A Physicist’s Guide to Mathematica

A Physicist’s Guide to Mathematica......Page 4
Copyright Page......Page 5
Contents......Page 8
Preface to the Second Edition......Page 14
Preface to the First Edition......Page 16
Part I: Mathematica with Physics......Page 22
1.1 The First Ten Minutes......Page 24
1.2.3 Graphics......Page 27
1.3 Online Help......Page 28
1.4 Warning Messages......Page 30
1.5 Packages......Page 31
1.6.2 Entering Greek Letters......Page 33
1.6.3 Getting Help......Page 34
1.6.4 Preparing Input......Page 35
1.7 Problems......Page 36
2.1.1 Arithmetic Operations......Page 40
2.1.3 Common Mathematical Constants......Page 41
2.1.4 Some Mathematical Functions......Page 42
2.1.6 Ways to Refer to Previous Results......Page 43
2.1.7 Standard Computations......Page 44
2.1.8 Exact versus Approximate Values......Page 45
2.1.9 Machine Precision versus Arbitrary Precision......Page 46
2.1.11 Matrices......Page 48
2.1.12 Double Square Brackets......Page 50
2.1.13 Linear Least-Squares Fit......Page 51
2.1.15 Random Numbers......Page 53
2.1.16 Numerical Solution of Polynomial Equations......Page 54
2.1.17 Numerical Integration......Page 55
2.1.18 Numerical Solution of Differential Equations......Page 60
2.1.19 Iterators......Page 64
2.1.20 Exercises......Page 65
2.2.1 Transforming Algebraic Expressions......Page 79
2.2.2 Transforming Trigonometric Expressions......Page 82
2.2.4 Using Assumptions......Page 85
2.2.5 Obtaining Parts of Algebraic Expressions......Page 88
2.2.6 Units, Conversion of Units, and Physical Constants......Page 90
2.2.7 Assignments and Transformation Rules......Page 93
2.2.8 Equation Solving......Page 97
2.2.9 Differentiation......Page 101
2.2.10 Integration......Page 107
2.2.11 Sums......Page 111
2.2.12 Power Series......Page 115
2.2.13 Limits......Page 117
2.2.14 Solving Differential Equations......Page 118
2.2.15 Immediate versus Delayed Assignments and Transformation Rules......Page 120
2.2.16 Defining Functions......Page 121
2.2.17 Relational and Logical Operators......Page 126
2.2.18 Fourier Transforms......Page 129
2.2.19 Evaluating Subexpressions......Page 133
2.2.20 Exercises......Page 135
2.3.1 Two-Dimensional Graphics......Page 165
2.3.2 Three-Dimensional Graphics......Page 195
2.3.3 Interactive Manipulation of Graphics......Page 200
2.3.4 Animation......Page 203
2.3.5 Exercise......Page 210
2.4.1 Defining Lists......Page 247
2.4.2 Generating and Displaying Lists......Page 248
2.4.3 Counting List Elements......Page 250
2.4.4 Obtaining List and Sublist Elements......Page 253
2.4.5 Changing List and Sublist Elements......Page 257
2.4.6 Rearranging Lists......Page 258
2.4.7 Restructuring Lists......Page 259
2.4.8 Combining Lists......Page 262
2.4.9 Operating on Lists......Page 264
2.4.10 Using Lists in Computations......Page 265
2.4.11 Analyzing Data......Page 276
2.4.12 Exercises......Page 289
2.5 Special Characters, Two-Dimensional Forms, and Format Types......Page 308
2.5.1 Special Characters......Page 309
2.5.2 Two-Dimensional Forms......Page 317
2.5.3 Input and Output Forms......Page 327
2.5.4 Exercises......Page 330
2.6 Problems......Page 335
3.1.1 Atoms......Page 350
3.1.2 Internal Representation......Page 352
3.1.3 Manipulation......Page 355
3.1.4 Exercises......Page 373
3.2 Patterns......Page 381
3.2.1 Blanks......Page 382
3.2.2 Naming Patterns......Page 383
3.2.3 Restricting Patterns......Page 384
3.2.4 Structural Equivalence......Page 391
3.2.5 Attributes......Page 392
3.2.6 Defaults......Page 394
3.2.7 Alternative or Repeated Patterns......Page 397
3.2.8 Multiple Blanks......Page 398
3.2.9 Exercises......Page 399
3.3.1 Pure Functions......Page 407
3.3.2 Selecting a Definition......Page 413
3.3.3 Recursive Functions and Dynamic Programming......Page 415
3.3.4 Functional Iterations......Page 419
3.3.5 Protection......Page 423
3.3.6 Upvalues and Downvalues......Page 425
3.3.7 Exercises......Page 429
3.4 Procedures......Page 435
3.4.1 Local Symbols......Page 436
3.4.2 Conditionals......Page 438
3.4.3 Loops......Page 444
3.4.4 Named Optional Arguments......Page 449
3.4.5 An Example: Motion of a Particle in One Dimension......Page 456
3.4.6 Exercises......Page 467
3.5.1 Graphics Objects......Page 473
3.5.2 Two-Dimensional Graphics......Page 476
3.5.3 Three-Dimensional Graphics......Page 498
3.5.4 Exercises......Page 534
3.6 Programming Styles......Page 537
3.6.1 Procedural Programming......Page 540
3.6.2 Functional Programming......Page 545
3.6.3 Rule-Based Programming......Page 548
3.6.4 Exercises......Page 555
3.7.1 Contexts......Page 558
3.7.2 Context Manipulation......Page 562
3.7.3 A Sample Package......Page 564
3.7.4 Template for Packages......Page 571
3.7.5 Exercises......Page 572
Part II: Physics with Mathematica......Page 574
4.1.1 The Problem......Page 576
4.1.3 Solution with Mathematica......Page 577
4.2.2 Physics of the Problem......Page 579
4.2.3 Solution with Mathematica......Page 580
4.3.1 The Problem......Page 582
4.3.2 Physics of the Problem......Page 583
4.3.3 Solution with Mathematica......Page 584
4.4.2 Physics of the Problem......Page 591
4.4.3 Solution with Mathematica......Page 594
4.5 Problems......Page 601
5.1.2 Physics of the Problem......Page 604
5.1.3 Solution with Mathematica......Page 607
5.2.2 Physics of the Problem......Page 612
5.2.3 Solution with Mathematica......Page 615
5.3.2 Physics of the Problem......Page 623
5.3.3 Solution with Mathematica......Page 624
5.4 Problems......Page 628
6.1.2 Physics of the Problem......Page 632
6.1.3 Solution with Mathematica......Page 633
6.2.2 Physics of the Problem......Page 637
6.2.3 Solution with Mathematica......Page 638
6.3.2 Physics of the Problem......Page 643
6.3.3 Solution with Mathematica......Page 645
6.4.2 Physics of the Problem......Page 647
6.4.3 Solution with Mathematica......Page 650
6.5.2 Physics of the Problem......Page 660
6.5.3 Solution with Mathematica......Page 665
6.6.2 Physics of the Problem......Page 668
6.6.3 Solution with Mathematica......Page 669
6.7 Problems......Page 671
A The Last Ten Minutes......Page 674
B Operator Input Forms......Page 676
C Solutions to Exercises......Page 680
D Solutions to Problems......Page 724
References......Page 730
Index......Page 734