# HP 49g+ User Manual

Graphing calculator.

hp 49g+
graphing calculator
user's manual

#### Summary of Contents for HP hp 49g+

• Page 1 49g+ graphing calculator user’s manual...
• Page 3 The present Guide contains examples that illustrate the use of the basic calculator functions and operations. The chapters in this user’s manual are organized by subject in order of difficulty: from the setting of calculator modes, to real and complex number calculations, operations with lists, vectors, and matrices, graphics, calculus applications, vector analysis, differential equations, probability and statistics.

Table of Contents Chapter 1 – Getting Started Basic Operations, 1-1 Batteries, 1-1 Turning the calculator on and off, 1-2 Adjusting the display contrast, 1-2 Contents of the calculator’s display, 1-2 Menus, 1-3 The TOOL menu, 1-3 Setting time and date, 1-4 Introducing the calculator’s keyboard, 1-4...
• Page 6 Creating algebraic expressions, 2-4 Using the Equation Writer (EQW) to create expressions, 2-5 Creating arithmetic expressions, 2-5 Creating algebraic expressions, 2-8 Organizing data in the calculator, 2-9 The HOME directory, 2-9 Subdirectories, 2-9 Variables, 2-10 Typing variable names, 2-10 Creating variables, 2-11...
• Page 7 Defining and using functions, 3-16 Reference, 3-18 Chapter 4 – Calculations with complex numbers Definitions, 4-1 Setting the calculator to COMPLEX mode, 4-1 Entering complex numbers, 4-2 Polar representation of a complex number, 4-2 Simple operations with complex numbers, 4-3...
• Page 8 The PARTFRAC function, 5-11 The FCOEF function, 5-11 The FROOTS function, 5-12 Step-by-step operations with polynomials and fractions, 5-12 Reference, 5-13 Chapter 6 – Solution to equations Symbolic solution of algebraic equations, 6-1 Function ISOL, 6-1 Function SOLVE, 6-2 Function SOLVEVX, 6-4 Function ZEROS, 6-4 Numerical solver menu, 6-5 Polynomial Equations, 6-6...
• Page 9 Chapter 8 – Vectors , 8-1 Entering vectors, 8-1 Typing vectors in the stack, 8-1 Storing vectors into variables in the stack, 8-2 Using the matrix writer (MTRW) to enter vectors, 8-2 Simple operations with vectors, 8-5 Changing sign, 8-5 Addition, subtraction, 8-5 Multiplication by a scalar, and division by a scalar, 8-6 Absolute value function, 8-6...
• Page 10 Solution by “division” of matrices, 9-10 References, 9-10 Chapter 10 – Graphics , 10-1 Graphs options in the calculator, 10-1 Plotting an expression of the form y = f(x), 10-2 Generating a table of values for a function, 10-3 Fast 3D plots, 10-5 Reference, 10-8 Chapter 11 –...
• Page 11 Solution to linear and non-linear equations, 14-1 Function LDEC, 14-2 Function DESOLVE, 14-3 The variable ODETYPE, 14-4 Laplace Transforms, 14-5 Laplace transforms and inverses in the calculator, 14-5 Fourier series, 14-6 Function FOURIER, 14-6 Fourier series for a quadratic function, 14-6 Reference, 14-8 Chapter 15 –...
• Page 12 Chapter 17 – Numbers in Different Bases The BASE menu, 17-1 Writing non-decimal numbers, 17-1 Reference, 17-2 Chapter 18 – Using SD cards Storing objects in the SD card, 18-1 Recalling an object from the SD card, 18-2 Purging an object from the SD card, 18-2 Limited Warranty –...
• ### Page 13: Chapter 1 - Getting Started

The following exercises are aimed at getting you acquainted with the hardware of your calculator. Batteries The calculator uses 3 AAA batteries as main power and a CR2032 lithium battery for memory backup. Before using the calculator, please install the batteries according to the following procedure.
• ### Page 14: Turning The Calculator On And Off

The \$(hold) - key combination produces a lighter display Contents of the calculator’s display Turn your calculator on once more. At the top of the display you will have two lines of information that describe the settings of the calculator.

The six labels associated with the keys A through F form part of a menu of functions. Since the calculator has only six soft menu keys, it only display 6 labels at any point in time. However, a menu can have more than six entries.
• ### Page 16: Setting Time And Date

TOOL menu is to press the I key (third key from the left in the second row of keys from the top of the keyboard). Setting time and date See Chapter 1 in the calculator’s User’s Guide to learn how to set time and date. Introducing the calculator’s keyboard The figure below shows a diagram of the calculator’s keyboard with the...
• Page 17 the blue ALPHA key, key (7,1), can be combined with some of the other keys to activate the alternative functions shown in the keyboard. For example, the P key, key(4,4), has the following six functions associated with it: Main function, to activate the SYMBolic menu „´...
• ### Page 18: Selecting Calculator Modes

… ), and ~ (P) keys. (CAT For detailed information on the calculator keyboard operation referee to Appendix B in the calculator’s User’s Guide. Selecting calculator modes This section assumes that you are now at least partially familiar with the use of choose and dialog boxes (if you are not, please refer to appendix A in the User’s Guide).
• ### Page 19: Operating Mode

The calculator offers two operating modes: Reverse Polish Notation (RPN) mode. mode (as indicated in the figure above), however, users of earlier HP calculators may be more familiar with the RPN mode. To select an operating mode, first open the CALCULATOR MODES input form by pressing the H button.
• Page 20 The display, for the RPN mode looks as follows: Notice that the display shows several levels of output labeled, from bottom to top, as 1, 2, 3, etc. This is referred to as the stack of the calculator. The Page 1-8...
• Page 21 3 upwards to occupy stack level 2. Finally, by pressing +, we are telling the calculator to apply the operator, or program, + to the objects occupying levels 1 and 2. The result, 5, is then placed in level 1.
• ### Page 22: Number Format And Decimal Dot Or Comma

Changing the number format allows you to customize the way real numbers are displayed by the calculator. You will find this feature extremely useful in operations with powers of tens or to limit the number of decimals in a result.
• ### Page 23: Standard Format

Press the right arrow key, ™, to highlight the zero in front of the option Press the @CHOOSE soft menu key and, using the up and down arrow Fix. keys, —˜, select, say, 3 decimals. calculator display. Enter number Page 1-11...
• ### Page 24: Scientific Format

