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# Computing with Maple (Chapman Hall/CRC Mathematics Series) [Paperback]

Francis Wright

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INTRODUCTION
Learning Computing
Background References
Fundamental Terminology
MAPLE Interfaces
The MAPLE Worksheet Interface
Exercises: The Worksheet Interface
REVIEW OF BASICS
MAPLE Syntax: Special Symbols
Assignment, Evaluation, Substitution, and Simplification
Common Errors
Sequences, Lists, and Sets
Characters and Strings
Exercises
TWO-DIMENSIONAL PLOTTING
Simple Plotting
The plots Package and Animation
A Graphical Investigation of the Cardioid
Exporting Plots (and Worksheets)
Exercises: The Cycloid
Appendix: Code to plot the Figures
THREE-DIMENSIONAL PLOTTING
The plot3d Function
Three-Dimensional Plotting Options
Interacting with Three-Dimensional Plots
Three-Dimensional Plotting Options
Using the plots Package
Three-Dimensional Bouncing Ball Animation
Exporting Three-Dimensional Plots
Exercises
Appendix: Code to Plot the Figures
NUMERICAL AND SEMI-NUMERICAL COMPUTATION
Number Systems
Floating-Point Computation in MAPLE
Multiple Roots
Aliases and Algebraic Numbers
Computing with Modular Integers
Exercises
Appendix: Code to Plot the Figures
NUMERICAL LINEAR ALGEBRA
Linear Algebra in MAPLE
Numerical Linear Algebra
Interaction: Linear Algebra
Viewing Large Matrices and Vectors
Using the LinearAlgebra Package
Solving Systems of Linear Equations
Special Matrices
Eigenvalue Problems
Ill-Conditioned Problems
Under- and Over-Determined Problems
Exercises
LOGIC AND CONTROL STRUCTURES
Relational Operators
Boolean Algebra
Boolean Operators in MAPLE: and, or, not
Conditional Execution: if
Piecewise-Defined Functions
Loops: do, while, for
Exercises
PROCEDURES AND RECURSION
Defining and Using Procedures
General Procedure Definition Syntax
Variable Scope
Procedure Arguments
Special Identifiers in Procedures
Terminating Procedure Execution
Examples: Integer Factorization
Displaying MAPLE Procedures
Procedure Options and Remember Tables
Recursion
Procedures that Output Plots
Recursive Plotting
Animating the Koch Snowflake Fractal
Program Design
Exercises
OPERATORS AND FUNCTIONS
Operators
Converting Between Expressions and Mappings
Composition of Mappings and Functions
The Derivative Operator D
Set Operations
Example of Recursive Integer and Polynomial Functions
Exercises
DATA TYPES
Primitive Types: whattype
Use of Type Information: Error Checking, Polymorphism
Alternative Types: {type1, type2, …}
The Main MAPLE Data Types
Type Testing: type and ::
Boolean Combination of Types: And, Or, Not
Structured or Nested Data Types
Special Procedure-Argument Types
Examples of Polymorphic Procedures
Defining New Types
Exercises
CONVENTIONAL PROGRAMMING
Operations on Structures
Implementing Vector and Matrix Algebra
Data Processing in MAPLE
Interactive Programs in MAPLE
Error Handling: try, catch
Debugging
Exercises
ALGEBRAIC PROGRAMMING
Univariate Polynomial Algorithms
Multivariate Polynomial Algorithms
Exercises
Introduction
Copying and Moving Cells
Working with Sequences
Tabulating Data
Case Study: The Simple Pendulum
Exercises
TEXT PROCESSING
Text Files
Counting Lines, Words, and Characters
Text Formatting
A Markov Chain Algorithm
Exercises
OBJECT ORIENTATION AND MODULES
Introduction to Object Orientation
Block Matrices
Modules as Records
Modules in More Detail
Module Constructors
Modules as Objects
Data Encapsulation
Accessing Block Matrix Elements
Square and Inverse Block Matrices
Modules and Types
Block Matrix Multiplication
Limitations of Modules as Objects