محاسبات با متا متیکا، ویرایش دوم

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 Computing with Mathematica® 4 Copyright Page 5 Contents 6 Preface 14 Part I: Learning the Basics 20 Chapter 1.Mathematica Basics: An Introduction 22 Introduction 22 Arithmetic 22 Mathematical Functions 24 Symbolic Computations 25 Exact and Approximate Solutions for Equations 26 Graphs of Functions of One Variable 28 Graphs of Parametric Equations 29 Graphs of Surfaces in Three Dimensions 30 Graphs of Contour Curves for Surfaces 30 Matrix Algebra 31 Random Numbers 32 Exercises 33 Chapter 2. Mathematica Basics: Help 38 Introduction 38 The ? and ?? Operators 38 The Help Browser 39 Interrupting Mathematica Computations 40 Memory Management in Mathematica 40 Exercises 41 Chapter 3. Mathematica Basics: Notebooks 44 Introduction 44 Notebook Toolbars 44 Format Preferences 44 Page Break Preferences 45 Cell Groupings 45 Tag Names 46 Links 47 In/Out Names 47 Hyperlinks to Documentation 48 Exercises 48 Chapter 4. Mathematica Basics: Text and Typesetting 50 Introduction 50 The BasicTypesetting and CompleteCharacters Palettes 50 Algebraic Manipulation Palette 52 Basic Input Palette 53 Basic Calculations Palette 53 Exercises 54 Chapter 5.Mathematica Basics: Packages 56 Introduction 56 Loading Standard Packages 56 Forgetting to Load a Package 58 Exercises 60 Part II: Designing Functions 62 Chapter 6.Values, Variables, and Assignments 64 Introduction 64 The Immediate Assignment Operator = for Values 65 The Delayed Assignment Operator := for Functions 68 Evaluation Issues for the Immediate and Delayed Assignment Operators 72 Computational Efficiency and the Assignment Operators 75 Exercises 77 Chapter 7.Functions 82 Introduction 82 Functions with a Single Argument 82 Functions with Several Arguments 88 Functions with Structured Arguments 90 Functions with Default Values for Arguments 94 Functions with a Varying Number of Arguments 99 Exercises 100 Chapter 8.Recursive Definitions 106 Introduction 106 Functions with a Single Recursive Argument 106 Functions with Several Recursive Arguments 111 Limitations to Recursive Computations 114 Exercises 118 Chapter 9.Substitution Rules and Optional Arguments 126 Introduction 126 Substitution Rules and the Replacement Mechanism 126 Substitution Rules and Interactive Computations 129 Options for Built-in Functions 130 Defining an Option for a Function 133 Exercises 136 Chapter 10.Four Spheres Packing Problem 138 Introduction 138 Analysis of the Problem 138 Computational Solution of the Problem 139 Graphic Rendering of the Solution 140 Exercises 142 Part III: Designing Programs 144 Chapter 11.List Processing Functions 146 Introduction 146 Processing Lists with the Map[ ] Function 146 Applications of the Map[ ] Function to Graphics Objects 153 List Manipulation, Element Extraction, and the Fold[ ] Function 159 The Functions Head[ ], Apply[ ], Outer[ ], Depth[ ], and Position[ ] 165 Exercises 172 Chapter 12.Iterations with Loops 178 Introduction 178 Using the Do[ ] Loop: Basics 178 Using the Do[ ] Loop: A Hula Hoop Animation 182 Using the While[ ] Loop: Basics 184 Using the While[ ] Loop: Termination Conditions and the Bisection Method 186 Using the For[ ] Loop: Basics 189 Using List Processing Functions as Alternatives for Loops 192 The Collatz Function 194 Exercises 195 Chapter 13.Computations with Modules and Local Variables 200 Introduction 200 Using the Module[ ] Function: Basics 200 Using the Module[ ] Function: Returning Numbers and Lists 203 Using the Module[ ] Function: Rendering Graphics Objects 207 Exercises 210 Part IV: Exploring Advanced Features 216 Chapter 14.Advanced Mathematica: Options 218 Introduction 218 Defining a Single Option for a Function 218 Defining Several Options for a Function 223 Using Built-in Graphics Options in User-Defined Functions 227 Defining Options for One Function That Are Options in Several Other Functions 230 Exercises 235 Chapter 15.Advanced Mathematica: Hyperlinks and Buttons 240 Introduction 240 Hyperlinks within a Notebook 240 Jumps within a Notebook without Hyperlinks 241 Hyperlinks between Notebooks 241 Hyperlinks to the Help Browser 241 Hyperlinks to Internet Resources 242 Hyperlinks as Buttons 243 Creating a Typesetting Palette 244 Creating a Palette of Expressions 246 Creating a Palette of Characters and Expressions 247 Creating an Evaluation Palette 248 Printing a Palette 250 Exercises 250 Chapter 16.Advanced Mathematica: Packages 252 Introduction 252 Contexts and Names 252 Initialization Cells 255 The Basic Scheme of a Package 255 Package Files 263 A Package for an Iteration Function 266 A Package for Gram-Schmidt Orthogonalization 269 Loading Packages 273 Exercises 275 Chapter 17.Advanced Mathematica: Files, Data Exchange, and Conversions 280 Introduction 280 Directories and File Paths 281 Import and Export of Data 282 Conversions to Other File Formats 285 Protected Functions 286 Exercises 289 Part V: Student Projects 292 Chapter 18.Student Projects 294 Introduction 296 Arnold’s Cat Map and Chaotic Mapping 299 Bouncing Balls 300 Collatz’s Function 301 Conway’s Challenge Sequence 302 Exponentially Damped Surfaces 303 Finite Automata 304 Fractals and Chaotic Boundary Sets 305 Fractals and Iterated Function Systems 307 Geometric Optics and Lens Systems 308 Groups of Rigid Motions 309 Growth Rates of Functions 310 Harmonic Coupled Oscillations 311 Hidden Patterns 312 Implementation of a Package 313 Interpolation of Curves with Cubic Splines 314 Juggling Balls 315 Leasing a Car 316 Markov Chains and Dynamic Models 317 Moiré Fringes 318 Oscillating Mass System 320 Pell’s Equation 321 Public Key Cryptography 322 Rainbows 324 Recurrence Relations 325 Spanning Trees of a Graph 326 Index 328
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 Computing With Mathematica is a student-friendly courseware which equips students with the necessary tools to use Mathematica to solve problems in their engineering, physics, statistics, mathematics, or computer science courses. As a tutorial, students will benefit from learning on their own how to use Mathematica for problem-solving in technical fields. The authors have designed an accessible interactive text which consists of 12 electronic Mathematica notebooks for computation and visualization. This learning program is ideal for introducing students to computing with Mathematica and for investigating topics.* Interactive, Mathematica-based text, electronic as well as printed version included* Examples, challenging exercises, and interactive explorations from a variety of disciplines * Wide variety of interesting and worth-while mathematical applications* Integration of student projects as an essential component of the course; collection of student projects included* Interactive text allows user to change examples and avenues of exploration" Computing with Mathematica, Second 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 Second Edition of this acclaimed book features: 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