Author | Heck, Andrรฉ. author |
---|---|
Title | Introduction to Maple [electronic resource] / by Andrรฉ Heck |
Imprint | New York, NY : Springer US, 1993 |
Connect to | http://dx.doi.org/10.1007/978-1-4684-0519-4 |
Descript | XIII, 497p. 84 illus. online resource |
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 Mapleโs 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 Grรถbner 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 Hรผckel Theory -- 18.4 Prolate Spheroidal Coordinates -- 18.5 Moore-Penrose Inverse -- 18.6 Exercises