Press the !!@@OK#@ soft menu key to complete the selection: Press the !!@@OK#@ soft menu key return to the calculator display. number now is shown as: Notice how the number is rounded, not truncated. Thus, the number 123.4567890123456, for this setting, is displayed as 123.457, and not as 123.456 because the digit after 6 is >...
• ### Page 25: Engineering Format

Fixed number of decimals in an earlier example). Press the !!@@OK#@ soft menu key return to the calculator display. number now is shown as: Because this number has three figures in the integer part, it is shown with four significative figures and a zero power of ten, while using the Engineering format.
• ### Page 26: Decimal Comma Vs. Decimal Point

Decimal points in floating-point numbers can be replaced by commas, if the user is more familiar with such notation. To replace decimal points for commas, change the FM option in the CALCULATOR MODES input form to commas, as follows (Notice that we have changed the Number Format to Std): •...
• ### Page 27: Coordinate System

To learn more about complex numbers and vectors, see Chapters 4 and 8, respectively, in this Guide. There are three coordinate systems available in the calculator: Rectangular (RECT), Cylindrical (CYLIN), and Spherical (SPHERE). To change coordinate system: •...
• ### Page 28: Selecting Cas Settings

To see the optional CAS settings use the following: • Press the H button to activate the CALCULATOR MODES input form. • To change CAS settings press the @@ CAS@@ soft menu key. The default values of the CAS setting are shown below: •...
• ### Page 29: Explanation Of Cas Settings

After having selected and unselected all the options that you want in the CAS MODES input form, press the @@@OK@@@ soft menu key. This will take you back to the CALCULATOR MODES input form. calculator display at this point, press the @@@OK@@@ soft menu key once more. Explanation of CAS settings •...
• ### Page 30: Selecting The Display Font

DISPLAY MODES input form, press the @@@OK@@@ soft menu key. This will take you back to the CALCULATOR MODES input form. calculator display at this point, press the @@@OK@@@ soft menu key once more. Selecting the display font First, press the H button to activate the CALCULATOR MODES input form.
• ### Page 31: Selecting Properties Of The Line Editor

When done with a font selection, press the @@@OK@@@ soft menu key to go back to the CALCULATOR MODES input form. to normal calculator display at this point, press the @@@OK@@@ soft menu key once more and see how the stack display change to accommodate the different font.
• ### Page 32: Selecting Properties Of The Stack

Selecting properties of the Stack First, press the H button to activate the CALCULATOR MODES input form. Within the CALCULATOR MODES input form, press the @@DISP@ soft menu key (D) to display the DISPLAY MODES input form. Press the down arrow key, ˜, once, to get to the Edit line.
• ### Page 33: Selecting Properties Of The Equation Writer (eqw)

Selecting properties of the equation writer (EQW) First, press the H button to activate the CALCULATOR MODES input form. Within the CALCULATOR MODES input form, press the @@DISP@ soft menu key (D) to display the DISPLAY MODES input form. Press the down arrow key, ˜, three times, to get to the EQW (Equation Writer) line.
• ### Page 34: Chapter 2 - Introducing The Calculator

In this chapter we present a number of basic operations of the calculator including the use of the Equation Writer and the manipulation of data objects in the calculator. Study the examples in this chapter to get a good grasp of the capabilities of the calculator for future applications.
• Page 35 In this case, when the expression is entered directly into the stack, as soon as you press the calculator will attempt to calculate a value for the expression. If the expression is entered between quotes, however, the calculator will reproduce the expression as entered. For example: ³...
• Page 36 … ï We will now enter the expression used above when the calculator is set to the RPN operating mode. We also set the CAS to Exact and the display to Textbook. The keystrokes to enter the expression between quotes are the same used earlier, i.e.,...
• ### Page 37: Creating Algebraic Expressions

Algebraic expressions include not only numbers, but also variable names. As an example, we will enter the following algebraic expression: We set the calculator operating mode to Algebraic, the CAS to Exact, and the display to Textbook. To enter this algebraic expression we use the following keystrokes: 2 * ~ l * R „...
• ### Page 38: Using The Equation Writer (eqw) To Create Expressions

Entering this expression when the calculator is set in the RPN mode is exactly the same as this Algebraic mode exercise. For additional information on editing algebraic expressions in the calculator’s display or stack see Chapter 2 in the calculator’s User’s Guide.
• Page 39 The cursor is shown as a left-facing key. The cursor indicates the current edition location. For example, for the cursor in the location indicated above, type now: * „ Ü 5 + 1 / 3 The edited expression looks as follows: Suppose that you want to replace the quantity between parentheses in the denominator (i.e., 5+1/3) with (5+ /2).
• Page 40 The expression now looks as follows: Suppose that now you want to add the fraction 1/3 to this entire expression, i.e., you want to enter the expression: First, we need to highlight the entire first term by using either the right arrow ) or the upper arrow ( ) keys, repeatedly, until the entire expression is ™...
• ### Page 41: Creating Algebraic Expressions

Creating algebraic expressions An algebraic expression is very similar to an arithmetic expression, except that English and Greek letters may be included. The process of creating an algebraic expression, therefore, follows the same idea as that of creating an arithmetic expression, except that use of the alphabetic keyboard is included. To illustrate the use of the Equation Writer to enter an algebraic equation we will use the following example.
• ### Page 42: Organizing Data In The Calculator

Chapter 2 of the calculator’s User’s Manual. Organizing data in the calculator You can organize data in your calculator by storing variables in a directory tree. The basis of the calculator’s directory tree is the HOME directory described next.
• ### Page 43: Variables

‘A’, ‘B’, ‘a’, ‘b’, ‘ ’, ‘ ’, ‘A1’, ‘AB12’, ‘ A12’,’Vel’,’Z0’,’z1’, etc. A variable can not have the same name as a function of the calculator. The reserved calculator variable names are the following: ALRMDAT, CST, EQ, EXPR, IERR, IOPAR, MAXR, MINR, PICT, PPAR, PRTPAR, VPAR, ZPAR, der_, e, i, n1,n2, …, s1, s2, …, DAT, PAR, ,...
• ### Page 44: Creating Variables

