Page 2 - Notice; Printing History
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 WARRANTY OF ANY KIND WITH REGARD TO THIS MANUAL, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF...
Page 3 - Preface
Preface You have in your hands a compact symbolic and numerical computer that will facilitate calculation and mathematical analysis of problems in a variety of disciplines, from elementary mathematics to advanced engineering and science subjects. This manual contains examples that illustrate the use...
Page 4 - Table of Contents
Page TOC-1 Table of Contents Chapter 1 – Getting Started , 1-1 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 calculato...
Page 5 - Chapter 3 – Calculations with real numbers
Page TOC-2 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 nam...
Page 6 - Chapter 5 – Algebraic and arithmetic operations; Expansion and factoring using trigonometric functions, 5-6
Page TOC-3 Unit conversions, 3-14 Physical constants in the calculator , 3-14 Defining and using functions , 3-16 Reference , 3-18 Chapter 4 – Calculations with complex numbers , 4-1 Definitions , 4-1 Setting the calculator to COMPLEX mode , 4-1 Entering complex numbers, 4-2 Polar representation of ...
Page 7 - Chapter 6 – Solution to equations
Page TOC-4 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 , 6-1 Symbolic solution of algebraic equations , 6-1 Function ISOL, 6-1 Function SOLVE, 6-2 Funct...
Page 8 - Chapter 9 – Matrices and linear algebra
Page TOC-5 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 sc...
Page 9 - Solution by “division” of matrices, 9-10; Chapter 10 – Graphics; Function; Chapter 12 – Multi-variate Calculus Applications
Page TOC-6 Solution with the inverse matrix, 9-10 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...
Page 12 - Basic Operations; Batteries; To install the main batteries
Page 1-1 Chapter 1 Getting started This chapter is aimed at providing basic information in the operation of your calculator. The exercises are aimed at familiarizing yourself with the basic operations and settings before actually performing a calculation. Basic Operations The following exercises are...
Page 14 - Menus
Page 1-3 For details on the meaning of these specifications see Chapter 2 in the calculator’s user’s guide. The second line shows the characters { HOME } indicating that the HOME directory is the current file directory in the calculator’s memory. At the bottom of the display you will find a number o...
Page 15 - CLEAR; Setting time and date; Introducing the calculator’s keyboard
Page 1-4 and Chapter 2 and Appendix L in the user’s guide for more information on editing) @VIEW B VIEW the contents of a variable @@ RCL @@ C ReCaLl the contents of a variable @@STO@ D STOre the contents of a variable ! PURGE E PURGE a variable CLEAR F CLEAR the display or stack These six functions...
Page 17 - Selecting calculator modes; button (second key from the left on the second row of keys from
Page 1-6 ~p ALPHA function, to enter the upper-case letter P ~„p ALPHA-Left-Shift function, to enter the lower-case letter p ~…p ALPHA-Right-Shift function, to enter the symbol π Of the six functions associated with a key only the first four are shown in the keyboard itself. The figure in next page ...
Page 18 - Operating Mode
Page 1-7 Press the !!@@OK#@ ( F ) soft menu key to return to normal display. Examples of selecting different calculator modes are shown next. Operating Mode The calculator offers two operating modes: the Algebraic mode, and the Reverse Polish Notation ( RPN ) mode. The default mode is the Algebraic ...
Page 20 - stack levels
Page 1-9 different levels are referred to as the stack levels , i.e., stack level 1, stack level 2, etc. Basically, what RPN means is that, instead of writing an operation such as 3 + 2, in the calculator by using 3+2` we write first the operands, in the proper order, and then the operator, i.e., 3`...
Page 21 - Number Format and decimal dot or comma; Number format
Page 1-10 5 . 2 3 23 3 3 1 5 3 e + ⋅ − ⋅ 3` Enter 3 in level 1 5` Enter 5 in level 1, 3 moves to level 2 3` Enter 3 in level 1, 5 moves to level 2, 3 to level 3 3* Place 3 and multiply, 9 appears in level 1 Y 1/(3 × 3), last value in lev. 1; 5 in level 2; 3 in level 3 - 5 - 1/(3 × 3) , o...
