hp 48gII graphing calculator user's guide H Edition 4 HP part number F2226-90020 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 MERCHANTABILITY, NON-INFRINGEMENT AND FITNESS FOR A PARTICULAR PURPOSE. HEWLETT-PACKARD CO. SHALL NOT BE LIABLE FOR ANY ERRORS OR FOR INCIDENTAL OR CONSEQUENTIAL DAMAGES IN CONNECTION WITH THE FURNISHING, PERFORMANCE, OR USE OF THIS MANUAL OR THE EXAMPLES CONTAINED HEREIN. © Copyright 2003 Hewlett-Packard Development Company, L.P. Reproduction, adaptation, or translation of this manual is prohibited without prior written permission of Hewlett-Packard Company, except as allowed under the copyright laws. Hewlett-Packard Company 4995 Murphy Canyon Rd, Suite 301 San Diego,CA 92123 Printing History Edition 4 April 2004 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. Although referred to as a calculator, because of its compact format resembling typical hand-held calculating devices, the hp 48gII should be thought of as a graphics/programmable hand-held computer. The hp 48gII can be operated in two different calculating modes, the Reverse Polish Notation (RPN) mode and the Algebraic (ALG) mode (see page 1-11 in user's guide for additional details). The RPN mode was incorporated into calculators to make calculations more efficient. In this mode, the operands in an operation (e.g., `2' and `3' in the operation `2+3') are entered into the calculator screen, referred to as the stack, and then the operator (e.g., `+' in the operation `2+3') is entered to complete the operation. The ALG mode, on the other hand, mimics the way you type arithmetic expressions in paper. Thus, the operation `2+3', in ALG mode, will be entered in the calculator by pressing the keys `2', `+', and `3', in that order. To complete the operation we use the ENTER key. Examples of applications of the different functions and operations in this calculator are illustrated in this user's guide in both modes. This guide contains examples that illustrate the use of the basic calculator functions and operations. The chapters in this user's guide are organized by subject in order of difficulty. Starting with the setting of calculator modes and display options, and continuing with real and complex number calculations, operations with lists, vectors, and matrices, detailed examples of graph applications, use of strings, basic programming, graphics programming, string manipulation, advanced calculus and multivariate calculus applications, advanced differential equations applications (including Laplace transform, and Fourier series and transforms), and probability and statistic applications. For symbolic operations the calculator includes a powerful Computer Algebraic System (CAS) that lets you select different modes of operation, e.g., complex numbers vs. real numbers, or exact (symbolic) vs. approximate (numerical) mode. The display can be adjusted to provide textbook-type expressions, which can be useful when working with matrices, vectors, fractions, summations, derivatives, and integrals. The high-speed graphics of the calculator are very convenient for producing complex figures in very little time. Thanks to the infrared port and the RS 232 cable available with your calculator, you can connect your calculator with other calculators or computers. The high-speed connection through infrared or RS 232 allows the fast and efficient exchange of programs and data with other calculators or computers. The calculator provides a flash memory card port to facilitate storage and exchange of data with other users. The programming capabilities of the calculator allow you or other users to develop efficient applications for specific purposes. Whether it is advanced mathematical applications, specific problem solution, or data logging, the programming languages available in your calculator make it into a very versatile computing device. We hope your calculator will become a faithful companion for your school and professional applications. Table of contents A note about screenshots in this guide, Note-1 