HP 49g+ User manual

hp 49g+ graphing calculator
user’s guide
H
Edition 4
HP part number F2228-90006

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© Copyright 2003 Hewlett-Packard Development Company, L.P.
Reproduction, adaptation, or translation of this manual is prohibited without
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Hewlett-Packard Company
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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
49g+ should be thought of as a graphics/programmable hand-held computer.
The hp 49g+ 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 USB cable available with your calculator,
you can connect your calculator with other calculators or computers. The
high-speed connection through infrared or USB 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.

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
SOFT menus vs. CHOOSE boxes, 1-4
Selecting SOFT menus or CHOOSE boxes, 1-5
The TOOL menu, 1-6
Setting time and date, 1-7
Introducing the calculator’s keyboard, 1-10
Setting calculator’s mode, 1-12
Operating mode, 1-13
Number format and decimal dot or comma, 1-17
Angle measure, 1-22
Coordinate system, 1-22
Beep, Key Click, and Last Stack, 1-24
Selecting CAS settings, 1-25
Selecting Display modes, 1-25
Selecting the display font, 1-26
Selecting properties of the line editor, 1-27
Selecting properties of the Stack, 1-27
Selecting properties of the Equation Writer (EQW), 1-28
Selecting the size of the header, 1-29
Selecting the clock display, 1-29
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
Creating algebraic expressions, 2-7

Page TOC-2
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
The inverse function, 3-3

Page TOC-3
Addition, subtraction, multiplication, division, 3-3
Using parentheses, 3-4
Absolute value function, 3-4
Squares and square roots, 3-5
Powers and roots, 3-5
Base-10 logarithms and powers of 10, 3-5
Using powers of 10 in entering data, 3-6
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 F0λ, 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-4
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
FACTORS, 5-10

Page TOC-5
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
UNITS convert menu, 5-27

Page TOC-6
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, 6-1
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
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
Application 2 - Velocity and acceleration in polar coordinates, 7-18