Mathematica for Physicists and Engineers - Kumar, K. B. Vijaya

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Résumé :

Preface xiii

Foreword xvii

About the Authors xix

1 Preliminary Notions 1

1.1 Introduction 1

1.2 Versions of Mathematica 1

1.3 Getting Started 2

1.4 Simple Calculations 2

1.4.1 Arithmetic Operations 2

1.4.2 Approximate Numerical Results 3

1.4.3 Algebraic Calculations 3

1.4.4 Defining Variables 4

1.4.5 Using the Previous Results 5

1.4.6 Suppressing the Output 6

1.4.7 Sequences of Operations 6

1.5 Built-in Functions 7

1.6 Additional Features 9

1.6.1 Arbitrary-Precision Calculations 9

1.6.2 Value for Symbols 10

1.6.3 Defining Naming and Evaluating Functions 10

1.6.4 Composition of Functions 11

1.6.5 Conditional Assignment 12

1.6.6 Warnings and Messages 13

1.6.7 Interrupting Calculations 13

1.6.8 Using Symbols to Tag Objects 13

2 Basic Mathematical Operations 15

2.1 Introduction 15

2.2 Basic Algebraic Operations 15

2.3 Basic Trigonometric Operations 20

2.4 Basic Operations with Complex Numbers 21

3 Lists and Tables 25

3.1 Introduction 25

3.2 Lists 25

3.3 Arrays 26

3.4 Tables 26

3.5 Extracting the Elements from the Arrays/Tables 29

4 Two-Dimensional Graphics 31

4.1 Introduction 31

4.2 Plotting Functions of a Single Variable 31

4.3 Additional Commands 34

4.4 Plot Styles 44

4.5 Probability Distribution 58

4.5.1 Binomial Distribution 58

4.5.2 Poisson Distribution 58

4.5.3 Normal or Gaussian Distribution 59

4.6 Some More Useful Commands 61

5 Parametric, Polar, Contour, Density, and List Plots 65

5.1 Introduction 65

5.2 Parametric Plotting 65

5.3 Polar Plots 72

5.3.1 Polar Plots of Circles 72

5.3.2 Polar Plots of Ellipse, Parabola, and Hyperbola 72

5.4 Implicit Plot 80

5.5 Contour Plots 81

5.6 Density Plot 85

5.7 ListPlot and ListLinePlot 85

5.8 LogPlot, LogLogPlot, ErrorListPlot 88

5.9 Least Square Fit 89

5.10 Plotting of Complex Numbers 92

6 Three-Dimensional Graphics 97

6.1 Introduction 97

6.2 Plotting Function of Two Variables 97

6.3 Parametric Plots 101

6.4 3D Plots in Cylindrical and Spherical Coordinates 102

6.5 ContourPlot3D 105

6.6 ListContourPlot3D 108

6.7 ListSurfacePlot3D 110

6.8 Surface of Revolution 112

6.9 Conicoids 114

7 Matrices 123

7.1 Introduction 123

7.2 Properties of Matrices 123

7.2.1 Matrix Multiplication 123

7.3 Types of Matrices 123

7.4 The Rank of the Matrix 124

7.5 Special Matrices 124

7.6 Creation of a Matrix and Matrix Operations 125

7.6.1 Extraction of the Submatrices or the Elements of the Matrices 126

7.7 Properties of the Special Matrices 133

7.8 Direct Sum of Matrices 137

7.9 Direct Product of Matrices 137

7.10 Examples from Group Theory 138

7.10.1 SO(3) Group 138

7.10.2 SU(n)Group 139

7.10.3 SU(2) Group 140

7.10.4 SU(3) Group 141

8 Solving Algebraic and Transcendental Equations 143

8.1 Introduction 143

8.2 Solving System of Linear Equations 143

8.2.1 Number of Equations Equal to Number of Unknowns 144

8.2.2 Number of Equations Less than the Number of Unknowns 146

8.2.3 Number of Equations More than Number of Unknowns 146

8.3 Nonlinear Algebraic Equations 147

8.4 Solving Complex Equations 149

8.5 Solving Transcendental Equations 153

9 Eigenvalues and Eigenvectors of a Matrix 161

9.1 I...

Biographie:

K. B. Vijaya Kumar is a professor of physics at the N.M.A.M Institute of Technology, Nitte, India. His research is focused on theoretical and computational nuclear and particle physics.

Antony P. Monteiro is working in the Department of Physics at St. Philomena College, Puttur, India. He has more than thirteen years of teaching experience and has authored several books in various fields of physics....

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