| Preface to the Third Edition | p. v |
| List of Tables | p. xv |
| Introduction to Computer Algebra | p. 1 |
| What is Computer Algebra? | p. 1 |
| Computer Algebra Systems | p. 2 |
| Some Properties of Computer Algebra Systems | p. 5 |
| Advantages of Computer Algebra | p. 11 |
| Limitations of Computer Algebra | p. 23 |
| Design of Maple | p. 29 |
| The First Steps: Calculus on Numbers | p. 33 |
| Getting Started | p. 33 |
| Getting Help | p. 36 |
| Integers and Rational Numbers | p. 41 |
| Irrational Numbers and Floating-Point Numbers | p. 46 |
| Algebraic Numbers | p. 53 |
| Complex Numbers | p. 58 |
| Exercises | p. 63 |
| Variables and Names | p. 65 |
| Assignment and Unassignment | p. 65 |
| Evaluation | p. 73 |
| Names of Variables | p. 77 |
| Basic Data Types | p. 83 |
| Attributes | p. 88 |
| Properties | p. 89 |
| Exercises | p. 93 |
| Getting Around with Maple | p. 95 |
| Maple Input and Output | p. 95 |
| The Maple Library | p. 101 |
| Reading and Writing Files | p. 106 |
| Importing and Exporting Numerical Data | p. 113 |
| Low-level I/O | p. 116 |
| Code Generation | p. 127 |
| Changing Maple to Your Own Taste | p. 133 |
| Exercises | p. 137 |
| Polynomials and Rational Functions | p. 139 |
| Univariate Polynomials | p. 139 |
| Multivariate Polynomials | p. 145 |
| Rational Functions | p. 147 |
| Conversions | p. 148 |
| Exercises | p. 151 |
| Internal Data Representation and Substitution | p. 153 |
| Internal Representation of Polynomials | p. 153 |
| Generalized Rational Expressions | p. 159 |
| Substitution | p. 161 |
| Exercises | p. 174 |
| Manipulation of Polynomials and Rational Expressions | p. 175 |
| Expansion | p. 175 |
| Factorization | p. 178 |
| Canonical Form and Normal Form | p. 181 |
| Normalization | p. 183 |
| Collection | p. 185 |
| Sorting | p. 187 |
| Exercises | p. 188 |
| Functions | p. 189 |
| Mathematical Functions | p. 189 |
| Arrow Operators | p. 193 |
| Piecewise Defined Functions | p. 195 |
| Maple Procedures | p. 201 |
| Recursive Procedure Definitions | p. 204 |
| Unapply | p. 208 |
| Operations on Functions | p. 209 |
| Anonymous Functions | p. 210 |
| Exercises | p. 211 |
| Differentiation | p. 213 |
| Symbolic Differentiation | p. 213 |
| Automatic Differentiation | p. 220 |
| Exercises | p. 224 |
| Integration and Summation | p. 225 |
| Indefinite Integration | p. 225 |
| Definite Integration | p. 234 |
| Numerical Integration | p. 239 |
| Integral Transforms | p. 241 |
| Assisting Maple's Integrator | p. 250 |
| Summation | p. 255 |
| Exercises | p. 260 |
| Series, Approximation, and Limits | p. 265 |
| Truncated Series | p. 265 |
| Approximation of Functions | p. 276 |
| Power Series | p. 281 |
| Limits | p. 285 |
| Exercises | p. 287 |
| Composite Data Types | p. 289 |
| Sequence | p. 289 |
| Set | p. 292 |
| List | p. 294 |
| Arrays | p. 300 |
| Table: table | p. 316 |
| Last Name Evaluation | p. 319 |
| Rectangular Table: rtable | p. 321 |
| Record Data Structure | p. 325 |
| Function Call | p. 326 |
| Conversion between Composite Data Types | p. 328 |
| Exercises | p. 331 |
| The Assume Facility | p. 333 |
| The Need for an Assume Facility | p. 333 |
| Basics of assume | p. 338 |
| An Algebra of Properties | p. 342 |
| Implementation of assume | p. 344 |
| Exercises | p. 350 |
| Hierarchy of Properties | p. 350 |
| Simplification | p. 353 |
| Automatic Simplification | p. 354 |
| expand | p. 356 |
| combine | p. 364 |
| simplify | p. 370 |
| convert | p. 375 |
| Trigonometric Simplification | p. 379 |