Page 25 - Decimal comma vs. decimal point; Angle Measure
Page 1-14 • 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 ch...
Page 27 - Rigorous
Page 1-16 Selecting CAS settings CAS stands for C omputer A lgebraic S ystem. This is the mathematical core of the calculator where the symbolic mathematical operations and functions are programmed. The CAS offers a number of settings can be adjusted according to the type of operation of interest. T...
Page 28 - Explanation of CAS settings; Selecting Display modes
Page 1-17 options above). Unselected options will show no check mark in the underline preceding the option of interest (e.g., the _Numeric, _Approx, _Complex, _Verbose, _Step/Step, _Incr Pow options above). • After having selected and unselected all the options that you want in the CAS MODES input f...
Page 29 - Textbook
Page 1-18 The calculator display can be customized to your preference by selecting different display modes. To see the optional display settings use the following: • First, press the H button to activate the CALCULATOR MODES input form. Within the CALCULATOR MODES input form, press the @@DISP@ soft ...
Page 30 - System Fonts; Selecting properties of the line editor; Edit
Page 1-19 ( D ) to display the DISPLAY MODES input form. The Font: field is highlighted, and the option Ft8_0:system 8 is selected. This is the default value of the display font. Pressing the @CHOOS soft menu key ( B ), will provide a list of available system fonts, as shown below: The options avail...
Page 31 - Stack
Page 1-20 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, ˜ , twice, to get to the Stack line. Thi...
Page 32 - Selecting properties of the equation writer (EQW); dX; EQW; References
Page 1-21 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 ...
Page 33 - Calculator objects; reals; Editing expressions in the stack; Creating arithmetic expressions; Fix
Page 2-1 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 c...
Page 36 - Creating algebraic expressions; Exact
Page 2-4 This expression is semi-symbolic in the sense that there are floating-point components to the result, as well as a √ 3. Next, we switch stack locations [using ™ ] and evaluate using function NUM, i.e., ™…ï . This latter result is purely numerical, so that the two results in the stack, altho...
Page 37 - Using the Equation Writer (EQW) to create expressions; (the third key in the fourth row from the top in the keyboard). The
Page 2-5 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. Using the Equation Writer...
Page 40 - combination of Greek and English letters, namely,
Page 2-8 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 t...
Page 41 - Organizing data in the calculator; The HOME directory
Page 2-9 Also, you can always copy special characters by using the CHARS menu ( …± ) if you don’t want to memorize the keystroke combination that produces it. A listing of commonly used ~‚ keystroke combinations is listed in Appendix D of the user’s guide. For additional information on editing, eval...
Page 42 - Typing variable names
Page 2-10 Variables Variables are similar to files on a computer hard drive. One variable can store one object (numerical values, algebraic expressions, lists, vectors, matrices, programs, etc). Variables are referred to by their names, which can be any combination of alphabetic and numerical charac...
Page 43 - To unlock the upper-case locked keyboard, press; Creating variables; The simplest way to create a variable is by using the
Page 2-11 To unlock the upper-case locked keyboard, press ~ Try the following exercises: ³~~math` ³~~m„a„t„h` ³~~m„~at„h` The calculator display will show the following (left-hand side is Algebraic mode, right-hand side is RPN mode): Creating variables The simplest way to create a variable is by usi...
Page 45 - RPN mode
Page 2-13 • RPN mode (Use H\ @@OK@@ to change to RPN mode). Use the following keystrokes to store the value of –0.25 into variable α : 0.25\` ~‚a` . At this point, the screen will look as follows: This expression means that the value –0.25 is ready to be stored into α . Press K to create the variabl...
Page 46 - Checking variables contents; Algebraic mode
Page 2-14 p1: ‚å‚é~„r³„ì* ~„rQ2™™™ ³ ~„p1™` 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, α . Checking variables contents The simplest way to check a variable content is by pressing the soft menu ke...
