Table of contents

1. Preface ……. II
2. Introduction to MuPAD ……. 1
   1. A brief history of MuPAD ……. 1
   2. MuPAD as a calculator ……. 2
   3. Solving equations ……. 6
   4. Transforming mathematical expressions ……. 9
   5. Differentiation and integration ……. 12
   6. Declaring functions ……. 14
   7. Graphs of functions in one variable ……. 18
   8. Graphs of functions of two variables ……. 19
   9. Selected mathematical structures in MuPAD ……. 20
   10. Looking for help ……. 24
   11. Using libraries ……. 26
   12. Tracing basic errors ……. 28
3. Mathematical graphics with MuPAD ……. 33
   1. Secrets of the Virtual Camera ……. 33
   2. The structure of MuPAD graphs ……. 41
   3. The gallery of mathematical plots ……. 41
      1. Function2d ……. 44
      2. Curve2d ……. 46
      3. Polar coordinates ……. 47
      4. Implicit2d ……. 49
      5. Function3d ……. 50
      6. Surfaces ……. 54
      7. Implicit3d ……. 55
      8. Spherical coordinates ……. 58
      9. Cylindrical coordinates ……. 60
      10. Curve3d and Tube ……. 63
   4. Plotting geometry models ……. 66
      1. Points, lines and polygons ……. 67
      2. Solids in MuPAD ……. 73
   5. Turtle graphics and L-systems ……. 77
      1. A brief introduction to turtle graphics ……. 78
      2. Lindenmayer systems ……. 83
   6. Animation step-by-step ……. 89
4. Introduction to calculus of one variable ……. 95
   1. Declaring functions of one variable ……. 95
   2. How does MuPAD plot graphs of functions? ……. 101
   3. Limits ……. 105
   4. The derivative ……. 110
   5. Curve-sketching with MuPAD ……. 114
   6. Taylor polynomials ……. 120
   7. Integration with MuPAD ……. 123
   8. Numerical integration ……. 127
   9. Solving differential equations ……. 132
5. Multivariable calculus ……. 135
   1. Functions of several variables ……. 135
   2. Visualizing functions of several variables ……. 138
   3. Limits of functions of several variables ……. 144
   4. Partial differentiation ……. 148
   5. Vector fields ……. 151
   6. Multiple integrals with MuPAD ……. 154
   7. Visualizing and calculating volumes ……. 160
6. Algebra with MuPAD ……. 165
   1. Numbers and domains ……. 165
   2. Complex numbers and quaternions ……. 170
   3. Polynomials ……. 176
   4. Systems of linear equations ……. 179
   5. Declarations of matrices ……. 184
   6. Visualization of matrices ……. 188
   7. Operations on matrices ……. 189
7. Data visualization and elementary statistics ……. 195
   1. Data formats ……. 196
   2. Plotting tabulated data ……. 201
   3. Frequency distributions ……. 209
   4. Measures of central tendency ……. 219
   5. Standard deviation ……. 224
   6. Correlation and regression ……. 226
8. A brief introduction to programming ……. 229
   1. Variables again ……. 230
   2. Procedures ……. 234
   3. Getting organized ……. 238
   4. Creating user libraries ……. 239
   5. Control structures ……. 241
   6. Logical conditions ……. 242
   7. Making decisions ……. 243
   8. Iterations ……. 247
   9. Sometimes iterations and conditions do not work ……. 254
   10. Recursion ……. 256
9. Index ……. 261

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