³ ~ ~ m „ a „ t „ h ~ ` ³ ~ ~ m „ ~ a t „ h ~ ` The calculator display will show the following (left-hand side is Algebraic mode, right-hand side is RPN mode):...
• Page 45 Press to create the variable. The variable is now shown in the soft menu key labels: The following are the keystrokes required to enter the remaining variables: A12: 3 V 5 K ~ a 1 2 ` ³ ~ „ r / „ Ü ~ „...
• ### Page 46: Rpn Mode

RPN mode (Use to change to RPN mode). Use the following @ @ O K @ @ keystrokes to store the value of –0.25 into variable : . At this point, the screen 0 . 2 5 \ ` ~ ‚ a ` will look as follows: This expression means that the value –0.25 is ready to be stored into .
• ### Page 47: Checking Variables Contents

‚ å ‚ é ~ „ r ³ „ ì * ~ „ r Q 2 ™ ™ ™ ³ ~ „ p 1 ™ ` K The screen, at this point, will look as follows: You will see six of the seven variables listed at the bottom of the screen: p1, z1, R, Q, A12, .
• ### Page 48: Using The Right-shift Key Followed By Soft Menu Key Labels

‚ @ L ‚ Listing the contents of all variables in the screen ‚ ˜ Use the keystroke combination to list the contents of all variables in the screen. For example: Press to return to normal calculator display. Page 2-15...
• ### Page 49: Deleting Variables

Deleting variables The simplest way of deleting variables is by using function PURGE. This function can be accessed directly by using the TOOLS menu ( ) , or by „ ¡ using the FILES menu @ @ O K @ @ Using function PURGE in the stack in Algebraic mode Our variable list contains variables p1, z1, Q, R, and .
• ### Page 50: Undo And Cmd Functions

Soft MENUs, and vice versa, through an exercise. Although not applied to a specific example, the present exercise shows the two options for menus in the calculator (CHOOSE boxes and soft MENUs). In this exercise, we use the ORDER command to reorder variables in a directory, we use: „...
• Page 51 There is an alternative way to access these menus as soft MENU keys, by setting system flag 117. (For information on Flags see Chapters 2 and 24 in the calculator’s User’s Guide). To set this flag try the following: — — — — — — —...
• Page 52 117 to soft MENU. The screen will @ C H E C K ! reflect that change: Press twice to return to normal calculator display. Now, we’ll try to find the ORDER command using similar keystrokes to those „ °...
• ### Page 53: References

References For additional information on entering and manipulating expressions in the display or in the Equation Writer see Chapter 2 of the calculator’s User’s Guide. For CAS (Computer Algebraic System) settings, see Appendix C in the calculator’s User’s Guide. For information on Flags see, Chapter 24 in the calculator’s User’s Guide.
• ### Page 54: Chapter 3 - Calculations With Real Numbers

Chapter 3 Calculations with real numbers This chapter demonstrates the use of the calculator for operations and functions related to real numbers. The user should be acquainted with the keyboard to identify certain functions available in the keyboard (e.g., SIN, COS, TAN, etc.).
• Page 55 6 . 3 ` 8 . 5 - 4 . 2 ` 2 . 5 * 2 . 3 ` 4 . 5 / Alternatively, in RPN mode, you can separate the operands with a space ( ) before pressing the operator key. Examples: 3 .
• Page 56 „ Ê \ 2 . 3 2 ` Example in RPN mode: 2 . 3 2 \ „ Ê The square function, SQ, is available through Example in ALG mode: „ º \ 2 . 3 ` Example in RPN mode: 2 .
• ### Page 57: Using Power Of 10 In Entering Data

enter the function XROOT followed by the arguments (y,x), separated by commas, e.g., ‚ » 3 ‚ í 2 7 ` In RPN mode, enter the argument y, first, then, x, and finally the function call, e.g., 2 7 ` 3 ‚ » Logarithms of base 10 are calculated by the keystroke combination (function LOG) while its inverse function (ALOG, or ‚...
• Page 58 LOG, ALOG, LN, EXP, SIN, COS, TAN, ASIN, ACOS, ATAN, can be combined with the fundamental operations ( complex expressions. The Equation Writer, whose operations is described in Chapter 2, is ideal for building such expressions, regardless of the calculator operation mode. ) . Arguments of these...
• ### Page 59: Real Number Functions In The Mth Menu

Using calculator menus: 1. We will describe in detail the use of the 4. HYPERBOLIC.. menu in this section with the intention of describing the general operation of calculator menus. Pay close attention to the process for selecting different options.
• Page 60 For example, in ALG mode, the keystroke sequence to calculate, say, tanh(2.5), is the following: @ @ O K @ @ @ @ O K @ @ „ ´ 4 In the RPN mode, the keystrokes to perform this calculation are the following: 2 .
• ### Page 61: Operations With Units

(2.5) = 0.98661.. expm(2.0) = 6.38905…. Operations with units Numbers in the calculator can have units associated with them. Thus, it is possible to calculate results involving a consistent system of units and produce a result with the appropriate combination of units.
• Page 62 Option 1. Tools.. contains functions used to operate on units (discussed later). Options 3. Length.. through 17.Viscosity.. contain menus with a number of units for each of the quantities described. For example, selecting option 8. Force.. shows the following units menu: The user will recognize most of these units (some, e.g., dyne, are not used very often nowadays) from his or her physics classes: N = newtons, dyn = dynes, gf = grams –...
• ### Page 63: Available Units

@ ) E N R G „ « Note: Use the key or the k eystroke sequence to navigate through the menus. Available units For a complete list of available units see Chapter 3 in the calculator’s User’s Guide. Page 3-10...
• ### Page 64: Attaching Units To Numbers

Note: If you forget the underscore, the result is the expression 5*N, where N here represents a possible variable name and not Newtons. To enter this same quantity, with the calculator in RPN mode, use the following keystrokes: 5 ‚ Û 8...
• ### Page 65: Operations With Units

_____________________________________________________ (*) In the SI system, this prefix is da rather than D. Use D for deka in the calculator, however. To enter these prefixes, simply type the prefix using the example, to enter 123 pm (picometer), use: 1 2 3 ‚ Ý ~ „ p ~ „ m...
• Page 66 which shows as 65_(m yd). To convert to units of the SI system, use function UBASE (find it using the command catalog, ‚ N Note: Recall that the ANS(1) variable is available through the keystroke combination ( associated with the key).
• ### Page 67: Unit Conversions

