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Getting Started with MuPAD

M. Majewski
Publisher: 
Springer Verlag
Publication Date: 
2005
Number of Pages: 
260
Format: 
Paperback
Price: 
29.95
ISBN: 
3-540-28635-7
Category: 
Manual
We do not plan to review this book.

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

Dummy View - NOT TO BE DELETED