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 SOFT menus vs. CHOOSE boxes, 1-3 Selecting SOFT menus or CHOOSE boxes, 1-4 The TOOL menu, 1-6 Setting time and date, 1-7 Introducing the calculator's keyboard, 1-10 Setting calculator's mode, 1-11 Operating mode, 1-12 Number format and decimal dot or comma, 1-16 Angle measure, 1-21 Coordinate system, 1-22 Beep, Key Click, and Last Stack, 1-23 Selecting CAS settings, 1-24 Selecting Display modes, 1-24 Selecting the display font, 1-25 Selecting properties of the line editor, 1-26 Selecting properties of the Stack, 1-26 Selecting properties of the Equation Writer (EQW), 1-27 Selecting the size of the header, 1-28 Selecting the clock display, 1-28 Chapter 2 - Introducing the calculator, 2-1 Calculator objects, 2-1 Editing expressions in the screen, 2-3 Creating arithmetic expressions, 2-3 Editing arithmetic expressions, 2-6 Page TOC-1 Creating algebraic expressions, 2-7 Editing algebraic expressions, 2-8 Using the Equation Writer (EQW) to create expressions, 2-10 Creating arithmetic expressions, 2-11 Editing arithmetic expressions, 2-16 Creating algebraic expressions, 2-19 Editing algebraic expressions, 2-20 Creating and editing summations, derivatives, and integrals, 2-28 Organizing data in the calculator, 2-32 Functions for manipulation of variables, 2-33 The HOME directory, 2-34 The CASDIR sub-directory, 2-35 Typing directory and variable names, 2-37 Creating sub-directories, 2-38 Moving among sub-directories, 2-42 Deleting sub-directories, 2-42 Variables, 2-46 Creating variables, 2-46 Checking variable contents, 2-51 Replacing the contents of variables, 2-53 Copying variables, 2-54 Reordering variables in a directory, 2-57 Moving variables using the FILES menu, 2-58 Deleting variables, 2-59 UNDO and CMD functions, 2-61 Flags, 2-62 Example of flag setting: general solution vs. principal value, 2-63 Other flags of interest, 2-64 CHOOSE boxes vs. SOFT menus, 2-65 Selected CHOOSE boxes, 2-66 Chapter 3 - Simple calculations with real numbers, 3-1 Checking calculator settings, 3-1 Checking calculator mode, 3-2 Real number calculations, 3-2 Changing sing of a number, variable, or expression, 3-3 Page TOC-2 The inverse function, 3-3 Addition, subtraction, multiplication, division, 3-3 Using parentheses, 3-4 Absolute value function, 3-4 Squares and square roots, 3-4 Powers and roots, 3-5 Base-10 logarithms and powers of 10, 3-5 Using powers of 10 in entering data, 3-5 Natural logarithms and exponential function, 3-6 Trigonometric functions, 3-6 Inverse trigonometric functions, 3-6 Differences between functions and operators, 3-7 Real number functions in the MTH menu, 3-7 Hyperbolic functions and their inverses, 3-9 Real number functions, 3-11 Special functions, 3-14 Calculator constants, 3-16 Operation with units, 3-17 The UNITS menu, 3-17 Available units, 3-18 Converting to base units, 3-21 Attaching units to numbers, 3-22 Operations with units, 3-25 Units manipulation tools, 3-27 Physical constants in the calculator, 3-28 Special physical functions, 3-31 Function ZFACTOR, 3-32 Function F0, 3-32 Function SIDENS, 3-32 Function TDELTA, 3-33 Function TINC, 3-33 Defining and using functions, 3-33 Functions defined by more than one expression, 3-35 The IFTE function, 3-35 Combined IFTE functions, 3-36 Page TOC-3 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 a complex number, 4-3 Simple operations with complex numbers, 4-4 Changing sign of a complex number, 4-4 Entering the unit imaginary number, 4-5 The CMPLX menus, 4-5 CMPLX menu through the MTH menu, 4-5 CMPLX menu in keyboard, 4-7 Functions applied to complex numbers, 4-8 Functions from the MTH menu, 4-8 Function DROITE: equation of a straight line, 4-9 Chapter 5 - Algebraic and arithmetic operations, 5-1 Entering algebraic objects, 5-1 Simple operations with algebraic objects, 5-2 Functions in the ALG menu, 5-3 COLLECT, 5-5 EXPAND, 5-5 FACTOR, 5-5 LNCOLLECT, 5-5 LIN, 5-5 PARTFRAC, 5-5 SOLVE, 5-5 SUBST, 5-5 TEXPAND, 5-5 Other forms of substitution in algebraic expressions, 5-6 Operations with transcendental