Examples of function CONVERT are shown below. Examples of the other UNIT/TOOLS functions are available in Chapter 3 of the calculator’s User’s Manual. For example, to convert 33 watts to btu’s use either of the following entries:...
• Page 68 The soft menu keys corresponding to this CONSTANTS LIBRARY screen include the following functions: when selected, constants values are shown in SI units (*) ENGL when selected, constants values are shown in English units (*) UNIT when selected, constants are shown with units attached VALUE when selected, constants are shown without units STK copies value (with or without units) to the stack QUIT...
• ### Page 69: Defining And Using Functions

To copy the value of Vm to the stack, select the variable name, and press , then, press . For the calculator set to the ALG, the screen will look ² S T K @ Q U I T @...
• Page 70 << x ‘LN(x+1) + EXP(x)’ >> This is a simple program in the default programming language of the HP 48 G series, and also incorporated in the HP 49 G series. This programming language is called UserRPL (See Chapters 20 and 21 in the calculator’s User’s Guide).
• ### Page 71: Reference

2 / 3 ` entered by using: @ @ @ H @ @ @ @ @ @ H @ @ @ Reference Additional information on operations with real numbers with the calculator is contained in Chapter 3 of the User’s Manual. Page 3-18...
• ### Page 72: Chapter 4 - Calculations With Complex Numbers

. The negative of z, –z = -x-iy = - re , can be thought of as the reflection of z about the origin. Setting the calculator to COMPLEX mode To work with complex numbers select the CAS complex mode: 2 ˜ ˜ ™...
• ### Page 73: Entering Complex Numbers

Entering complex numbers Complex numbers in the calculator can be entered in either of the two Cartesian representations, namely, x+iy, or (x,y). The results in the calculator will be shown in the ordered-pair format, i.e., (x,y). For example, with the calculator in ALG mode, the complex number (3.5,-1.2), is entered as:...
• ### Page 74: Simple Operations With Complex Numbers

) . The results follow the rules of algebra with the caveat that + - * / = -1. Operations with complex numbers are similar to those with real numbers. For example, with the calculator in ALG mode and the CAS set to Complex, try the following operations: Page 4-3...
• ### Page 75: The Cmplx Menus

(5-2i)/(3+4i) = (0.28,-1.04) 1/(3+4i) = (0.12, -0.16) ; The CMPLX menus There are two CMPLX (CoMPLeX numbers) menus available in the calculator. One is available through the MTH menu (introduced in Chapter 3) and one ‚ ß directly into the keyboard ( next.
• ### Page 76: Cmplx Menu In The Keyboard

CONJ(z): Produces the complex conjugate of z Examples of applications of these functions are shown next. Recall that, for ALG mode, the function must precede the argument, while in RPN mode, you enter the argument first, and then select the function. Also, recall that you can get these functions as soft menu labels by changing the setting of system flag 117 (See Chapter 3).
• ### Page 77: Functions Applied To Complex Numbers

Note: When using trigonometric functions and their inverses with complex numbers the arguments are no longer angles. Therefore, the angular measure selected for the calculator has no bearing in the calculation of these functions with complex arguments. Function DROITE: equation of a straight line...
• ### Page 78: Reference

‚ N Function DROITE is found in the command catalog ( Reference Additional information on complex number operations is presented in Chapter 4 of the calculator’s User’s Guide. Page 4-7...
• ### Page 79: Chapter 5 - Algebraic And Arithmetic Operations

Chapter 5 Algebraic and arithmetic operations An algebraic object, or simply, algebraic, is any number, variable name or algebraic expression that can be operated upon, manipulated, and combined according to the rules of algebra. Examples of algebraic objects are the following: A number: 12.3, 15.2_m, ‘...
• ### Page 80: Simple Operations With Algebraic Objects

After building the object, press to show it in the stack (ALG and RPN modes shown below): Simple operations with algebraic objects Algebraic objects can be added, subtracted, multiplied, divided (except by zero), raised to a power, used as arguments for a variety of standard functions (exponential, logarithmic, trigonometry, hyperbolic, etc.), as you would any real or complex number.
• Page 81 In ALG mode, the following keystrokes will show a number of operations with the algebraics contained in variables variable menu): @ @ A 1 @ @ @ @ A 2 @ @ @ @ A 1 @ @ @ @ A 2 @ @ @ @ A 1 @ @ ‚...
• ### Page 82: Functions In The Alg Menu

CHOOSE boxes, the ALG menu shows the following functions: Rather than listing the description of each function in this manual, the user is invited to look up the description using the calculator’s help facility: . To locate a particular function, type the first letter of the function.
• Page 83 Copy the examples provided onto your stack by pressing for the EXPAND entry shown above, press the following example copied to the stack (press Thus, we leave for the user to explore the applications of the functions in the ALG (or ALGB) menu. This is a list of the commands: For example, for function SUBST, we find the following CAS help facility entry: Note: Recall that, to use these, or any other functions in the RPN mode,...
• ### Page 84: Operations With Transcendental Functions

Operations with transcendental functions The calculator offers a number of functions that can be used to replace expressions containing logarithmic and exponential functions ( ) , as „ Ð well as trigonometric functions ( ‚ Ñ Expansion and factoring using log-exp functions produces the following menu: „...
• ### Page 85: Functions In The Arithmetic Menu

(acos(x)) with its expression in terms of arcsine (asin(x)). Description of these commands and examples of their applications are available in the calculator’s help facility ( explore this facility to find information on the commands in the TRIG menu. Functions in the ARITHMETIC menu The ARITHMETIC menu is triggered through the keystroke combination „...
• ### Page 86: Polynomials

The functions associated with the ARITHMETIC submenus: INTEGER, POLYNOMIAL, MODULO, and PERMUTATION, are the following: Additional information on applications of the ARITHMETIC menu functions are presented in Chapter 5 in the calculator’s User’s Guide. Polynomials Polynomials are algebraic expressions consisting of one or more terms containing decreasing powers of a given variable.
• ### Page 87: The Variable Vx

The variable VX A variable called VX exists in the calculator’s {HOME CASDIR} directory that takes, by default, the value of ‘X’. independent variable for algebraic and calculus applications. Avoid using the variable VX in your programs or equations, so as to not get it confused with the CAS’...
• ### Page 88: The Peval Function