Page 49 - Using function PURGE in the stack in RPN mode; UNDO and CMD functions; CHOOSE boxes
Page 2-17 Using function PURGE in the stack in RPN mode Assuming that our variable list contains the variables p1, z1, Q, R, and α . We will use command PURGE to delete variable p1 . Press ³ @@p1@@ ` I @PURGE@ . The screen will now show variable p1 removed: To delete two variables simultaneously, sa...
Page 51 - soft MENU
Page 2-19 Press the @CHECK! soft menu key to set flag 117 to soft MENU . The screen will reflect that change: Press @@OK@@ twice to return to normal calculator display. Now, we’ll try to find the ORDER command using similar keystrokes to those used above, i.e., we start with „° . Notice that instead...
Page 53 - Examples of real number calculations; Real
Page 3-1 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.). Also, it is...
Page 56 - Using powers of 10 in entering data
Page 3-4 enter the function XROOT followed by the arguments ( y,x ), separated by commas, e.g., ‚»3‚í 27` In RPN mode, enter the argument y , first, then, x , and finally the function call, e.g., 27`3‚» • Logarithms of base 10 are calculated by the keystroke combination ‚Ã (function LOG) while its i...
Page 57 - ) to form more complex
Page 3-5 2.45` ‚¹ 2.3\` „¸ • Three trigonometric functions are readily available in the keyboard: sine ( S ), cosine ( T ), and tangent ( U ). Arguments of these functions are angles in either degrees, radians, grades. The following examples use angles in degrees (DEG): In ALG mode: S30` T45` U135` ...
Page 58 - Real number functions in the MTH menu; Hyperbolic functions and their inverses; MTH
Page 3-6 Real number functions in the MTH menu The MTH ( „´ ) menu include a number of mathematical functions mostly applicable to real numbers. With the default setting of CHOOSE boxes for system flag 117 (see Chapter 2), the MTH menu shows the following functions: The functions are grouped by the ...
Page 60 - The UNITS menu
Page 3-8 Finally, in order to select, for example, the hyperbolic tangent (tanh) function, simply press @@TANH@ . Note: To see additional options in these soft menus, press the L key or the „« keystroke sequence. For example, to calculate tanh(2.5), in the ALG mode, when using SOFT menus over CHOOSE...
Page 62 - Available units
Page 3-10 Pressing on the appropriate soft menu key will open the sub-menu of units for that particular selection. For example, for the @)SPEED sub-menu, the following units are available: Pressing the soft menu key @)UNITS will take you back to the UNITS menu. Recall that you can always list the fu...
Page 63 - Attaching units to numbers
Page 3-11 Attaching units to numbers To attach a unit object to a number, the number must be followed by an underscore ( ‚Ý , key(8,5)). Thus, a force of 5 N will be entered as 5_N. Here is the sequence of steps to enter this number in ALG mode, system flag 117 set to CHOOSE boxes : 5‚Ý ‚Û 8 @@OK@@ ...
Page 64 - Operations with units
Page 3-12 ____________________________________________________ Prefix Name x Prefix Name x ____________________________________________________ Y yotta +24 d deci -1 Z zetta +21 c centi -2 E exa +18 m milli -3 P peta +15 µ micro -6 T tera +12 n nano -9 G giga +9 p pico -12 M mega +6 f femto -15 k,K ...
Page 66 - Unit conversions; Physical constants in the calculator; constants library
Page 3-14 These operations produce the following output: Unit conversions The UNITS menu contains a TOOLS sub-menu, which provides the following functions: CONVERT(x,y): convert unit object x to units of object y UBASE(x): convert unit object x to SI units UVAL(x): extract the value from unit object...
Page 68 - Defining and using functions; (associated with the
Page 3-16 To copy the value of Vm to the stack, select the variable name, and press ! ²STK , then, press @QUIT@ . For the calculator set to the ALG, the screen will look like this: The display shows what is called a tagged value , Vm:359.0394 . In here, Vm, is the tag of this result. Any arithmetic ...
