Preface ........................................................ 9
A Short Tour .................................................. 16
Formula Entry ................................................. 16
Numerical Calculations ........................................ 17
Symbolic Mathematics .......................................... 17
Graphics ...................................................... 19
Programming ................................................... 22
Some of the Most Important Functions .......................... 23
Part 1: The Basics ............................................ 27
1.1. The Structure of the Program ............................. 28
1.1.1. The Front End ..................................... 28
1.1.2. The Kernel ........................................ 29
1.2. Online Documentation ..................................... 31
1.3. Formulas ................................................. 32
1.3.1. Formats ........................................... 32
1.3.2. Entering Formulas and Special Characters .......... 34
1.4. Simple Calculations ...................................... 37
1.4.1. Conventions ....................................... 37
1.4.2. Numerical Calculations ............................ 41
1.4.3. Algebraic Manipulation ............................ 44
1.4.4. Transformation Rules and Definitions .............. 46
1.4.5. Equations ......................................... 51
1.4.6. Calculus .......................................... 59
Part 2: Graphics .............................................. 67
2.1. Graphs of Functions of One Variable ...................... 68
2.2. Graphs of Functions of Two Variables ..................... 80
2.2.1. Surfaces .......................................... 81
2.2.2. Contours .......................................... 86
2.2.3. Density Plots ..................................... 89
2.3. Parametric Plots ......................................... 92
2.3.1. Two-Dimensional Parametric Plots .................. 92
2.3.2. Three-Dimensional Parametric Plots ................ 93
2.4. Tools from Standard Packages ............................ 100
2.4.1. Three-Dimensional Contour Plots .................. 100
2.4.2. Tools for Two-Dimensional Graphics ............... 101
2.4.3. Tools for Three-Dimensional Graphics ............. 102
2.4.4. Legends .......................................... 103
2.4.5. Vector Fields .................................... 105
2.5. Animations .............................................. 110
2.6. Exporting to Other Programs ............................. 113
Part 3: Lists and Graphics Programming ....................... 115
3.1. Lists ................................................... 116
3.1.1. Creating One-Dimensional Lists ................... 116
3.1.2. Manipulating Lists ............................... 117
3.1.3. Multidimensional Lists ........................... 120
3.2. Calculating with Lists .................................. 120
3.2.1. Automatic Operations ............................. 120
3.2.2. Mapping Functions on Lists ....................... 121
3.2.3. Pure Functions ................................... 122
3.2.4. Using List Elements as Arguments ................. 124
3.2.5. Plotting Lists ................................... 126
3.3. Linear Algebra .......................................... 131
3.4. Graphics Programming .................................... 136
3.4.1. Graphics Objects ................................. 136
3.4.2. Graphics3D Objects ............................... 139
3.4.3. Objects from Standard Packages ................... 140
3.5. Application: Animating a Mechanism ...................... 146
Part 4: Introduction to Programming .......................... 151
4.1. Expressions ............................................. 152
4.2. Patterns ................................................ 155
4.2.1. Simple Patterns .................................. 155
4.2.2. Constraints ...................................... 157
4.2.3. More Complicated Patterns ........................ 162
4.2.4. A Simple Integrator .............................. 163
4.3. Evaluation .............................................. 167
4.3.1. Associated Definitions ........................... 167
4.3.2. Attributes ....................................... 168
4.3.3. The Evaluation Process ........................... 169
4.4. Programming Tools ....................................... 172
4.4.1. Local Variables .................................. 172
4.4.2. Functional Programming ........................... 173
4.4.3. Rule-Based and Recursive Programming ............. 176
4.4.4. Procedural Programming ........................... 179
4.4.5. Modularity ....................................... 181
4.4.6. Compiling Numerical Calculations ................. 183
4.5. Further Information ..................................... 185
4.5.1. Internet ......................................... 185
4.5.2. Math Source ...................................... 185
4.5.3. Literature ....................................... 185
Index ........................................................ 187
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