ARITHMETIC menu, it must be accessed from the function catalog Example: PEVAL([1,5,6,1],5) = 281. Additional applications of polynomial functions are presented in Chapter 5 in the calculator’s User’s Guide. Fractions Fractions can be expanded and factored by using functions EXPAND and FACTOR, from the ALG menu (‚×). For example: EXPAND(‘(1+X)^3/((X-1)(X+3))’) = ‘(X^3+3*X^2+3*X+1)/(X^2+2*X-3)’...
• ### Page 89: The Propfrac Function

The PROPFRAC function The function PROPFRAC converts a rational fraction into a “proper” fraction, i.e., an integer part added to a fractional part, if such decomposition is possible. For example: PROPFRAC(‘5/4’) = ‘1+1/4’ PROPFRAC(‘(x^2+1)/x^2’) = ‘1+1/x^2’ The PARTFRAC function The function PARTFRAC decomposes a rational fraction into the partial fractions that produce the original fraction.
• ### Page 90: The Froots Function

This is very useful to see the steps of a synthetic division. The example of dividing is shown in detail in Appendix C of the calculator’s User’s Guide. The following example shows a lengthier synthetic division:...
• ### Page 91: Reference

Reference Additional information, definitions, and examples of algebraic and arithmetic operations are presented in Chapter 5 of the calculator’s User’s Guide. Page 5-13...
• ### Page 92: Chapter 6 - Solution To Equations

ZEROS provides the zeros, or roots, of a polynomial. Function ISOL Function ISOL(Equation, variable) will produce the solution(s) to Equation by isolating variable. For example, with the calculator set to ALG mode, to solve for t in the equation at -bt = 0 we can use the following:...
• ### Page 93: Function Solve

Using the RPN mode, the solution is accomplished by entering the equation in the stack, followed by the variable, before entering function ISOL. Right before the execution of ISOL, the RPN stack should look as in the figure to the left.
• Page 94 SOLVE produces four solutions, shown in the last output line. The very last solution is not visible because the result occupies more characters than the width of the calculator’s screen. However, you can still see all the solutions by ˜...
• ### Page 95: Function Solvevx

Function SOLVEVX The function SOLVEVX solves an equation for the default CAS variable contained in the reserved variable name VX. By default, this variable is set to ‘X’. Examples, using the ALG mode with VX = ‘X’, are shown below: In the first case SOLVEVX could not find a solution.
• ### Page 96: Numerical Solver Menu

Numerical Solver features of the calculator. Numerical solver menu The calculator provides a very powerful environment for the solution of single algebraic or transcendental equations. To access this environment we start ‚ Ï...
• ### Page 97: Polynomial Equations

Following, we present applications of items 3. Solve poly.., 5. Solve finance, and 1. Solve equation.., in that order. Appendix 1-A, in the calculator’s User’s Guide, contains instructions on how to use input forms with examples for the numerical solver applications. Item 6. MSLV (Multiple equation SoLVer) will be presented later in this Chapter.
• ### Page 98: Generating Polynomial Coefficients Given The Polynomial's Roots

Generating polynomial coefficients given the polynomial's roots Suppose you want to generate the polynomial whose roots are the numbers [1, 5, -2, 4]. To use the calculator for this purpose, follow these steps: ‚ Ï ˜ ˜ @ @ O K @ @ ˜...
• ### Page 99: Generating An Algebraic Expression For The Polynomial

Generating an algebraic expression for the polynomial You can use the calculator to generate an algebraic expression for a polynomial given the coefficients or the roots of the polynomial. The resulting expression will be given in terms of the default CAS variable X.
• ### Page 100: Financial Calculations

This application can also be started by using the keystroke combination key). Detailed explanations of these types of calculations are presented in Chapter 6 of the calculator’s User’s Manual. Solving equations with one unknown through NUM.SLV The calculator's NUM.SLV menu provides item different types of equations in a single variable, including non-linear algebraic and transcendental equations.
• ### Page 101: Solution To Simultaneous Equations With Mslv

Then, enter the SOLVE environment and select Solve equation…, by using: . The corresponding screen will be shown as: ‚ Ï @ @ O K @ @ The equation we stored in variable EQ is already loaded in the Eq field in the SOLVE EQUATION input form.
• Page 102 Notice that function MSLV requires three arguments: 1. A vector containing the equations, i.e., ‘[SIN(X)+Y,X+SIN(Y)=1]’ 2. A vector containing the variables to solve for, i.e., ‘[X,Y]’ 3. A vector containing initial values for the solution, i.e., the initial values of both X and Y are zero for this example. In ALG mode, press to copy the example to the stack, press @ E C H O...
• ### Page 103: Reference

The final solution is X = 1.8238, Y = -0.9681. Reference Additional information on solving single and multiple equations is provided in Chapters 6 and 7 of the calculator’s User’s Guide. Page 6-12...
• ### Page 104: Chapter 7 - Operations With Lists

Chapter 7 Operations with lists Lists are a type of calculator’s object that can be useful for data processing. This chapter presents examples of operations with lists. To get started with the examples in this Chapter, we use the Approximate mode (See Chapter 1).
• ### Page 105: Addition, Subtraction, Multiplication, Division

Addition, subtraction, multiplication, division Multiplication and division of a list by a single number is distributed across the list, for example: Subtraction of a single number from a list will subtract the same number from each element in the list, for example: Addition of a single number to a list produces a list augmented by the number, and not an addition of the single number to each element in the list.
• ### Page 106: Functions Applied To Lists

Note: If we had entered the elements in lists L4 and L3 as integers, the infinite symbol would be shown whenever a division by zero occurs. To produce the following result you need to re-enter the lists as integer (remove decimal points) using Exact mode: If the lists involved in the operation have different lengths, an error message (Invalid Dimensions) is produced.
• ### Page 107: Lists Of Complex Numbers

INVERSE (1/x) Lists of complex numbers You can create a complex number list, say, L5 = L1 ADD i L2 (type the instruction as indicated here), as follows: Functions such as LN, EXP, SQ, etc., can also be applied to a list of complex numbers, e.g., Lists of algebraic objects The following are examples of lists of algebraic objects with the function SIN...
• Page 108 With system flag 117 set to SOFT menus, the MTH/LIST menu shows the following functions: The operation of the MTH/LIST menu is as follows: LIST : Calculate increment among consecutive elements in list LIST : Calculate summation of elements in the list LIST : Calculate product of elements in the list SORT...
• ### Page 109: The Seq Function

