1 Introduction to Computer Algebra.- 1.1 What is Computer Algebra?.- 1.2 Computer Algebra Systems.- 1.3 Some Properties of Computer Algebra Systems.- 1.4 Advantages of Computer Algebra.- 1.5 Limitations of Computer Algebra.- 1.6 Design of Maple.- 2 The First Steps: Calculus on Numbers.- 2.1 Getting Started.- 2.2 Getting Help.- 2.3 Integers and Rational Numbers.- 2.4 Irrational Numbers and Floating-Point Numbers.- 2.5 Algebraic Numbers.- 2.6 Complex Numbers.- 2.7 Exercises.- 3 Variables and Names.- 3.1 Assignment and Unassignment.- 3.2 Evaluation.- 3.3 Names of Variables.- 3.4 Basic Data Types.- 3.5 Attributes.- 3.6 Properties.- 3.7 Exercises.- 4 Getting Around with Maple.- 4.1 Maple Input and Output.- 4.2 The Maple Library.- 4.3 Reading and Writing Files.- 4.4 Importing and Exporting Numerical Data.- 4.5 Low-Level I/O.- 4.6 Code Generation.- 4.7 Changing Maple to Your Own Taste.- 4.8 Exercises.- 5 Polynomials and Rational Functions.- 5.1 Univariate Polynomials.- 5.2 Multivariate Polynomials.- 5.3 Rational Functions.- 5.4 Conversions.- 5.5 Exercises.- 6 Internal Data Representation and Substitution.- 6.1 Internal Representation of Polynomials.- 6.2 Generalized Rational Expressions.- 6.3 Substitution.- 6.4 Exercises.- 7 Manipulation of Polynomials and Rational Expressions.- 7.1 Expansion.- 7.2 Factorization.- 7.3 Canonical Form and Normal Form.- 7.4 Normalization.- 7.5 Collection.- 7.6 Sorting.- 7.7 Exercises.- 8 Functions.- 8.1 Mathematical Functions.- 8.2 Arrow Operators.- 8.3 Piecewise Defined Functions.- 8.4 Maple Procedures.- 8.5 Recursive Procedure Definitions.- 8.6 unapply.- 8.7 Operations on Functions.- 8.8 Anonymous Functions.- 8.9 Exercises.- 9 Differentiation.- 9.1 Symbolic Differentiation.- 9.2 Automatic Differentiation.- 9.3 Exercises.- 10 Integration and Summation.- 10.1 Indefinite Integration.- 10.2 Definite Integration.- 10.3 Numerical Integration.- 10.4 Integral Transforms.- 10.5 Assisting Maple's Integrator.- 10.6 Summation.- 10.7 Exercises.- 11 Series, Approximation, and Limits.- 11.1 Truncated Series.- 11.2 Approximation of Functions.- 11.3 Power Series.- 11.4 Limits.- 11.5 Exercises.- 12 Composite Data Types.- 12.1 Sequence.- 12.2 Set.- 12.3 List.- 12.4 Array.- 12.5 Table.- 12.6 Last Name Evaluation.- 12.7 Function Call.- 12.8 Conversion Between Composite Data Types.- 12.9 Exercises.- 13 The Assume Facility.- 13.1 The Need for an Assume Facility.- 13.2 Basics of assume.- 13.3 An Algebra of Properties.- 13.4 Implementation of assume.- 13.5 Exercises.- 13.6 Hierarchy of Properties.- 14 Simplification.- 14.1 Automatic Simplification.- 14.2 expand.- 14.3 combine.- 14.4 simplify.- 14.5 convert.- 14.6 Trigonometric Simplification.- 14.7 Simplification w.r.t. Side Relations.- 14.8 Control Over Simplification.- 14.9 Defining Your Own Simplification Routines.- 14.10 Exercises.- 14.11 Simplification Chart.- 15 Graphics.- 15.1 Some Basic Two-Dimensional Plots.- 15.2 Options of plot.- 15.3 The Structure of Two-Dimensional Graphics.- 15.4 The plottools Package.- 15.5 Special Two-Dimensional Plots.- 15.6 Two-Dimensional Geometry.- 15.7 Plot Aliasing.- 15.8 A Common Mistake.- 15.9 Some Basic Three-Dimensional Plots.- 15.10 Options of plot3d.- 15.11 The Structure of Three-Dimensional Graphics.- 15.12 Special Three-Dimensional Plots.- 15.13 Data Plotting.- 15.14 Animation.- 15.15 List of Plot Options.- 15.16 Exercises.- 16 Solving Equations.- 16.1 Equations in One Unknown.- 16.2 Abbreviations in solve.- 16.3 Some Difficulties.- 16.4 Systems of Equations.- 16.5 The Gröbner Basis Method.- 16.6 Inequalities.- 16.7 Numerical Solvers.- 16.8 Other Solvers in Maple.- 16.9 Exercises.- 17 Differential Equations.- 17.1 First Glance at ODEs.- 17.2 Analytic Solutions.- 17.3 Taylor Series Method.- 17.4 Power Series Method.- 17.5 Numerical Solutions.- 17.6 DEtools.- 17.7 Perturbation Methods.- 17.8 Partial Differential Equations.- 17.9 Lie Point Symmetries of PDEs.- 17.10 Exercises.- 18 Linear Algebra: The linalg Package.- 18.1 Loading the linalg Package.- 18.2 Creating New Vectors and Matrices.- 18.3 Vector and Matrix Arithmetic.- 18.4 Basic Matrix Functions.- 18.5 Structural Operations.- 18.6 Vector Operations.- 18.7 Standard Forms of Matrices.- 18.8 Exercises.- 19 Linear Algebra: Applications.- 19.1 Kinematics of the Stanford Manipulator.- 19.2 A Three-Compartment Model of Cadmium Transfer.- 19.3 Molecular-Orbital Hückel Theory.- 19.4 Vector Analysis.- 19.5 Moore-Penrose Inverse.- 19.6 Exercises.- References.

A fully revised, second edition of the best-selling Introduction to Maple, now compatible through Maple V Release 4. It shows not only what can be done by Maple, but also how it can be done. Emphasis is on understanding the Maple system more than on factual knowledge of built-in possibilities, and, to this end, the book contains both elementary and more sophisticated examples and many exercises. Numerous new examples have been added to show how to use Maple as a problem solver, how to assist the system during computations, and how to extend its built-in facilities. Introduction to Maple is not simply a readable manual, but also provides the necessary background for those wanting to extend the built-in knowledge of Maple by implementing new algorithms. Readers should have a background in mathematics higher than beginner level.