| Simplification w.r.t. Side Relations | p. 382 |
| Control Over Simplification | p. 386 |
| Defining Your Own Simplification Routines | p. 391 |
| Exercises | p. 397 |
| Simplification Chart | p. 399 |
| Graphics | p. 401 |
| Some Basic Two-Dimensional Plots | p. 403 |
| Options of plot | p. 407 |
| The Structure of Two-Dimensional Graphics | p. 418 |
| The plottools Package | p. 422 |
| Special Two-Dimensional Plots | p. 426 |
| Two-Dimensional Geometry | p. 436 |
| Plot Aliasing | p. 438 |
| A Common Mistake | p. 439 |
| Some Basic Three-Dimensional Plots | p. 441 |
| Options of plot3d | p. 442 |
| The Structure of Three-Dimensional Graphics | p. 448 |
| Special Three-Dimensional Plots | p. 452 |
| Data Plotting | p. 459 |
| Animation | p. 469 |
| List of Plot Options | p. 472 |
| Exercises | p. 477 |
| Solving Equations | p. 481 |
| Equations in One Unknown | p. 481 |
| Abbreviations in solve | p. 483 |
| Some Difficulties | p. 485 |
| Systems of Equations | p. 492 |
| The Grobner Basis Method | p. 501 |
| Inequalities | p. 508 |
| Numerical Solvers | p. 510 |
| Other Solvers in Maple | p. 512 |
| Exercises | p. 519 |
| Differential Equations | p. 521 |
| First Glance at ODEs | p. 522 |
| Analytic Solutions | p. 524 |
| Lie Point Symmetries for ODEs | p. 538 |
| Taylor Series Method | p. 560 |
| Power Series Method | p. 561 |
| Numerical Solutions | p. 566 |
| Graphical Methods | p. 580 |
| Change of Coordinates | p. 586 |
| Perturbation Methods | p. 590 |
| Partial Differential Equations | p. 600 |
| Lie Point Symmetries of PDEs | p. 615 |
| Exercises | p. 617 |
| The LinearAlgebra Package | p. 619 |
| Loading the LinearAlgebra Package | p. 619 |
| Creating Vectors and Matrices | p. 621 |
| Vector and Matrix Arithmetic | p. 629 |
| Basic Matrix Functions | p. 634 |
| Structural Operations | p. 641 |
| Vector Operations | p. 645 |
| Standard Forms of Matrices | p. 646 |
| Numeric Linear Algebra | p. 656 |
| Exercises | p. 660 |
| Linear Algebra: Applications | p. 663 |
| Kinematics of the Stanford Manipulator | p. 663 |
| A 3-Compartment Model of Cadmium Transfer | p. 669 |
| Molecular-Orbital Huckel Theory | p. 680 |
| Vector Calculus | p. 687 |
| Moore-Penrose Inverse | p. 693 |
| Exercises | p. 694 |
| A Bird's-Eye View of Grobner Bases | p. 697 |
| Introduction | p. 697 |
| Elementary Solution Methods | p. 702 |
| Heuristic Method | p. 702 |
| Gaussian Elimination-Like Method | p. 702 |
| Conclusion | p. 703 |
| Basics of the Grobner Basis Method | p. 703 |
| Term Ordering | p. 704 |
| Polynomial Reduction and Normal Form | p. 710 |
| Characterization of a Grobner Basis | p. 712 |
| The Buchberger Algorithm | p. 714 |
| Improvements of Buchberger's Algorithm | p. 716 |
| Properties and Applications of Grobner Bases | p. 719 |
| Equivalence of Systems of Polynomial Equations | p. 720 |
| Dimension, Hilbert Series and Hilbert Polynomial | p. 721 |
| Solvability of Polynomial Equations | p. 725 |
| Finite Solvability of Polynomial Equations | p. 729 |
| Counting of Finite Solutions | p. 730 |
| Converting a System of Polynomial Equations into Triangular Form | p. 732 |
| Finding a Univariate Polynomial | p. 734 |
| Decomposition of Ideals | p. 735 |
| An Example From Robotics | p. 739 |
| Implicitization of Parametric Objects | p. 740 |
| Invertibility of Polynomial Mappings | p. 742 |
| Simplification of Expressions | p. 742 |
| Working over General Algebras | p. 743 |
| Exercises | p. 745 |
| References | p. 747 |
| Index | p. 761 |
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