For example, the following call to function MAP applies the function SIN(X) to the list {1,2,3}: Reference For additional references, examples, and applications of lists see Chapter 8 in the calculator’s User’s Guide. Page 7-6...
• ### Page 110: Chapter 8 - Vectors

[ ' t ' , ' t ^ 2 ' , ' S I N ( t ) ' ] Typing vectors in the stack With the calculator in ALG mode, a vector is typed into the stack by opening a set of brackets ( ) and typing the components or elements of the „...
• ### Page 111: Storing Vectors Into Variables In The Stack

) or spaces ( ) . Notice that after pressing ‚ í the calculator shows the vector elements separated by spaces. Storing vectors into variables in the stack Vectors can be stored into variables. The screen shots below show the vectors...
• Page 112 key is used to edit the contents of a selected cell in the @ E D I T matrix writer. key, when selected, will produce a vector, as opposed to a @ V E C @ @ matrix of one row and many columns. key is used to decrease the width of the columns in the W I D spreadsheet.
• Page 113 key will add a row full of zeros at the location of the @ + R O W @ selected cell of the spreadsheet. key will delete the row corresponding to the selected cell of @ - R O W the spreadsheet.
• ### Page 114: Simple Operations With Vectors

(3) Move the cursor up two positions by using The second row will disappear. (4) Press . A row of three zeroes appears in the second row. @ + R O W @ (5) Press . The first column will disappear. @ - C O L @ (6) Press .
• ### Page 115: Multiplication By A Scalar, And Division By A Scalar

Attempting to add or subtract vectors of different length produces an error message: Multiplication by a scalar, and division by a scalar Multiplication by a scalar or division by a scalar is straightforward: Absolute value function The absolute value function (ABS), when applied to a vector, produces the magnitude of the vector.
• ### Page 116: The Mth/vector Menu

The MTH/VECTOR menu „ ´ The MTH menu ( ) contains a menu of functions that specifically to vector objects: The VECTOR menu contains the following functions (system flag 117 set to CHOOSE boxes): Magnitude The magnitude of a vector, as discussed earlier, can be found with function „...
• ### Page 117: Cross Product

Attempts to calculate a cross product of vectors of length other than 2 or 3, produce an error message: Reference Additional information on operations with vectors, including applications in the physical sciences, is presented in Chapter 9 of the calculator’s User’s Guide. Page 8-8...
• ### Page 118: Chapter 9 - Matrices And Linear Algebra

Entering matrices in the stack In this section we present two different methods to enter matrices in the calculator stack: (1) using the Matrix Editor, and (2) typing the matrix directly into the stack. Using the matrix editor As with the case of vectors, discussed in Chapter 9, matrices can be entered into the stack by using the matrix editor.
• ### Page 119: Typing The Matrix Directly Into The Stack

Press once more to place the matrix on the stack. The ALG mode stack is shown next, before and after pressing , once more: If you have selected the textbook display option (using and checking @ ) D I S P ! ), the matrix will look like the one shown above.
• ### Page 120: Operations With Matrices

Operations with matrices Matrices, like other mathematical objects, can be added and subtracted. They can be multiplied by a scalar, or among themselves. An important operation for linear algebra applications is the inverse of a matrix. Details of these operations are presented next. To illustrate the operations we will create a number of matrices that we will store in the following variables.
• ### Page 121: Multiplication

In RPN mode, try the following eight examples: A 2 2 B 2 2 A 2 3 B 2 3 A 3 2 B 3 2 A 3 3 B 3 3 Multiplication There are different multiplication operations that involve matrices. These are described next.
• ### Page 122: Matrix Multiplication

Matrix multiplication Matrix multiplication is defined by C . Notice that matrix multiplication is only possible if the number of columns in the first operand is equal to the number of rows of the second operand. The general term in the product, c , is defined as , 2 ,...
• ### Page 123: The Identity Matrix

I is the identity matrix of the same dimensions as A. The inverse of a matrix is obtained in the calculator by using the inverse function, INV (i.e., the key). Examples of the inverse of some of the matrices stored earlier are...
• ### Page 124: Characterizing A Matrix (the Matrix Norm Menu)

„ ´ sequence . This menu is described in detail in Chapter 10 of the calculator’s User’s Guide. Some of these functions are described next. Function DET Function DET calculates the determinant of a square matrix. For example, Function TRACE...
• ### Page 125: Using The Numerical Solver For Linear Systems

, if we define the following matrix and vectors: Using the numerical solver for linear systems There are many ways to solve a system of linear equations with the calculator. One possibility is through the numerical solver solver screen, shown below (left), select the option 4. Solve lin sys.., and press .
• Page 126 This system has the same number of equations as of unknowns, and will be referred to as a square system. In general, there should be a unique solution to the system. The solution will be the point of intersection of the three planes in the coordinate system (x To enter matrix A you can activate the Matrix Writer while the A: field is selected.
• ### Page 127: Solution With The Inverse Matrix

= A b. For the example used earlier, we can find the solution in the calculator as follows (First enter matrix A and vector b once more): Solution by “division” of matrices While the operation of division is not defined for matrices, we can use the calculator’s...
• ### Page 128: Chapter 10 - Graphics

Right in front of the TYPE field you will, most likely, see the option Function highlighted. This is the default type of graph for the calculator. To see the list of available graph types, press the soft menu key labeled .
• ### Page 129: Plotting An Expression Of The Form Y = F(x)

Function is selected as the TYPE, and that ‘X’ is selected as the independent variable (INDEP). return to normal calculator display. The PLOT SET UP window should look similar to this: Enter the PLOT environment by pressing simultaneously if in RPN mode).
• ### Page 130: Generating A Table Of Values For A Function

Y(X) = X/(X+10), in the range -5 < X < 5 following these instructions: (wait till the calculator finishes the @ L A B E L @ M E N U @ ) P I C T .
• Page 131 EQ, and type the function expression: ‘X/(X+10)’ To accept the changes made to the PLOT SETUP screen press You will be returned to normal calculator display. The next step is to access the Table Set-up screen by using the keystroke „ õ...
• ### Page 132: Fast 3d Plots