Page 70 - . The other examples shown above can be; Reference
Page 3-18 between quotes that contain that local variable, and show the evaluated expression. To activate the function in ALG mode, type the name of the function followed by the argument between parentheses, e.g., @@@H@@@ „Ü2` . Some examples are shown below: In the RPN mode, to activate the functio...
Page 72 - Entering complex numbers; . The results in the calculator; Polar representation of a complex number; can also change the coordinate to POLAR using
Page 4-2 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...
Page 73 - Simple operations with complex numbers; Complex
Page 4-3 The result shown above represents a magnitude, 3.7, and an angle 0.33029…. The angle symbol ( ∠ ) is shown in front of the angle measure. Return to Cartesian or rectangular coordinates by using function RECT (available in the catalog, ‚N ). A complex number in polar representation is writte...
Page 74 - The CMPLX menus; CMPLX menu through the MTH menu
Page 4-4 (3+5i) + (6-3i) = (9,2); (5-2i) - (3+4i) = (2,-6) (3-i)(2-4i) = (2,-14); (5-2i)/(3+4i) = (0.28,-1.04) 1/(3+4i) = (0.12, -0.16) ; -(5-3i) = -5 + 3i The CMPLX menus There are two CMPLX (CoMPLeX numbers) menus available in the calculator. One is available through the MTH menu (introduced in Ch...
Page 75 - CMPLX menu in keyboard; . With system flag 117 set to CHOOSE
Page 4-5 Examples of applications of these functions are shown next in RECT coordinates. 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...
Page 76 - Function DROITE takes as argument two complex numbers, say, x
Page 4-6 Functions applied to complex numbers Many of the keyboard-based functions and MTH menu functions defined in Chapter 3 for real numbers (e.g., SQ, ,LN, e x , etc.), can be applied to complex numbers. The result is another complex number, as illustrated in the following examples. Note: When u...
Page 77 - Function DROITE is found in the command catalog (
Page 4-7 Function DROITE is found in the command catalog ( ‚N ). If the calculator is in APPROX mode, the result will be Y = 5.*(X-5.)-3. Reference Additional information on complex number operations is presented in Chapter 4 of the calculator’s user’s guide.
Page 78 - So’; Entering algebraic objects
Page 5-1 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: ...
Page 79 - Simple operations with algebraic objects; The keystrokes corresponding to RPN mode are:
Page 5-2 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 (ex...
Page 81 - Functions in the ALG menu
Page 5-4 Functions in the ALG menu The ALG (Algebraic) menu is available by using the keystroke sequence ‚× (associated with the 4 key). With system flag 117 set to CHOOSE boxes , the ALG menu shows the following functions: Rather than listing the description of each function in this manual, the use...
Page 83 - Operations with transcendental functions; well as trigonometric functions (; Expansion and factoring using log-exp functions; The; Expansion and factoring using trigonometric functions; The TRIG menu, triggered by using
Page 5-6 Operations with transcendental functions The calculator offers a number of functions that can be used to replace expressions containing logarithmic and exponential functions ( „Ð ), as well as trigonometric functions ( ‚Ñ ). Expansion and factoring using log-exp functions The „Ð produces th...
Page 84 - Functions in the ARITHMETIC menu
Page 5-7 These functions allow to simplify expressions by replacing some category of trigonometric functions for another one. For example, the function ACOS2S allows to replace the function arccosine (acos(x)) with its expression in terms of arcsine (asin(x)). Description of these commands and examp...
Page 85 - FACTORS:; Polynomials; The HORNER function; The function HORNER (
Page 5-8 FACTORS: SIMP2: The functions associated with the ARITHMETIC submenus: INTEGER, POLYNOMIAL, MODULO, and PERMUTATION, are presented in detail in Chapter 5 in the calculator’s user’s guide. The following sections show some applications to polynomials and fractions. Polynomials Polynomials are...
