Introduction to Maple

By: Andre HECK

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Hardcover | 1 April 2003 | Edition Number 3

At a Glance

Hardcover
848 Pages

Edition Type
Revised

Dimensions(cm)
24.77 x 15.88 x 4.45

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This is a fully revised edition of the best-selling Introduction to Maple. The book presents the modern computer algebra system Maple, teaching the reader not only what can be done by Maple, but also how and why it can be done. The book also provides the necessary background for those who want the most of Maple or want to extend its built-in knowledge. Emphasis is on understanding the Maple system more than on factual knowledge of built-in possibilities. To this end, the book contains both elementary and more sophisticated examples as well as many exercises. The typical reader should have a background in mathematics at the intermediate level. Andre Heck began developing and teaching Maple courses at the University of Nijmegen in 1987. In 1989 he was appointed managing director of the CAN Expertise Center in Amsterdam. CAN, Computer Algebra in the Netherlands, stimulates and coordinates the use of computer algebra in education and research. In 1996 the CAN Expertise Center was integrated into the Faculty of Science at the University of Amsterdam, into what became the AMSTEL Institute. The institute program focuses on the innovation of computer activities in mathematics and science education on all levels of education. The author is actively involved in the research and development aimed at the integrated computer learning environment Coach for mathematics and science education at secondary school level.

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Non-Fiction Computing & I.T.Computer Science Mathematics Algebra Business Applications Mathematical & Statistical Software Computer Programming & Software Development Calculus & Mathematical Analysis Numerical Analysis Databases Data Capture & Analysis

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
Table of Contents provided by Ingram. All Rights Reserved.

Introduction to Maple

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