1 Introduction to MuPAD ................................................................... 1
1.1 A brief history of MuPAD ........................................................................1
1.2 MuPAD as a calculator ........................................................................... 2
1.3 Solving equations ................................................................................... 6
1.4 Transforming mathematical expressions ..............................................9
1.5 Differentiation and integration ............................................................ 12
1.6 Declaring functions ...............................................................................14
1.7 Graphs of functions in one variable ..................................................... 18
1.8 Graphs of functions of two variables ................................................... 19
1.9 Selected mathematical structures in MuPAD ..................................... 20
1.10 Looking for help ................................................................................. 24
1.11 Using libraries .....................................................................................26
1.12 Tracing basic errors ............................................................................28
2 Mathematical graphics with MuPAD .............................................33
2.1 Secrets of the Virtual Camera .............................................................. 33
2.2 The structure of MuPAD graphs ..........................................................41
2.3 The gallery of mathematical plots ........................................................41
2.3.1 Function2d ................................................................................. 44
2.3.2 Curve2d ......................................................................................46
2.3.3 Polar coordinates ....................................................................... 47
2.3.4 Implicit2d ...................................................................................49
2.3.5 Function3d .................................................................................50
2.3.6 Surfaces ...................................................................................... 54
2.3.7 Implicit3d ................................................................................... 55
2.3.8 Spherical coordinates ................................................................ 58
2.3.9 Cylindrical coordinates ..............................................................60
2.3.10 Curve3d and Tube ....................................................................63
2.4 Plotting geometry models ....................................................................66
2.4.1 Points, lines and polygons ..........................................................67
2.4.2 Solids in MuPAD ........................................................................73
2.5 Turtle graphics and L-systems .............................................................77
2.5.1 A brief introduction to turtle graphics .......................................78
2.5.2 Lindenmayer systems ................................................................83
2.6 Animation step-by-step .......................................................................89
3 Introduction to calculus of one variable ........................................95
2.1 Declaring functions of one variable ..................................................... 95
3.2 How does MuPAD plot graphs of functions? .....................................101
3.3 Limits ..................................................................................................105
3.4 The derivative ..................................................................................... 110
3.5 Curve-sketching with MuPAD ............................................................114
3.6 Taylor polynomials ............................................................................ 120
3.7 Integration with MuPAD ....................................................................123
3.8 Numerical integration ........................................................................127
Getting started with MuPAD
3.9 Solving differential equations ............................................................132
4Multivariable calculus ................................................................. 135
4.1 Functions of several variables ............................................................ 135
4.2 Visualizing functions of several variables ......................................... 138
4.3 Limits of functions of several variables .............................................144
4.4 Partial differentiation ........................................................................ 148
4.5 Vector fields ........................................................................................ 151
4.6 Multiple integrals with MuPAD .........................................................154
4.7 Visualizing and calculating volumes ................................................. 160
5 Algebra with MuPAD ................................................................... 165
5.1 Numbers and domains ....................................................................... 165
5.2 Complex numbers and quaternions .................................................. 170
5.3 Polynomials ........................................................................................ 176
5.4 Systems of linear equations ............................................................... 179
5.5 Declarations of matrices .................................................................... 184
5.6 Visualization of matrices ................................................................... 188
5.7 Operations on matrices ......................................................................189
6 Data visualization and elementary statistics ................................195
6.1 Data formats ....................................................................................... 196
6.2 Plotting tabulated data ...................................................................... 201
6.3 Frequency distributions .................................................................... 209
6.4 Measures of central tendency ............................................................ 219
6.5 Standard deviation .............................................................................224
6.6 Correlation and regression ................................................................226
7 A brief introduction to programming ..........................................229
7.1 Variables again ................................................................................... 230
7.2 Procedures ..........................................................................................234
7.3 Getting organized ...............................................................................238
7.4 Creating user libraries ....................................................................... 239
7.5 Control structures ...............................................................................241
7.5.1 Logical conditions .....................................................................242
7.5.2 Making decisions ......................................................................243
7.5.3 Iterations .................................................................................. 247
7.5.4 Sometimes iterations and conditions do not work ................. 254
7.6 Recursion ........................................................................................... 256
8. Index ......................................................................................... 261
VI