Page 87 - The PEVAL function; given an array of coefficients [; Fractions; The SIMP2 function
Page 5-10 Note : you could get the latter result by using PARTFRAC: PARTFRAC(‘(X^3-2*X+2)/(X-1)’) = ‘X^2+X-1 + 1/(X-1)’. The PEVAL function The function PEVAL (Polynomial EVALuation) can be used to evaluate a polynomial p(x) = a n ⋅ x n +a n-1 ⋅ x n-1 + …+ a 2 ⋅ x 2 +a 1 ⋅ x+ a 0 , given an array of...
Page 88 - Note
Page 5-11 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 funct...
Page 89 - The FROOTS function; Step-by-step operations with polynomials and fractions
Page 5-12 The FROOTS function The function FROOTS, in the ARITHMETIC/POLYNOMIAL menu, obtains the roots and poles of a fraction. As an example, applying function FROOTS to the result produced above, will result in: [1 –2. –3 –5. 0 3. 2 1. –5 2.]. The result shows poles followed by their multiplicity...
Page 91 - Symbolic solution of algebraic equations; Function ISOL; Equation
Page 6-1 Chapter 6 Solution to equations Associated with the 7 key there are two menus of equation-solving functions, the Symbolic SOLVer ( „Î ), and the NUMerical SoLVer ( ‚Ï ). Following, we present some of the functions contained in these menus. Symbolic solution of algebraic equations Here we de...
Page 92 - with the; Function SOLVE
Page 6-2 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. After applying ISOL, the result is shown in the figure...
Page 95 - Numerical solver menu; This produces a drop-
Page 6-5 To use function ZEROS in RPN mode, enter first the polynomial expression, then the variable to solve for, and then function ZEROS. The following screen shots show the RPN stack before and after the application of ZEROS to the two examples above (Use Complex mode in the CAS):: The Symbolic S...
Page 96 - Polynomial Equations; Solve poly...
Page 6-6 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 (Multip...
Page 99 - Function STEQ
Page 6-9 Financial calculations The calculations in item 5. Solve finance.. in the Numerical Solver ( NUM.SLV ) are used for calculations of time value of money of interest in the discipline of engineering economics and other financial applications. This application can also be started by using the ...
Page 100 - Solution to simultaneous equations with MSLV; Function MSLV is available in the
Page 6-10 Then, enter the SOLVE environment and select Solve equation… , by using: ‚Ï @@OK@@ . The corresponding screen will be shown as: The equation we stored in variable EQ is already loaded in the Eq field in the SOLVE EQUATION input form. Also, a field labeled x is provided. To solve the equati...
Page 103 - Creating and storing lists; To create a list in ALG mode, first enter the braces key; Operations with lists of numbers; Changing sign
Page 7-1 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). Creating and storing lists ...
Page 105 - Functions applied to lists; Real number functions from the keyboard (ABS, e
Page 7-3 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 opera...
Page 106 - Lists of complex numbers
Page 7-4 ABS 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 before), 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 followin...
Page 108 - The SEQ function; The SEQ function, available through the command catalog (; The MAP function; The MAP function, available through the command catalog (
Page 7-6 The SEQ function The SEQ function, available through the command catalog ( ‚N ), takes as arguments an expression in terms of an index, the name of the index, and starting, ending, and increment values for the index, and returns a list consisting of the evaluation of the expression for all ...
Page 109 - Entering vectors; Typing vectors in the stack
Page 8-1 Chapter 8 Vectors This Chapter provides examples of entering and operating with vectors, both mathematical vectors of many elements, as well as physical vectors of 2 and 3 components. Entering vectors In the calculator, vectors are represented by a sequence of numbers enclosed between brack...
Page 110 - the calculator shows the vector elements separated by spaces.; Storing vectors into variables in the stack; Vectors can also be entered by using the Matrix Writer
Page 8-2 ( ‚í ) or spaces ( # ). Notice that after pressing ` , in either mode, 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 u 2 = [1, 2] , u 3 = [-3, 2, -2] , v...
Page 113 - Simple operations with vectors; Addition, subtraction
Page 8-5 (3) Move the cursor up two positions by using —— . Then press @-ROW . The second row will disappear. (4) Press @+ROW@ . A row of three zeroes appears in the second row. (5) Press @-COL@ . The first column will disappear. (6) Press @+COL@ . A column of two zeroes appears in the first column....
