harmful interference in a Notice...
  • 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 questions regarding this FCC declaration, contact: Hewlett-Packard Company P. O. Box 692000, Mail Stop 510101 Houston, Texas 77269-2000 Or, call 1-281-514-3333...
  • Page 427 hp40g+.book Page 7 Friday, December 9, 2005 1:03 AM Japanese Notice （VCCI） の基準に基づ く ク ラ ス B 情報技術装置です。 こ の装 置は、 家庭環境で使用する こ と を目的 と し ていますが、 この 装置がラ ジオやテ レ ビ ジ ョ ン受信機に近接 し て使用 さ れる と 、 受信障害を引き起...
  • Page 428 hp40g+.book Page 8 Friday, December 9, 2005 1:03 AM...

  • Page 429: Index

    hp40g+.book Page 1 Friday, December 9, 2005 1:03 AM Index ABCUV 14-62 ABS 14-45 absolute value 13-6 ACOS2S 14-38 add 13-4 ADDTMOD 14-51 ALGB menu 14-10 algebraic entry 1-19 alpha characters typing 1-6 alphabetical sorting 22-6 angle measure 1-10 in statistics 10-12 setting 1-11 animation 20-5 creating 20-5...
  • Page 430 hp40g+.book Page 2 Friday, December 9, 2005 1:03 AM bad guesses error message 7-7 batteries R-4 Bernoulli’s number 14-65 box-and-whisker plot 10-16 branch commands CASE...END 21-18 IF...THEN...ELSE...END 21-18 IFERR...THEN...ELSE 21-18 branch structures 21-17 build your own table 2-19 calculus operations 13-7 CAS 14-1 15-1 configuration 15-3...
  • 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 fitting 10-12 10-17...
  • Page 432 hp40g+.book Page 4 Friday, December 9, 2005 1:03 AM notes 20-2 programs 21-5 Editline Program catalog 21-2 editors 1-30 EGCD 14-55 eigenvalues 18-11 eigenvectors 18-11 element storing 18-6 E-lessons 1-12 engineering number format 1-11 EPSX0 14-29 equals for equations 13-17 logical test 13-19 Equation Writer 14-2 15-1...
  • Page 433 hp40g+.book Page 5 Friday, December 9, 2005 1:03 AM glossary R-1 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...
  • Page 434 hp40g+.book Page 6 Friday, December 9, 2005 1:03 AM using symbolic variables 13-23 independent values adding to table 2-19 independent variable defined for Tracing mode 21-33 inference confidence intervals 11-15 hypothesis tests 11-8 One-Proportion Z-Interval 11-17 One-Sample Z-Interval 11-15 One-Sample Z-Test 11-8 Two-Proportion Z-Interval 11-17 Two-Proportion Z-Test 11-11 Two-Sample T-Interval 11-19...
  • Page 435 hp40g+.book Page 7 Friday, December 9, 2005 1:03 AM finding statistical values in list ele- ments 19-9 generate a series 19-8 list function syntax 19-6 list variables 19-1 returning position of element in 19-8 reversing order in 19-8 sending and receiving 19-6 sorting elements 19-9 storing elements 19-1 19-4...
  • Page 436 hp40g+.book Page 8 Friday, December 9, 2005 1:03 AM redimension 21-24 replacing portion of matrix or vec- tor 21-25 sending or receiving 18-4 singular value decomposition 18-13 singular values 18-13 size 18-12 spectral norm 18-13 spectral radius 18-13 start Matrix Editor 21-24 storing elements 18-3 18-5 storing matrix elements 18-6...
  • Page 437 hp40g+.book Page 9 Friday, December 9, 2005 1:03 AM mixed fraction 1-11 scientific 1-10 Standard 1-10 numeric precision 17-9 Numeric view adding values 2-19 automatic 2-16 build your own table 2-19 display defining function for col- umn 2-17 recalculating 2-19 setup 2-16 2-19 automatic 1-1...
  • 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 21-31 grid 21-32 in menu map R-9 indep 21-33 labels 21-34 recenter 21-34 ycross 21-37 polynomial...
  • Page 439 10-13 formula 10-12 user-defined fit 10-13 relative error statistical 10-18 REMAINDER 14-59 REORDER 14-68 resetting aplet 22-3 calculator R-3 memory R-3 result copying to edit line 1-22 reusing 1-22 rigorous 14-6 RISCH 14-24 root interactive 3-10 nth 13-6...
  • Page 440 hp40g+.book Page 12 Friday, December 9, 2005 1:03 AM date 21-27 time 21-27 SEVAL 14-68 SIGMA 14-68 SIGMAVX 14-69 SIGN 14-46 sign reversal 7-6 SIMPLIFY 14-32 simplify 14-68 14-70 SINCOS 14-31 14-40 sine 13-4 inverse hyperbolic 13-9 singular value decomposition matrix 18-13 singular values matrix 18-13...
  • Page 441 hp40g+.book Page 13 Friday, December 9, 2005 1:03 AM Labels 21-34 Recenter 21-34 S1mark-S5mark 21-34 Ycross 21-37 step size of independent variable 21-36 step-by-step 14-6 STORE 14-14 storing list elements 19-1 19-4 19-6 matrix elements 18-3 18-5 results of calculation 17-2 value 17-2 strings literal in symbolic operations...
  • Page 442 hp40g+.book Page 14 Friday, December 9, 2005 1:03 AM COT 13-20 CSC 13-20 HALFTAN 14-40 SEC 13-20 SINCOS 14-40 TAN2CS2 14-40 TAN2SC 14-41 TAN2SC2 14-41 TRIGCOS 14-44 TRIGSIN 14-44 TRIGTAN 14-44 TRIGSIN 14-44 TRIGTAN 14-44 TRUNC 14-28 truncating values to decimal places 13-17 TSIMP 14-70 tstep 21-36...
  • Page 443 hp40g+.book Page 15 Friday, December 9, 2005 1:03 AM in 2-9 options 2-9 options within a table 2-18 out 2-9 redrawing table of numbers op- tions 2-18 square 2-10 un-zoom 2-11 within Numeric view 2-18 X-zoom 2-9 Y-zoom 2-10 I-15...
  • Page 444 hp40g+.book Page 16 Friday, December 9, 2005 1:03 AM...

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