Mastering Mathematica(R) (eBook)

Programming Methods and Applications

John W. Gray (Autor)

eBook Download: PDF

2014 | 1. Auflage
666 Seiten
Elsevier Science (Verlag)
978-1-4832-1403-0 (ISBN)

Infos

Mastering Mathematica©: Programming Methods and Applications presents the mathematical results and turn them into precise algorithmic procedures that can be executed by a computer. This book provides insight into more complex situations that can be investigated by hand. Organized into four parts, this book begins with an overview of the use of a pocket calculator. This text then looks in more detail at numerical calculations and solving equations, both algebraic and differential equations. Other parts consider the built-in graphics and show how to make pictures without programming. This book discusses as well the four styles of programming, namely, functional programming, imperative programming, rewrite programing, and object oriented programming. The reader is also introduced to differentiable mapping to show the analysis of critical points of functions and the developments in differential geometry that are required to study minimal surfaces. This book is a valuable resource for graduate students in mathematics, mathematics education, engineering, and the sciences.

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.

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Mastering Mathematica(R): Programming Methods and Applications presents the mathematical results and turn them into precise algorithmic procedures that can be executed by a computer. This book provides insight into more complex situations that can be investigated by hand. Organized into four parts, this book begins with an overview of the use of a pocket calculator. This text then looks in more detail at numerical calculations and solving equations, both algebraic and differential equations. Other parts consider the built-in graphics and show how to make pictures without programming. This book discusses as well the four styles of programming, namely, functional programming, imperative programming, rewrite programing, and object oriented programming. The reader is also introduced to differentiable mapping to show the analysis of critical points of functions and the developments in differential geometry that are required to study minimal surfaces. This book is a valuable resource for graduate students in mathematics, mathematics education, engineering, and the sciences.

Inhalt

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

Produkt-Details

• Erscheint lt. Verlag: 10.5.2014
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik
• Themenwelt: Technik
• ISBN-10: 1-4832-1403-6 / 1483214036
• ISBN-13: 978-1-4832-1403-0 / 9781483214030