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Computing with Maple



PAPERBACK by Wright, Francis (Queen Mary & Westfield College, University of London, UK)


552 pages
27 SEP 2001


Powerful, flexible, easy to use-small wonder that the use of MAPLE (R) continues to increase, particularly since the latest releases of MAPLE. The built-in nature of its numerical and graphical facilities gives MAPLE a distinct advantage over traditional programming languages, yet to date, no textbook has used that advantage to introduce programming concepts. Moreover, few books based on MAPLE's latest versions even exist. Computing with MAPLE presents general programming principles using MAPLE as a concrete example of a programming language. The author first addresses the basic MAPLE functions accessible for interactive use then moves to actual programming, discussing all of the programming facilities that MAPLE provides, including control structures, data types, graphics, spreadsheets, text processing, and object oriented programming. Reflecting MAPLE's primary function as a computational tool, the book's emphasis is on mathematical examples, and it includes a full chapter devoted to algebraic programming. Classroom tested since 1995, the material in Computing with MAPLE is particularly appropriate for an intermediate-level introductory course in programming for both mathematics and computing students. It includes numerous exercises and test questions, with MAPLE worksheets, contact information, and supplementary material available on the Internet.


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 More About Variable Scope 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 SPREADSHEETS Introduction Copying and Moving Cells Working with Sequences Tabulating Data Programming Spreadsheets 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 Operator Overloading Using a Private MAPLE Library Modules as Packages Adding Online Help Exercises BIBLIOGRAPHY