Essential Maple 7. An Introduction for Scientific Programmers

What’s in This Book

Acknowledgements

Contents

List of Figures

1 Basics

1.1 Getting Started

1.1.1 Basic Command Syntax

1.1.2 Use of Context-Sensitive Menus to Execute Maple Commands

1.1.3 Sample Maple Sessions

1.1.4 Arithmetic

1.1.5 Interrupting a Maple Computation

1.1.6 Saving Work

1.2 Some Things to Watch Out For

1.2.1 Good Worksheet Hygiene

1.2.2 Common Syntax Errors

1.2.3 Assigning Values to Variables

1.2.4 Removing Values from Variables

1.2.5 sign versus signum versus csgn

1.2.6 Accidental Creation of a Remember Table

1.2.7 Fences: Parentheses ( ) versus Braces { } versus Brackets [ ] versus Angle Brackets

1.2.8 Quotation marks: Left versus Right versus String

1.2.9 Precedence of Operators

1.2.10 Protected and Reserved Names

1.2.11 Having Different Assumptions about Domains

1.3 Documenting YourWork

1.4 The Three Levels of Maple “Black Boxes”

1.5 No Nontrivial Software Package is Bug-Free

1.6 Evaluation Rules

1.6.1 Working With Complex Numbers and Expressions

1.6.2 Inert Functions

1.7 The assume Facility

2 Useful One-Word Commands

2.1 Simplification

2.1.1 normal

2.1.2 collect

2.1.3 factor

2.1.4 expand

2.1.5 combine

2.1.6 simplify

2.2 Solving Equations

2.2.1 solve

2.2.2 fsolve

2.2.3 dsolve

2.2.4 rsolve

2.2.5 Linear Equations

2.2.6 Other Solvers

2.2.7 Systems of Polynomial Equations

2.3 Manipulations from Calculus

2.3.1 diff

2.3.2 int

2.3.3 limit

2.3.4 series

2.4 Adding Terms versus the Finite-Difference Calculus

2.5 Floating-Point Evaluation

2.5.1 Using evalhf

2.5.2 Signed Zero

2.6 The Most Helpful Maple Utilities

2.6.1 I/O Utilities

2.6.2 alias and macro

2.6.3 Interacting with the Operating System and External Calls

2.6.4 Mapping Functions Onto Compound Objects

2.6.5 Code Generation

2.7 Plotting in Maple

2.7.1 Two-Dimensional Plots

2.7.2 Three-Dimensional Plots

2.7.3 Contour Plots and Other Plots

2.7.4 Common Errors

2.7.5 Getting Hard Copy of your Plots

2.8 Packages in Maple

2.8.1 The MATLAB Link

2.8.2 numapprox

2.8.3 Units

2.8.4 MathML

3 Programming in Maple

3.1 Procedures

3.1.1 Structured Types

3.1.2 Example: Modified Gram–Schmidt

3.2 Operators and Modules

3.2.1 A Module for Finite-Difference Operators

3.2.2 Remarks on Mathematical Operators

3.3 Data Structures

3.4 Local versus Global versus Environment Variables

3.4.1 Exporting Local Variables

3.4.2 Global Variables

3.4.3 Environment Variables

3.4.4 Nested Lexical Scopes

3.5 Recursion and option remember

3.6 Variable Number or Type of Arguments

3.7 Returning More Than One Result

3.8 Debugging Maple Programs

3.9 Sample Maple Programs

3.9.1 Parametric Solution of Algebraic Equations

3.9.2 Path Following in p(x, y) = 0

3.9.3 Large Expression Management, Revisited

3.9.4 Fourier Sine Series, Revisited

3.9.5 Solution of y (t) = ay(t - 1)

Appendix A A Primer on Complex Variables

A.1 Polar Coordinates and the Two-Argument Arctan Function

A.2 The Exponential Function

A.3 The Natural Logarithm

A.4 Trig Functions and Hyperbolic Functions

A.5 Inverse Trigs and Hyperbolics

Bibliography

Index

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