Page 115 - ) contains a menu of functions that specifically to; Magnitude
Page 8-7 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 ABS. This f...
Page 116 - Cross product
Page 8-8 Cross product Function CROSS (option 3 in the MTH/VECTOR menu) is used to calculate the cross product of two 2-D vectors, of two 3-D vectors, or of one 2-D and one 3-D vector. For the purpose of calculating a cross product, a 2-D vector of the form [A x , A y ], is treated as the 3-D vector...
Page 117 - Entering matrices in the stack; Using the Matrix Writer; . Make sure that the option
Page 9-1 Chapter 9 Matrices and linear algebra This chapter shows examples of creating matrices and operations with matrices, including linear algebra applications. Entering matrices in the stack In this section we present two different methods to enter matrices in the calculator stack: (1) using th...
Page 118 - Typing in the matrix directly into the stack
Page 9-2 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 H @)DISP! and checking off Textbook ), the matrix will look like the one shown above. Otherwise, the display w...
Page 119 - Operations with matrices; Addition and subtraction
Page 9-3 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 ill...
Page 120 - Multiplication; Multiplication by a scalar
Page 9-4 In RPN mode, try the following eight examples: A22 ` B22 `+ A22 ` B22 `- A23 ` B23 `+ A23 ` B23 `- A32 ` B32 `+ A32 ` B32 `- A33 ` B33 `+ A33 ` B33 `- Multiplication There are different multiplication operations that involve matrices. These are described next. The examples are shown in alge...
Page 121 - for
Page 9-5 Matrix multiplication Matrix multiplication is defined by C m × n = A m × p ⋅ B p × n . 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 ij , is defined a...
Page 123 - Characterizing a matrix (The matrix NORM menu); . This menu is described in detail in Chapter 10 of the; Function DET; A system of
Page 9-7 Characterizing a matrix (The matrix NORM menu) The matrix NORM (NORMALIZE) menu is accessed through the keystroke 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 t...
Page 124 - Using the numerical solver for linear systems
Page 9-8 This system of linear equations can be written as a matrix equation, A n × m ⋅ x m × 1 = b n × 1 , if we define the following matrix and vectors: m n nm n n m m a a a a a a a a a A × = L M O M M L L 2 1 2 22 21 1 12 11 , 1 2 1 × = m m x x x x ...
Page 125 - and
Page 9-9 . 6 13 13 , , 4 2 2 8 3 1 5 3 2 3 2 1 − − = = − − − = b x A and x x x 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 sys...
Page 127 - Graphs options in the calculator; Please notice that if you are using the; window, which includes the; field as illustrated
Page 10-1 Chapter 10 Graphics In this chapter we introduce some of the graphics capabilities of the calculator. We will present graphics of functions in Cartesian coordinates and polar coordinates, parametric plots, graphics of conics, bar plots, scatterplots, and fast 3D plots. Graphs options in th...
Page 128 - Plotting an expression of the form
Page 10-2 Plotting an expression of the form y = f(x) As an example, let's plot the function, ) 2 exp( 2 1 ) ( 2 x x f − = π • First, enter the PLOT SETUP environment by pressing, „ô . Make sure that the option Function is selected as the TYPE , and that ‘X’ is selected as the independent variable (...
Page 129 - LL; Generating a table of values for a function
Page 10-3 VIEW, then press @AUTO to generate the V-VIEW automatically. The PLOT WINDOW screen looks as follows: • Plot the graph: @ERASE @DRAW (wait till the calculator finishes the graphs) • To see labels: @EDIT L @LABEL @MENU • To recover the first graphics menu: LL @)PICT • To trace the curve: @T...
Page 130 - Type; Start
Page 10-4 • We will generate values of the function f(x), defined above, for values of x from –5 to 5, in increments of 0.5. First, we need to ensure that the graph type is set to FUNCTION in the PLOT SETUP screen ( „ô , press them simultaneously, if in RPN mode). The field in front of the Type opti...
