The Maple Book: 1st Edition (Hardback) book cover

The Maple Book

1st Edition

By Frank Garvan

Chapman and Hall/CRC

496 pages | 64 B/W Illus.

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Hardback: 9781584882329
pub: 2001-11-28
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pub: 2001-11-28
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Description

Maple is a very powerful computer algebra system used by students, educators, mathematicians, statisticians, scientists, and engineers for doing numerical and symbolic computations. Greatly expanded and updated from the author's MAPLE V Primer, The MAPLE Book offers extensive coverage of the latest version of this outstanding software package, MAPLE 7.0

The MAPLE Book serves both as an introduction to Maple and as a reference. Organized according to level and subject area of mathematics, it first covers the basics of high school algebra and graphing, continues with calculus and differential equations then moves on to more advanced topics, such as linear algebra, vector calculus, complex analysis, special functions, group theory, number theory and combinatorics. The MAPLE Book includes a tutorial for learning the Maple programming language. Once readers have learned how to program, they will appreciate the real power of Maple.

The convenient format and straightforward style of The MAPLE Book let users proceed at their own pace, practice with the examples, experiment with graphics, and learn new functions as they need them. All of the Maple commands used in the book are available on the Internet, as are links to various other files referred to in the book. Whatever your level of expertise, you'll want to keep The MAPLE Book next to your computer.

Table of Contents

GETTING STARTED

Starting a MAPLE Session

Different Versions of MAPLE

Basic Syntax

Editing Mistakes

Help

A Sample Session and Context Menus

Palettes

Spreadsheets

Quitting MAPLE

MAPLE AS A CALCULATOR

Exact Arithmetic and Basic Functions

Floating-Point Arithmetic

HIGH SCHOOL ALGEBRA

Polynomials and Rational Functions

Equations

Fun with Integers

Unit Conversion

Trigonometry

DATA TYPES

Sequences

Sets

Lists

Tables

Arrays

Data Conversions

Other Data Types

CALCULUS

Defining Functions

Composition of Functions

Summation and Product

Limits

Differentiation

Extrema

Integration

Taylor and Series Expansions

The Student Package

GRAPHICS

2-Dimensional Plotting

3-Dimensional Plotting

Animation

MAPLE PROGRAMMING

The MAPLE Procedure

Conditional Statements

The "for" loop

Type Declaration

The "while" Loop

Recursive Procedures

Explicit Return

Error Statement

args and nargs

Input and Output

Benerating C and Fortran Code

Viewing Built-in MAPLE Code

The MAPLE Interactive Debugger

Writing your own Packages

Answers to Programming Exercises

DIFFERENTIAL EQUATIONS

Solving Ordinary Differential Equations

First-Order Differential Equation

Numerical Solutions

Second- and Higher-Order Des

Series Solutions

The Laplace Transform

The Detools Package

Solving Systems of Ordinary Differential Equations

Plotting Solutions to Ordinary Differential Equations

Partial Differential Equations

LINEAR ALGEBRA

Vectors, Arrays, and Matrices

Matrix Context Menu

Elementary Row and Colum Operations

Gaussian Elimination

Inverses, Determinants, Minors, and the Adjoint

Special Matrices and Vectors

Systems of Linear Equations

Row Space, Column Space, and Nullspace

Eigenvectors and Diagonalization

Jordan Form

Inner Products and Vector and Matrix Norms

Least Squares Problems

QR-Factorization and the Gram-Schmidt Process

LU-Factorization

Other Linear Algebra Functions

The linalg Package

MULTIVARIABLE AND VECTOR CALCULUS

Vectors

Lines and Planes

Vector-Valued Functions

The Gradient and Directional Derivatives

Extrema

Multiple Integrals

Vector Field

Line Integrals

Green's Theorem

Surface Integrals

COMPLEX ANALYSIS

Arithmetic of Complex Numbers

Polar Form

nth Roots

The Cauchy-Riemann Equations and Harmonic Functions

Elementary Functions

Conformal Mapping

Taylor Series and Laurent Series

Contour Integrals

Residues and Poles

OPENING, SAVING, AND EXPORTING WORKSHEETS

Opening and Existing Worksheet

Saving a Worksheet

Opening a MAPLE Text Fle

Exporting Worksheets and LaTeX

DOCUMENT PREPARATION

Adding Text

Inserting Math into Text

Adding Titles and Headings

Creating a Subsection

Cutting and Pasting

Bookmarks and Hypertext

MORE GRAPHICS

The plottoos Package

The geometry Package

The geom3d Package

SPECIAL FUNCTIONS

Overview of Mathematical Functions

Bessel Functions

The GamMa Function

Hypergeometric Functions

Elliptic Integrals

The AGM

Jacobi's Theta Functions

Elliptic Functions

The Riemann Zeta Function

Orthogonal Polynomials

Integral Transforms

Fast Fourier Transform

Asymptotic Expansion

STATISTICS

Introduction

Data Sets

Numerical Methods for Describing Data

Transforming Data

Graphical Methods for Describing Data

Linear Regression

ANOVA

Distributions

OVERVIEW OF OTHER PACKAGES

Finite Fields

Polynomials

Group Theory

Combinatorics

Number Theory

Numerical Approximation

Miscellaneous Packages

New Packages

APPENDICES

MAPLE Resources

Glossary of Commands

Further Reading

REFERENCES

INDEX

Subject Categories

BISAC Subject Codes/Headings:
MAT000000
MATHEMATICS / General
MAT003000
MATHEMATICS / Applied
MAT021000
MATHEMATICS / Number Systems