Computing with Mathematica
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Table of contents
- Contentsv
- Prefacexiii
- Part I: Learning the Basics1
- Chapter 1.Mathematica Basics: An Introduction3
- Introduction3
- Arithmetic3
- Mathematical Functions5
- Symbolic Computations6
- Exact and Approximate Solutions for Equations7
- Graphs of Functions of One Variable9
- Graphs of Parametric Equations10
- Graphs of Surfaces in Three Dimensions11
- Graphs of Contour Curves for Surfaces11
- Matrix Algebra12
- Random Numbers13
- Exercises14
- Chapter 2. Mathematica Basics: Help19
- Introduction19
- The ? and ?? Operators19
- The Help Browser20
- Interrupting Mathematica Computations21
- Memory Management in Mathematica21
- Exercises22
- Chapter 3. Mathematica Basics: Notebooks25
- Introduction25
- Notebook Toolbars25
- Format Preferences25
- Page Break Preferences26
- Cell Groupings26
- Tag Names27
- Links28
- In/Out Names28
- Hyperlinks to Documentation29
- Exercises29
- Chapter 4. Mathematica Basics: Text and Typesetting31
- Introduction31
- The BasicTypesetting and CompleteCharacters Palettes31
- Algebraic Manipulation Palette33
- Basic Input Palette34
- Basic Calculations Palette34
- Exercises35
- Chapter 5.Mathematica Basics: Packages37
- Introduction37
- Loading Standard Packages37
- Forgetting to Load a Package39
- Exercises41
- Part II: Designing Functions43
- Chapter 6.Values, Variables, and Assignments45
- Introduction45
- The Immediate Assignment Operator = for Values46
- The Delayed Assignment Operator := for Functions49
- Evaluation Issues for the Immediate and Delayed Assignment Operators53
- Computational Efficiency and the Assignment Operators56
- Exercises58
- Chapter 7.Functions63
- Introduction63
- Functions with a Single Argument63
- Functions with Several Arguments69
- Functions with Structured Arguments71
- Functions with Default Values for Arguments75
- Functions with a Varying Number of Arguments80
- Exercises81
- Chapter 8.Recursive Definitions87
- Introduction87
- Functions with a Single Recursive Argument87
- Functions with Several Recursive Arguments92
- Limitations to Recursive Computations95
- Exercises99
- Chapter 9.Substitution Rules and Optional Arguments107
- Introduction107
- Substitution Rules and the Replacement Mechanism107
- Substitution Rules and Interactive Computations110
- Options for Built-in Functions111
- Defining an Option for a Function114
- Exercises117
- Chapter 10.Four Spheres Packing Problem119
- Introduction119
- Analysis of the Problem119
- Computational Solution of the Problem120
- Graphic Rendering of the Solution121
- Exercises123
- Part III: Designing Programs125
- Chapter 11.List Processing Functions127
- Introduction127
- Processing Lists with the Map[ ] Function127
- Applications of the Map[ ] Function to Graphics Objects134
- List Manipulation, Element Extraction, and the Fold[ ] Function140
- The Functions Head[ ], Apply[ ], Outer[ ], Depth[ ], and Position[ ]146
- Exercises153
- Chapter 12.Iterations with Loops159
- Introduction159
- Using the Do[ ] Loop: Basics159
- Using the Do[ ] Loop: A Hula Hoop Animation163
- Using the While[ ] Loop: Basics165
- Using the While[ ] Loop: Termination Conditions and the Bisection Method167
- Using the For[ ] Loop: Basics170
- Using List Processing Functions as Alternatives for Loops173
- The Collatz Function175
- Exercises176
- Chapter 13.Computations with Modules and Local Variables181
- Introduction181
- Using the Module[ ] Function: Basics181
- Using the Module[ ] Function: Returning Numbers and Lists184
- Using the Module[ ] Function: Rendering Graphics Objects188
- Exercises191
- Part IV: Exploring Advanced Features197
- Chapter 14.Advanced Mathematica: Options199
- Introduction199
- Defining a Single Option for a Function199
- Defining Several Options for a Function204
- Using Built-in Graphics Options in User-Defined Functions208
- Defining Options for One Function That Are Options in Several Other Functions211
- Exercises216
- Chapter 15.Advanced Mathematica: Hyperlinks and Buttons221
- Introduction221
- Hyperlinks within a Notebook221
- Jumps within a Notebook without Hyperlinks222
- Hyperlinks between Notebooks222
- Hyperlinks to the Help Browser222
- Hyperlinks to Internet Resources223
- Hyperlinks as Buttons224
- Creating a Typesetting Palette225
- Creating a Palette of Expressions227
- Creating a Palette of Characters and Expressions228
- Creating an Evaluation Palette229
- Printing a Palette231
- Exercises231
- Chapter 16.Advanced Mathematica: Packages233
- Introduction233
- Contexts and Names233
- Initialization Cells236
- The Basic Scheme of a Package236
- Package Files244
- A Package for an Iteration Function247
- A Package for Gram-Schmidt Orthogonalization250
- Loading Packages254
- Exercises256
- Chapter 17.Advanced Mathematica: Files, Data Exchange, and Conversions261
- Introduction261
- Directories and File Paths262
- Import and Export of Data263
- Conversions to Other File Formats266
- Protected Functions267
- Exercises270
- Part V: Student Projects273
- Chapter 18.Student Projects275
- Introduction277
- Arnold’s Cat Map and Chaotic Mapping280
- Bouncing Balls281
- Collatz’s Function282
- Conway’s Challenge Sequence283
- Exponentially Damped Surfaces284
- Finite Automata285
- Fractals and Chaotic Boundary Sets286
- Fractals and Iterated Function Systems288
- Geometric Optics and Lens Systems289
- Groups of Rigid Motions290
- Growth Rates of Functions291
- Harmonic Coupled Oscillations292
- Hidden Patterns293
- Implementation of a Package294
- Interpolation of Curves with Cubic Splines295
- Juggling Balls296
- Leasing a Car297
- Markov Chains and Dynamic Models298
- Moiré Fringes299
- Oscillating Mass System301
- Pell’s Equation302
- Public Key Cryptography303
- Rainbows305
- Recurrence Relations306
- Spanning Trees of a Graph307
- Index309
Computing with Mathematica, 2nd edition is engaging and interactive. It is designed to teach readers how to use Mathematica efficiently for solving problems arising in fields such as mathematics, computer science, physics, and engineering. The text moves from simple to complex, often following a specific example on a number of different levels. This gradual increase in
complexity allows readers to steadily build their competence without being overwhelmed.
The 2nd edition of this acclaimed book features:
* An enclosed CD for Mac and Windows that contains the entire text as a
collection of Mathematica notebooks
* Substantive real world examples
* Challenging exercises, moving from simple to complex
* A collection of interactive projects from a variety of applications
"I really think this is an almost perfect text." -Stephen Brick,
University of South Alabama
* Substantive real world examples
* Challenging exercises, moving from simple to complex examples
* Interactive explorations (on the included CD-ROM) from a variety of topics using a multitude of interesting mathematical applications