With the option In highlighted, press that the x-increment is now 0.25 rather than 0.5. Simply, what the calculator does is to multiply the original increment, 0.5, by the zoom factor, 0.5, to produce the new increment of 0.25. Thus, the zoom in option is useful when you want more resolution for the values of x in your table.
• Page 133 @ @ @ O K @ @ @ Make sure that ‘X’ is selected as the variables. Press to return to normal calculator display. @ @ @ O K @ @ @ „ ò Press , simultaneously if in RPN mode, to access the PLOT WINDOW screen.
• Page 134 @ C A N C L Press , or , to return to normal calculator display. @ @ @ O K @ @ @ Try also a Fast 3D plot for the surface z = f(x,y) = sin (x „ ô...
• ### Page 135: Reference

PLOT WINDOW environment. Then, press @ C A N C L , or , to return to normal calculator display. @ @ @ O K @ @ @ Reference Additional information on graphics is available in Chapters 12 and 22 in the calculator’s User’s Guide.
• ### Page 136: Chapter 11 - Calculus Applications

Chapter 11 Calculus Applications In this Chapter we discuss applications of the calculator’s functions to operations related to Calculus, e.g., limits, derivatives, integrals, power series, etc. The CALC (Calculus) menu Many of the functions presented in this Chapter are contained in the „...
• ### Page 137: Functions Deriv And Dervx

where the limit is to be calculated. ‚ N ~ „ l command catalog ( SERIES… of the CALC menu (see above). Function lim is entered in ALG mode as limit . In RPN mode, enter the function first, then the expression ‘x=a’, and finally function lim.
• ### Page 138: Anti-derivatives And Integrals

= dF/dx, and C = constant. Functions INT, INTVX, RISCH, SIGMA and SIGMAVX The calculator provides functions INT, INTVX, RISCH, SIGMA and SIGMAVX to calculate anti-derivatives of functions. Functions INT, RISCH, and SIGMA work with functions of any variable, while functions INTVX, and SIGMAVX utilize functions of the CAS variable VX (typically, ‘x’).
• ### Page 139: Definite Integrals

Please notice that functions SIGMAVX and SIGMA are designed for integrands that involve some sort of integer function like the factorial (!) function shown above. Their result is the so-called discrete derivative, i.e., one defined for integer numbers only. Definite integrals In a definite integral of a function, the resulting anti-derivative is evaluated at the upper and lower limit of an interval (a,b) and the evaluated values subtracted.
• ### Page 140: Functions Taylr, Taylr0, And Series

where f (x) represents the n-th derivative of f(x) with respect to x, f If the value x = 0, the series is referred to as a Maclaurin’s series. Functions TAYLR, TAYLR0, and SERIES Functions TAYLR, TAYLR0, and SERIES are used to generate Taylor polynomials, as well as Taylor series with residuals.
• ### Page 141: Reference

In the right-hand side figure above, we are using the line editor to see the series expansion in detail. Reference Additional definitions and applications of calculus operations are presented in Chapter 13 in the calculator’s User’s Guide. ƒ µ , and then enter...
• ### Page 142: Chapter 12 - Multi-variate Calculus Applications

You can use the derivative functions in the calculator: DERVX, DERIV, , described in detail in Chapter 11 of this Guide, to calculate partial derivatives (DERVX uses the CAS default variable VX, typically, ‘X’). Some examples of first-order partial derivatives are shown next.
• ### Page 143: Multiple Integrals

Calculating a double integral in the calculator is straightforward. A double integral can be built in the Equation Writer (see example in Chapter 2), as shown below. This double integral is calculated directly in the Equation Writer by selecting the entire expression and using function .
• ### Page 144: Chapter 13 - Vector Analysis Applications

Chapter 13 Vector Analysis Applications This chapter describes the use of functions HESS, DIV, and CURL, for calculating operations of vector analysis. The del operator The following operator, referred to as the ‘del’ or ‘nabla’ operator, is a vector- based operator that can be applied to a scalar or vector function: When applied to a scalar function we can obtain the gradient of the function, and when applied to a vector function we can obtain the divergence and the curl of that function.
• ### Page 145: Divergence

CURL. For example, for the function F(X,Y,Z) = [XY,X calculated as follows: CURL([X*Y,X^2+Y^2+Z^2,Y*Z],[X,Y,Z]) Reference For additional information on vector analysis applications see Chapter 15 in the calculator’s User’s Guide. ,YZ], the divergence is ,YZ], the curl is Page 13-2...
• ### Page 146: Chapter 14 - Differential Equations

Chapter 14 Differential Equations The CALC/DIFF menu „ Ö Solution to linear and non-linear equations...
• ### Page 147: Function Ldec

Function LDEC ' X ^ 3 - 4 * X ^ 2 - 1 1 * X + 3 0 ' L D E C...
• ### Page 148: Function Desolve

' X ^ 2 ' ' X ^ 3 - 4 * X ^ 2 - 1 1 * X + 3 0 ' L D E C Function DESOLVE ' d 1 y ( x ) + x ^ 2 * y ( x ) = 5 ' ' y ( x ) ' D E S O L V E exp(...
• ### Page 149: The Variable Odetype

The variable ODETYPE 1st order linear @ O D E T Y Note µ µ @ O D E T Y @ O D E T Y Exact Linear w/ cst coeff...
• ### Page 150: Laplace Transforms

Laplace Transforms Laplace transform and inverses in the calculator f ( X ) L A P L A P ( F ( X ) ) ∫...
• ### Page 151: Fourier Series

Fourier series exp( ∑ exp( ,..., ,... ∫ Function FOURIER „ Ö Fourier series for a quadratic function...
• Page 152 „ § ` J ` 2 K @ ) C A S D I @ P E R I O D ‚ ×...

