The Maple Book
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Features
Summary
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