functions, 5-7 Expansion and factoring using log-exp functions, 5-8 Expansion and factoring using trigonometric functions, 5-8 Functions in the ARITHMETIC menu, 5-9 DIVIS, 5-10 Page TOC-4 FACTORS, 5-10 LGCD, 5-10 PROPFRAC, 5-10 SIMP2, 5-10 INTEGER menu, 5-10 POLYNOMIAL menu, 5-11 MODULO menu, 5-12 Applications of the ARITHMETIC menu, 5-12 Modular arithmetic, 5-12 Finite arithmetic in the calculator, 5-15 Polynomials, 5-18 Modular arithmetic with polynomials, 5-19 The CHINREM function, 5-19 The EGCD function, 5-19 The GCD function, 5-19 The HERMITE function, 5-20 The HORNER function, 5-20 The variable VX, 5-20 The LAGRANGE function, 5-21 The LCM function, 5-21 The LEGENDRE function, 5-22 The PCOEF function, 5-22 The PROOT function, 5-22 The PTAYL function, 5-22 The QUOTIENT and REMAINDER functions, 5-23 The EPSX0 function and the CAS variable EPS, 5-23 The PEVAL function, 5-23 The TCHEBYCHEFF function, 5-24 Fractions, 5-24 The SIMP2 function, 5-24 The PROPFRAC function, 5-24 The PARTFRAC function, 5-25 The FCOEF function, 5-25 The FROOTS function, 5-26 Step-by-step operations with polynomial fractions, 5-26 The CONVERT menu and algebraic operations, 5-27 Page TOC-5 UNITS convert menu, 5-27 BASE convert menu, 5-28 TRIGONOMETRIC convert menu, 5-28 MATRICES convert menu, 5-28 REWRITE convert menu, 5-28 Chapter 6 - Solution to single equations, 6-1 Symbolic solution of algebraic equations, 6-2 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 Financial calculations, 6-9 Solving equations with one unknown through NUM.SLV, 6-14 The SOLVE soft menu, 6-27 The ROOT sub-menu, 6-27 Function ROOT, 6-27 Variable EQ, 6-28 The SOLVR sub-menu, 6-28 The DIFFE sub-menu, 6-30 The POLY sub-menu, 6-30 The SYS sub-menu, 6-31 The TVM sub-menu, 6-31 Chapter 7 - Solving multiple equations, 7-1 Rational equation systems, 7-1 Example 1 - Projectile motion, 7-1 Example 2 - Stresses in a thick wall cylinder, 7-2 Example 3 ­ System of polynomial equations, 7-4 Solution to simultaneous equations with MSLV, 7-4 Example 1 - Example from the help facility, 7-5 Example 2 - Entrance from a lake into an open channel, 7-6 Using the Multiple Equation Solver (MES), 7-10 Application 1 - Solution of triangles, 7-10 Page TOC-6 Application 2 - Velocity and acceleration in polar coordinates, 7-18 Chapter 8 - Operations with Lists, 8-1 Definitions, 8-1 Creating and storing lists, 8-1 Composing and decomposing lists, 8-2 Operations with lists of numbers, 8-3 Changing sign, 8-3 Addition, subtraction, multiplication, division, 8-3 Real number functions from the keyboard, 8-5 Real number functions from the MTH menu, 8-5 Examples of functions that use two arguments, 8-6 Lists of complex numbers, 8-7 Lists of algebraic objects, 8-8 The MTH/LIST menu, 8-8 Manipulating elements of a list, 8-10 List size, 8-10 Extracting and inserting elements, 8-10 Element position in the list, 8-11 HEAD and TAIL functions, 8-11 The SEQ function, 8-11 The MAP function, 8-12 Defining functions that use lists, 8-13 Applications of lists, 8-14 Harmonic mean of a list, 8-15 Geometric mean of a list, 8-16 Weighted average, 8-17 Statistics of grouped data, 8-18 Chapter 9 - Vectors, 9-1 Definitions, 9-1 Entering vectors, 9-2 Typing vectors in the stack, 9-2 Storing vectors into variables, 9-3 Page TOC-7 Using the Matrix Writer (MTWR) to enter vectors, 9-3 Building a vector with ARRY, 9-6 Identifying, extracting, and inserting vector elements, 9-7 Simple operations with vectors, 9-9 Changing sign, 9-9 Addition, subtraction, 9-9 Multiplication and division by a scalar, 9-10 Absolute value function, 9-10 The MTH/VECTOR menu, 9-10 Magnitude, 9-11 Dot product, 9-11 Cross product, 9-11 Decomposing a vector, 9-12 Building a two-dimensional vector, 9-12 Building a three-dimensional vector, 9-13 Changing coordinate system, 9-13 Application of vector operations, 9-16 Resultant of forces, 9-16 Angle between vectors, 9-16 Moment of a force, 9-17 Equation of a plane in space, 9-18 Row vectors, column vectors, and lists, 9-19 Function OBJ , 9-20 Function LIST, 9-20 Func ...