Introduction to Maple / Andre Heck.

CONTENIDO
1 Introduction to Computer Algebra 1
1.1 What is Computer Algebra? 1
1.2 Computer Algebra Systems 2
1.3 Some Properties of Computer Algebra Systems 5
1.4 Advantages of Computer Algebra 11
1.5 Limitations of Computer Algebra 24
1.6 Design of Maple 30
2 The First Steps: Calculus on Numbers 35
2.1 Getting Started 35
2.2 Getting Help 38
2.3 Integers and Rational Numbers 44
2.4 Irrational Numbers and Floating-Point Numbers 48
2.5 Algebraic Numbers 54
2.6 Complex Numbers 59
3 Variables and Names 65
3.1 Assignment and Unassignment 65
3.2 Evaluation 73
3.3 Names of Variables 77
3.4 Basic Data Types 82
3.5 Attributes 86
3.6 Properties 87
4 Getting Around with Maple 95
4.1 Maple Input and Output 95
4.2 The Maple Library 101
4.3 Reading and Writing Files 105
4.4 Importing and Exporting Numerical Data 110
4.5 Low-level I/O 113
4.6 Code Generation 123
4.7 Changing Maple to Your Own Taste 129
5 Polynomials and Rational Functions 135
5.1 Univariate Polynomials 135
5.2 Multivariate Polynomials 140
5.3 Rational Functions 142
5.4 Conversions 144
6 Internal Data Representation and Substitution 149
6.1 Internal Representation of Polynomials 149
6.2 Generalized Rational Expressions 155
6.3 Substitution 158
7 Manipulation of Polynomials and Rational Expressions 173
7.1 Expansion 173
7.2 Factorization 176
7.3 Canonical Form and Normal Form 179
7.4 Normalization 181
7.5 Collection 183
7.6 Sorting 186
8 Functions 189
8.1 Mathematical Functions 189
8.2 Arrow Operators 193
8.3 Piecewise Defined Functions 195
8.4 Maple Procedures 202
8.5 Recursive Procedure Definitions 204
8.6 Unapply 209
8.7 Operations on Functions 210
8.8 Anonymous Functions 211
9 Differentiation 213
9.1 Symbolic Differentiation 213
9.2 Automatic Differentiation 221
10 Integration and Summation 227
10.1 Indefinite Integration 227
10.2 Definite Integration 236
10.3 Numerical Integration 241
10.4 Integral Transforms 242
10.5 Assisting Maple's Integrator 252
10.6 Summation 256
11 Series, Approximation, and Limits 267
11.1 Truncated Series 267
11.2 Approximation of Functions 278
11.3 Power Series 285
11.4 Limits 288
12 Composite Data Types 293
12.1 Sequence 293
12.2 Set 296
12.3 List 298
12.4 Arrays 304
12.5 Table: table 310
12.6 Last Name Evaluation 314
12.7 Function Call 317
12.10 Conversion between Composite Data Types 319
13 The Assume Facility 325
13.1 The Need for an Assume Facility 325
13.2 Basics of assume 329
13.3 An Algebra of Properties 332
13.4 Implementation of assume 335
13.6 Hierarchy of Properties 340
14 Simplification 343
14.1 Automatic Simplification 344
14.2 expand 346
14.3 combine 353
14.4 simplify 358
14.5 convert 364
14.6 Trigonometric Simplification 367
14.7 Simplification w.r.t. Side Relations 370
14.8 Control Over Simplification 374
14.9 Defining Your Own Simplification Routines 378
14.11 Simplification Chart 399
15 Graphics 387
15.1 Some Basic Two-Dimensional Plots 389
15.2 Options of plot 493
15.3 The Structure of Two-Dimensional Graphics 406
15.4 The plottools Package 412
15.5 Special Two-Dimensional Plots 416
15.6 Two-Dimensional Geometry 429
15.7 Plot Aliasing 432
15.8 A Common Mistake 433
15.9 Some Basic Three-Dimensional Plots 434
15.10 Options of plot3d 436
15.11 The Structure of Three-Dimensional Graphics 444
15.12 Special Three-Dimensional Plots 449
15.13 Data Plotting 457
15.14 Animation 467
15.15 List of Plot Options 469
16 Solving Equations 479
16.1 Equations in One Unknown 479
16.2 Abbreviations in solve 480
16.3 Some Difficulties 481
16.4 Systems of Equations 488
16.5 The Grobner Basis Method 499
16.6 Inequalities 505
16.7 Numerical Solvers 507
16.8 Other Solvers in Maple 509
17 Differential Equations 519
17.1 First Glance at ODEs 519
17.2 Analytic Solutions 520
17.3 Taylor Series Method 532
17.4 Power Series Method 534
17.5 Numerical Solutions 536
17.6 DEtools 548
17.7 Perturbation Methods 555
17.8 Partial Differential Equations 567
17.9 Lie Point Symmetries of PDEs 569
18 Linear Algebra: The linalg Package 575
18.1 Loading the Linalg Package 575
18.2 Creating New Vectors and Matrices 576
18.3 Vector and Matrix Arithmetic 580
18.4 Basic Matrix Functions 584
18.5 Structural Operations 589
18.6 Vector Operations 589
18.7 Standard Forms of Matrices 592
19 Linear Algebra: Applications 601
19.1 Kinematics of the Stanford Manipulator 601
19.2 A Three-Compartment Model of Cadmium Transfer 606
19.3 Molecular-Orbital Huckel Theory 618
19.4 Vector Analysis 623
19.5 Moore-Penrose Inverse 631