The fully revised edition of this best-selling title presents the modern computer algebra system Maple. It teaches the reader not only what can be done by Maple, but also how and why it can be done. The book provides the necessary background for those who want the most of Maple or want to extend its built-in knowledge, containing both elementary and more sophisticated examples as well as many exercises.

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 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 Evaluation.- 3.2 Unassignment.- 3.3 Full Evaluation.- 3.4 Names of Variables.- 3.5 Basic Data Types.- 3.6 Exercises.- 4 Getting Around with Maple.- 4.1 Input and Output.- 4.2 The Maple Library.- 4.3 Reading and Writing Files.- 4.4 Formatted I/O.- 4.5 Code Generation.- 4.6 Changing Maple to your own Taste.- 4.7 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 Maple Procedures.- 8.4 Recursive Procedure Definitions.- 8.5 unapply.- 8.6 Operations on Functions.- 8.7 Anonymous Functions.- 8.8 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 Truncated Series Expansions, Power Series, and Limits.- 11.1 Truncated Series Expansions.- 11.2 Power Series.- 11.3 Limits.- 11.4 Exercises.- 12 Composite Data Types.- 12.1 Sequence.- 12.2 Set.- 12.3 List.- 12.4 Array.- 12.5 convert and map.- 12.6 Exercises.- 13 Simplification.- 13.1 Automatic Simplification.- 13.2 expand.- 13.3 combine.- 13.4 simplify.- 13.5 convert.- 13.6 Trigonometric Simplification.- 13.7 Simplification w.r.t. Side Relations.- 13.8 Exercises.- 14 Graphics.- 14.1 Some Basic Two-Dimensional Plots.- 14.2 Options of plot.- 14.3 The Structure of Two-Dimensional Graphics.- 14.4 Special Two-Dimensional Plots.- 14.5 Plot Aliasing.- 14.6 A Common Mistake.- 14.7 Some Basic Three-Dimensional Plots.- 14.8 Options of plot3d.- 14.9 The Structure of Three-Dimensional Graphics.- 14.10 Special Three-Dimensional Plots.- 14.11 Animation.- 14.12 Exercises.- 15 Solving Equations.- 15.1 Equations in One Unknown.- 15.2 Abbreviations in solve.- 15.3 Some Difficulties.- 15.4 Systems of Equations.- 15.5 The Gröbner Basis Method.- 15.6 Numerical Solvers.- 15.7 Other Solvers in Maple.- 15.8 Exercises.- 16 Differential Equations.- 16.1 First Glance at ODEs.- 16.2 Analytic Solutions.- 16.3 Taylor Series Method.- 16.4 Power Series Method.- 16.5 Numerical Solutions.- 16.6 Perturbation Methods.- 16.7 Liesymm.- 16.8 Exercises.- 17 Linear Algebra: Basics.- 17.1 Basic Operations on Matrices.- 17.2 Last Name Evaluation.- 17.3 The Linear Algebra Package.- 17.4 Exercises.- 18 Linear Algebra: Applications.- 18.1 Kinematics of the Stanford Manipulator.- 18.2 A 3-Compartment Model of Cadmium Transfer.- 18.3 Molecular-orbital Hückel Theory.- 18.4 Prolate Spheroidal Coordinates.- 18.5 Moore-PenroseInverse.- 18.6 Exercises.