Mastering Mathematica®

John Gray is a professor of mathematics and computer science at University of Illinois in Urbana. He was responsible for establishing a course on mathematical software at U. of I., where they have used Mathematica since its inception. This course has empowered numerous mathematicians, engineers, scientists, teachers, and students with the ability to use Mathematica as a programming language, and has also contributed to the development of this book.

Preface	p. xiii
How to Use the CD-ROM	p. xix
Mastering Mathematica as a Symbolic Pocket Calculator
A Quick Trip through Elementary Mathematics	p. 3
Opening Remarks	p. 3
Grade School Arithmetic	p. 4
High School Algebra and Trigonometry	p. 12
College Calculus, Differential Equations, and Linear Algebra	p. 25
Graduate School	p. 37
Practice	p. 38
Exercises	p. 39
Interacting with Mathematica	p. 45
The Different Aspects of Mathematica	p. 45
Interacting with the Kernel	p. 47
Interacting with the Notebooks Front End	p. 55
Producing Documents Using the Front End	p. 56
Using Packages	p. 63
Saving Work to be Reused	p. 67
Practice	p. 68
Exercises	p. 69
More about Numbers and Equations	p. 71
Introduction	p. 71
Numbers	p. 71
Solving Algebraic Equations	p. 82
Solving Ordinary Differential Equations	p. 99
Practice	p. 125
Exercises	p. 127
Built-In Graphics and Sound	p. 131
Plotting Commands and Optional Arguments	p. 131
Two-Dimensional Graphics	p. 133
Three-Dimensional Graphics	p. 146
Animation	p. 151
Sound	p. 152
Practice	p. 153
Exercises	p. 153
Mastering Mathematica as a Programming Language
The Mathematica Language	p. 157
Everything Is an Expression	p. 157
Lists, Arrays, Intervals, and Sets	p. 173
Other Aspects	p. 180
Practice	p. 183
Exercises	p. 183
Functional Programming	p. 187
Some Functional Aspects of Mathematica	p. 187
Defining Functions	p. 189
Applying Functions to Values	p. 196
Functional Programs	p. 206
Practice	p. 214
Exercises	p. 215
Rule Based Programming	p. 219
Introduction	p. 219
Rewrite Rules in Mathematica	p. 221
Pattern Matching	p. 232
Using Patterns in Rules	p. 239
Restricting Pattern Matching with Predicates	p. 242
Examples of Restricted Rewrite Rules	p. 252
Practice	p. 261
Exercises	p. 262
Procedural Programming	p. 265
Introduction	p. 265
Basic Operations	p. 268
Modules and Blocks	p. 278
Examples	p. 280
Practice	p. 303
Exercises	p. 304
Object-Oriented Programming	p. 307
Introduction	p. 307
The Duality between Functions and Data	p. 308
Object-Oriented Programming in Mathematica	p. 321
The Hierarchy of Point Classes	p. 331
Exercises	p. 337
Implementation	p. 337
Graphics Programming	p. 339
Introduction to Graphics Primitives	p. 339
Two-Dimensional Graphics Objects, Graphics Modifiers, and Options	p. 343
Combining Built-In Graphics with Graphics Primitives	p. 354
Graphics Arrays and Graphics Rectangles	p. 357
Examples of Two-Dimensional Graphics	p. 359
Three-Dimensional Graphics Primitives	p. 365
Exercises	p. 377
Some Finer Points	p. 379
Introduction	p. 379
Packages	p. 379
Attributes	p. 392
Named Optional Arguments	p. 395
Evaluation	p. 403
General Recursive Functions	p. 411
Substitution and the Lambda Calculus	p. 417
Exercises	p. 430
Mastering Knowledge Representation in Mathematica
Polya Pattern Analysis	p. 433
Introduction	p. 433
The Geometric Approach	p. 434
The Algebraic Approach	p. 456
Object-Oriented Graph Theory	p. 465
Introduction	p. 465
Representations of Graphs	p. 466
Products	p. 486
Other Graph Constructions in the Class graph	p. 493
Some Graph Algorithms	p. 499
Exercises	p. 507
Implementation	p. 508
Differentiable Mappings	p. 511
Introduction	p. 511
Differentiable Mappings	p. 513
Critical Points and Minimal Surfaces	p. 527
Critical Points	p. 527
Minimal Surfaces	p. 538
Answers
Answers: Part I	p. 555
Answers	p. 555
Answers	p. 558
Answers: Part II	p. 567
Answers	p. 567
Answers	p. 570
Answers	p. 579
Answers	p. 589
References	p. 611
Index	p. 615
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Mastering Mathematica®

Author Biography

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