Page 131 - Fast 3D plots
Page 10-5 • • The @ZOOM key, when pressed, produces a menu with the options: In , Out , Decimal, Integer , and Trig . Try the following exercises: • • With the option In highlighted, press @@@OK@@@ . The table is expanded so that the x-increment is now 0.25 rather than 0.5. Simply, what the calculat...
Page 135 - Function lim; The calculator provides function
Page 11-1 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 c...
Page 136 - lim
Page 11-2 where the limit is to be calculated. Function lim is available through the command catalog ( ‚N~„l ) or through option 2. LIMITS & SERIES… of the CALC menu (see above). Function lim is entered in ALG mode as lim(f(x),x=a) to calculate the limit ) ( lim x f a x → . In RPN mode, enter th...
Page 137 - Anti-derivatives and integrals; dx
Page 11-3 Anti-derivatives and integrals An anti-derivative of a function f(x) is a function F(x) such that f(x) = dF/dx. One way to represent an anti-derivative is as a indefinite integral, i.e., C x F dx x f + = ∫ ) ( ) ( if and only if, f(x) = dF/dx, and C = constant. Functions INT, INTVX, RISCH,...
Page 138 - Definite integrals; Infinite series; by
Page 11-4 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...
Page 139 - where f
Page 11-5 where f (n) (x) represents the n-th derivative of f(x) with respect to x, f (0) (x) = f(x). If the value x 0 = 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 T...
Page 142 - Multiple integrals; dydx
Page 12-2 To define the functions f(x,y) and g(x,y,z), in ALG mode, use: DEF(f(x,y)=x*COS(y)) ` DEF(g(x,y,z)= √ (x^2+y^2)*SIN(z) ` To type the derivative symbol use ‚ ¿ . The derivative )) , ( ( y x f x ∂ ∂ , for example, will be entered as ∂ x(f(x,y)) ` in ALG mode in the screen. Multiple integrals...
Page 143 - The del operator; Gradient; The gradient of a scalar function; grad; Function HESS can be used to obtain the gradient of a; of the function with respect to the n-variables,
Page 13-1 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...
Page 144 - Divergence; The divergence of a vector function,; divF; Function DIV can be used to calculate the divergence of a; Curl; The curl of a vector field; curl; . The curl of vector field can be calculated with function CURL.
Page 13-2 Alternatively, use function DERIV as follows: Divergence The divergence of a vector function, F (x,y,z) = f(x,y,z) i +g(x,y,z) j +h(x,y,z) k , is defined by taking a “dot-product” of the del operator with the function, i.e., F divF • ∇ = . Function DIV can be used to calculate the divergen...
Page 145 - Solution to linear and non-linear equations
Page 14-1 Chapter 14 Differential Equations In this Chapter we present examples of solving ordinary differential equations (ODE) using calculator functions. A differential equation is an equation involving derivatives of the independent variable. In most cases, we seek the dependent function that sa...
Page 146 - Function LDEC; the right-hand side of the ODE
Page 14-2 Function LDEC The calculator provides function LDEC (Linear Differential Equation Command) to find the general solution to a linear ODE of any order with constant coefficients, whether it is homogeneous or not. This function requires you to provide two pieces of input: • the right-hand sid...
Page 147 - Function DESOLVE; DESOLVE
Page 14-3 The solution is: which is equivalent to y = K 1 ⋅ e –3x + K 2 ⋅ e 5x + K 3 ⋅ e 2x + (450 ⋅ x 2 +330 ⋅ x+241)/13500. Function DESOLVE The calculator provides function DESOLVE (Differential Equation SOLVEr) to solve certain types of differential equations. The function requires as input the ...
Page 148 - The variable ODETYPE
Page 14-4 The variable ODETYPE You will notice in the soft-menu key labels a new variable called @ODETY (ODETYPE). This variable is produced with the call to the DESOL function and holds a string showing the type of ODE used as input for DESOLVE. Press @ODETY to obtain the string “ 1st order linear ...
