Mastering Mathematica(R) (eBook)

Front Cover 1
Mastering Mathematica: Programming Methods and Applications 4
Copyright Page 5
Table of Contents 6
Preface 14
How to Use the Disk 20
Part I: 
22 
CHAPTER 1. A Quick 
24 
1 Opening Remarks 24
2 Grade School Arithmetic 25
3 High School Algebra and Trigonometry 31
4 College Calculus, Differential Equations and Linear Algebra 44
5 Graduate School 55
6 Practice 56
7 Exercises 57
CHAPTER 
62 
1 The Different Aspects of Mathematica 62
2 Interacting with the Kernel 63
3 Interacting with the Front-End 69
4 Using Packages 74
5 Saving Work to be Reused 78
6 Practice 80
7 Exercises 80
CHAPTER 
82 
1 Introduction 82
2 Numbers 82
3 Solving Algebraic Equations 91
4 Solving Ordinary Differential Equations 108
5 Practice 132
6 Exercises 133
CHAPTER 
138 
1 Plotting Commands and Optional Arguments 138
2 Two-Dimensional Graphics 140
3 Three-Dimensional Graphics 153
4 Animation 158
5 Sound 159
6 Practice 160
7 Exercises 161
Part II: Mastering Mathematica as a Programming Language 162
CHAPTER 
164 
1 Everything Is an Expression 164
2 Lists, Arrays, Intervals, and Sets 176
3 Thread, Inner and Outer 182
4 Other Aspects 185
5 Practice 187
6 Exercises 188
CHAPTER 
190 
1 Some Functional Aspects of Mathematica 190
2 Functional Programs 203
3 Practice 211
4 Exercises 212
CHAPTER 
216 
1 Introduction 216
2 Rewrite Rules in Mathematica 218
3 Pattern Matching 228
4 Using Patterns in Rules 234
5 Restricting Pattern Matching with Predicates 237
6 Examples of Restricted Rewrite Rules 247
7 Practice 256
8 Exercises 256
CHAPTER 
260 
1 Introduction 260
2 Basic Operations 262
3 Modules, Blocks and With 272
4 Examples 274
5 Practice 297
6 Exercises 298
CHAPTER 
302 
1 Introduction 302
2 The Duality Between Functions and Data 303
3 Object-Oriented Programming in Mathematica 314
4 The Hierarchy of Point Classes 323
5 Exercises 328
6 Implementation 328
CHAPTER 
330 
1 Introduction to Graphics Primitives 330
2 Two-Dimensional Graphics Objects, Graphics Modifiers and Options 334
3 Combining Built-in Graphics with Graphics Primitives 346
4 Graphics Arrays and Graphics Rectangles 348
5 Examples of Two-Dimensional Graphics 351
6 Three-Dimensional Graphics Primitives 357
7 Exercises 370
CHAPTER 
372 
1 Introduction 372
2 Packages 372
3 Attributes 382
4 Named Optional Arguments 386
5 Evaluation 394
6 Unbounded Search 401
7 Substitution and the Lambda Calculus 406
8 Exercises 414
Part III: Mastering Knowledge Representation in Mathematica 416
CHAPTER 12. Polya's Pattern 
418 
1 Introduction 418
2 Construction of Some Permutation Groups 419
3 The Geometric Approach 424
4 The Algebraic Approach 437
5 Implementation 445
CHAPTER 
446 
1 Introduction 446
2 Representations of Graphs 447
3 Products 466
4 Other Constructions in the Class graph 472
5 Some Graph Algorithms 478
6 Exercises 485
7 Implementation 486
CHAPTER 
490 
1 Introduction 490
2 Differentiable Mappings 491
3 Making Plots of Differentiable Mappings 498
4 Examples 500
5 Dimension[domain] == 1: Curves 504
6 Implementation 505
CHAPTER 
506 
1 Introduction 506
2 Critical Points 506
3 Minimal Surfaces 517
4 Implementation 529
Part IV: Answers 530
CHAPTER 1. 
532 
CHAPTER 3. 
548 
CHAPTER 5. 
566 
CHAPTER 6. 
576 
CHAPTER 
594 
CHAPTER 
614 
References 644
Index 648