Reference...
• ### Page 154: Chapter 15 - Probability Distributions

Chapter 15 Probability Distributions In this Chapter we provide examples of applications of the pre-defined probability distributions in the calculator. The MTH/PROBABILITY.. sub-menu - part 1 The MTH/PROBABILITY.. sub-menu is accessible through the keystroke „ ´ sequence With system flag 117 set to CHOOSE boxes, the following functions are available in the PROBABILITY..
• ### Page 155: Random Numbers

~ ‚ 2 Example of applications of these functions are shown next: Random numbers The calculator provides a random number generator that returns a uniformly distributed random real number between 0 and 1. number, use function RAND from the MTH/PROBABILITY sub-menu.
• ### Page 156: The Mth/prob Menu - Part 2

The Student-t distribution The Student-t, or simply, the t-, distribution has one parameter , known as the degrees of freedom of the distribution. The calculator provides for values of the upper-tail (cumulative) distribution function for the t-distribution, function Page 15-3...
• ### Page 157: The Chi-square Distribution

The Chi-square ( ) distribution has one parameter , known as the degrees of freedom. The calculator provides for values of the upper-tail (cumulative) distribution function for the -distribution using [UTPC] given the value of x and the parameter . The definition of this function is, therefore, UTPC( ,x) = P(X>x) = 1 - P(X<x).
• ### Page 158: Chapter 16 - Statistical Applications

Chapter 16 Statistical Applications The calculator provides the following pre-programmed statistical features ‚ Ù accessible through the keystroke combination (the key): Entering data Applications number 1, 2, and 4 from the list above require that the data be available as columns of the matrix DAT.
• Page 159 When ready, press The selected values will be listed, appropriately labeled, in the screen of your calculator. For example: Sample vs. population The pre-programmed functions for single-variable statistics used above can be...
• ### Page 160: Obtaining Frequency Distributions

Obtaining frequency distributions The application 2 . F r e q u e n c i e s . . frequency distributions for a set of data. The data must be present in the form of a column vector stored in variable ‚...
• ### Page 161: Fitting Data To A Function Y = F(x)

This information indicates that our data ranges from -9 to 9. To produce a frequency distribution we will use the interval (-8,8) dividing it into 8 bins of width 2 each. Select the program 2 . F r e q u e n c i e s . . data is already loaded in DAT, and the option Col should hold the value 1 since we have only one column in DAT.
• Page 162 data sets (x,y), stored in columns of the DAT matrix. For this application, you need to have at least two columns in your DAT variable. For example, to fit a linear relationship to the data shown in the table below: First, enter the two columns of data into variable DAT by using the matrix writer, and function STO .
• ### Page 163: Obtaining Additional Summary Statistics

1 shows the covariance of x-y. For definitions of these parameters see Chapter 18 in the User’s Guide. For additional information on the data-fit feature of the calculator see Chapter 18 in the User’s Guide. Obtaining additional summary statistics The application 4.
• ### Page 164: Confidence Intervals

Press to obtain the following results: @ @ @ O K @ @ @ Confidence intervals The application 6. Conf Interval can be accessed by using . The application offers the following options: @ @ @ O K @ @ @ These options are to be interpreted as follows: 1.
• Page 165 @ H E L P interval in terms of random numbers generated by a calculator. To scroll down the resulting screen use the down-arrow key done with the help screen. This will return you to the screen shown above.
• ### Page 166: Hypothesis Testing

@ @ @ O K @ @ @ interval environment. The results will be listed in the calculator’s display. Additional examples of confidence interval calculations are presented in Chapter 18 in the calculator’s User’s Guide. Hypothesis testing A hypothesis is a declaration made about a population (for instance, with respect to its mean).
• Page 167 Press to access the confidence interval feature in the @ @ @ O K @ @ @ calculator. Press to select option 1. Z-Test: 1 . @ @ @ O K @ @ @ Enter the following data and press You are then asked to select the alternative hypothesis: = 0.05, test the...
• ### Page 168: Reference

Select . Then, press @ @ @ O K @ @ @ Then, we reject H , against H 5.656854. The P-value is 1.54 10 1.959964, corresponding to critical x range of {147.2 152.8}. This information can be observed graphically by pressing the soft-menu key @ G R A P H Reference Additional materials on statistical analysis, including definitions of concepts,...
• ### Page 169: Chapter 17 - Numbers In Different Bases

Numbers in non-decimal systems, referred to as binary integers, are written „ â preceded by the # symbol ( +2x10 +1x10 + 0x2 = 32+0+0+4+2+0 = 38. ‚ ã ( the key). With system ) in the calculator. To select the current , the Page 17-1...
• ### Page 170: Reference

To write a number in a particular system, start the number with # and end with either h (hexadecimal), d (decimal), o (octal), or b (binary), examples: Reference For additional details on numbers from different bases see Chapter 19 in the calculator’s User’s Guide. is selected, @ H E X Page 17-2...
• ### Page 171: Chapter 18 - Using Sd Cards

Chapter 18 Using SD cards The calculator provides a memory card port where you can insert an SD flash card for backing up calculator objects, or for downloading objects from other sources. The SD card in the calculator will appear as port number 3.
• ### Page 172: Recalling An Object From The Sd Card

Enter object, type the name of the stored object using port 3 (e.g., :3:VAR1), press K. Recalling an object from the SD card To recall an object from the SD card onto the screen, use function RCL, as follows: • In algebraic mode: Press „©, type the name of the stored object using port 3 (e.g., :3:VAR1), press `.
• ### Page 173: Limited Warranty

If HP receives notice of such defects during the warranty period, HP will, at its option, either repair or replace products which prove to be defective. Replacement products may be either new or like-new.
• ### Page 174: Service

8. The only warranties for HP products and services are set forth in the express warranty statements accompanying such products and services.
• Page 175 +27-11-541 9573 +32-2-7126219 +420-5-41422523 Telephone numbers +61-3-9841-5211 +61-3-9841-5211 Telephone numbers 0-810-555-5520 Sao Paulo 3747-7799; ROTC 0-800-157751 Mx City 5258-9922; ROTC 01-800-472-6684 0800-4746-8368 800-360999 9-800-114726 0-800-10111 1-800-711-2884 1-800-999-5105 1-877-232-0589 0-800-011-0524 Telephone numbers 1800-HP INVENT (905) 206-4663 or 800- HP INVENT Page W-3...
• ### Page 176: Regulatory Information

This section contains information that shows how the hp 49g+ graphing calculator complies with regulations in certain regions. Any modifications to the calculator not expressly approved by Hewlett-Packard could void the authority to operate the 49g+ in these regions. This calculator generates, uses, and can radiate radio frequency energy and may interfere with radio and television reception.