Page 149 - Laplace Transforms; in step 2 into the solution to the differential equation f(t).; Laplace transform and inverses in the calculator; L P; dt
Page 14-5 Laplace Transforms The Laplace transform of a function f(t) produces a function F(s) in the image domain that can be utilized to find the solution of a linear differential equation involving f(t) through algebraic methods. The steps involved in this application are three: 1. Use of the Lap...
Page 150 - ILAP; Fourier series; in; Function FOURIER; Function FOURIER provides the coefficient c; Fourier series for a quadratic function; Determine the coefficients c
Page 14-6 and you will notice that the CAS default variable X in the equation writer screen replaces the variable s in this definition. Therefore, when using the function LAP you get back a function of X, which is the Laplace transform of f(X). Example 2 – Determine the inverse Laplace transform of ...
Page 153 - . With system flag 117 set to CHOOSE boxes, the; Factorials, combinations, and permutations
Page 15-1 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...
Page 154 - Example of applications of these functions are shown next:; Random numbers
Page 15-2 We can calculate combinations, permutations, and factorials with functions COMB, PERM, and ! from the MTH/PROBABILITY.. sub-menu. The operation of those functions is described next: • COMB(n,r): Calculates the number of combinations of n items taken r at a time • PERM(n,r): Calculates the ...
Page 155 - and select the PROBABILITY option:; The Normal distribution; and variance
Page 15-3 The MTH/PROB menu - part 2 In this section we discuss four continuous probability distributions that are commonly used for problems related to statistical inference: the normal distribution, the Student’s t distribution, the Chi-square ( χ 2 ) distribution, and the F-distribution. The func...
Page 159 - Obtaining frequency distributions
Page 16-3 Obtaining frequency distributions The application 2. Frequencies.. in the STAT menu can be used to obtain frequency distributions for a set of data. The data must be present in the form of a column vector stored in variable Σ DAT. To get started, press ‚Ù˜ @@@OK@@@ . The resulting input fo...
Page 162 - Obtaining additional summary statistics; summary stats...
Page 16-6 Level 3 shows the form of the equation. Level 2 shows the sample correlation coefficient, and level 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 ...
Page 165 - Hypothesis testing; can be accessed by using
Page 16-9 The graph shows the standard normal distribution pdf (probability density function), the location of the critical points ± z α/2 , the mean value (23.2) and the corresponding interval limits (21.88424 and 24.51576). Press @TEXT to return to the previous results screen, and/or press @@@OK@@...
Page 168 - The BASE menu; The BASE menu is accessible through; Writing non-decimal numbers; ) in the calculator. To select the current
Page 17-1 Chapter 17 Numbers in Different Bases Besides our decimal (base 10, digits = 0-9) number system, you can work with a binary system (base 2, digits = 0,1), an octal system (base 8, digits = 0-7), or a hexadecimal system (base 16, digits=0-9,A-F), among others. The same way that the decimal ...
Page 170 - Using SD cards; Storing objects in the SD card; , type the name of the stored object using port 3
Page 18-1 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. Accessing an object from the SD card is p...
Page 172 - Limited Warranty
Page W-1 Limited Warranty hp 49g+ graphing calculator; Warranty period: 12 months 1. HP warrants to you, the end-user customer, that HP hardware, accessories and supplies will be free from defects in materials and workmanship after the date of purchase, for the period specified above. If HP receives...
Page 173 - Service
Page W-2 7. TO THE EXTENT ALLOWED BY LOCAL LAW, THE REMEDIES IN THIS WARRANTY STATEMENT ARE YOUR SOLE AND EXCLUSIVE REMEDIES. EXCEPT AS INDICATED ABOVE, IN NO EVENT WILL HP OR ITS SUPPLIERS BE LIABLE FOR LOSS OF DATA OR FOR DIRECT, SPECIAL, INCIDENTAL, CONSEQUENTIAL (INCLUDING LOST PROFIT OR DATA), ...
Page 175 - Regulatory information; USA; Connections to Peripheral Devices; Union
Page W-4 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. ...
