Mathematica for Physicists and Engineers

K. B. Vijaya Kumar is a professor of physics in the Department 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. Prof. K. B. Vijaya Kumar was a Commonwealth Academic Staff fellow (1998-1999), a World Academy of Sciences-UNESCO fellow at the Institute of Theoretical Physics, Beijing (2003-2006), and visiting scientist at the Research Center Jülich, Germany (2005) and at the Institute for Theoretical Physics, University of Tübingen, Germany (2006- 2009).
 
Dr. Antony Prakash Monteiro is working in the Department of Physics at St. Philomena College, Puttur, India. He has more than thirteen years of teaching experience at undergraduate and postgraduate levels and has authored several books in various fields of physics. He is the recipient of the Vision Group on Science and Technology Award for Research Publications 2017-18 for his high-impact research publications. His research interest is aimed at computational and theoretical nuclear and particle physics.

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In diesem Lehrbuch wird die Anwendung des leistungsstarken Computeralgebrasystems Mathematica zur Lösung realer Probleme in Physik und Ingenieurwesen mit hohem Praxisbezug dargestellt.

CHAPTER 1 - Preliminary Notions
1.1 Introduction
1.2 Versions of Mathematica
1.3 Getting Started
1.4 Simple Calculations
1.4.1 Arithmetic Operations
1.4.2 Approximate Numerical Results
1.4.3 Algebraic Calculations
1.4.4 Defining Variables
1.4.5 Using the Previous Results
1.4.6 Suppressing the Output
1.4.7 Sequence of Operations
1.5 Built-in Functions
1.6 Additional Features
1.6.1 Arbitrary-Precision Calculations
1.6.2 Value of Symbols
1.6.3 Defining, Naming and Evaluating Functions
1.6.4 Composition of Functions
1.6.5 Conditional Assignment
1.6.6 Warnings and Messages
1.6.7 Interrupting Calculations
1.6.8 Using Symbols to Tag Objects
 
CHAPTER 2 - Basic Mathematical Operations
2.1 Introduction
2.2 Basic Algebraic Operations
2.3 Basic Trigonometric Operations
2.4 Basic Operations with Complex Numbers
 
CHAPTER 3 - Lists and Tables
3.1 Lists
3.2 Arrays
3.3 Tables
3.4 Extracting the Elements from the Array/Tables
 
CHAPTER 4 - Two-Dimensional Graphics
4.1 Introduction
4.2 Plotting Functions of a Single Variable
4.3 Additional Commands
4.4 Plot Styles
4.5 Probability Distribution
4.5.1 Binomial Distribution
4.5.2 Poisson Distribution
4.5.3 Normal or Gaussian Distribution
 
CHAPTER 5 - Parametric, Polar, Contour, Density and List Plots
5.1 Introduction
5.2 Parametric plotting
5.3 Polar Plots
5.3.1 Polar Plots of Circles
5.3.2 Polar Plots of Ellipses, Parabola and Hyperbola
5.4 Implicit Plots
5.5 Contour Plots
5.6 Density Plots
5.7 List Plots
5.8 LogPlot, LogLogPlot, ErrorListPlot
5.9 Least Square Fit
 
CHAPTER 6 - Three-Dimensional Graphics
6.1 Introduction
6.2 Plotting The Functions of Two Variables
6.3 Parametric Plots
6.4 3D Plots in Cylindrical and Spherical Coordinates
6.5 ContourPlot3D
6.6 ListContourPlot3D
6.7 ListSurfacePlot3D
6.8 Surface of Revolution
 
CHAPTER 7 - Matrices
7.1 Introduction
7.2 Properties of Matrices
7.3 Types of Matrices
7.4 The Rank of the Matrix
7.5 Special Matrices
7.6 Creation of the Matrix
7.6.1 Extraction of the Sub Matrices or the Elements of the Matrices
7.7 Properties of the Special Matrices
7.8 The Direct Sum of Matrices
7.9 The Direct Product of Matrices
7.10 Examples from Group Theory
7.10.1 SO(3) Group
7.10.2 SU(n) Group
7.10.3 SU(2) Group
7.10.4 SU(3) Group
 
CHAPTER 8 - Solving Algebraic and Transcendental Equations
8.1 Solving Systems of Linear Equations
8.1.1 Number of Equations Equal to the Number of Unknowns
8.1.2 Number of Equations Less Than the Number of Unknowns
8.1.3 Number of Equations More Than the Number of Unknowns
8.2 Non- Linear Algebraic Equations
8.3 Solving Transcendental Equations
 
CHAPTER 9 - Eigenvalues and Eigenvectors of a Matrix: Matrix Diagonalization
9.1 Introduction
9.2 Eigenvalues and Vectors of a Matrix
9.2.1 Distinct Eigenvalues having Independent Eigenvectors
9.2.2 Multiple Eigenvalues having Independent Eigenvectors
9.2.3 Multiple Eigenvalues not having Independent Eigenvectors
9.3 The Cayley-Hamilton Theorem
9.4 Diagonalization of a Matrix
9.4.1 Gram-Schmidt Orthogonalization Method
9.4.2 Diagonalizability of a Matrix
9.4.3 Case of a Non-diagonalizable Matrix
9.5 Some More Properties of Special Matrices
9.6 Power of a Matrix
9.6.1 Roots of a Matrix
9.6.2 Exponential of a Matrix
9.6.3 Logarithm of a Matrix
9.7 Power of a Matrix by Diagonalization
9.8 Bilinear, Quadratic and Hermitian Forms
9.9 Principal Axes Transformation
 
CHAPTER 10 - Differential Calculus
10.1 Introduction
10.2 Limits
10.2.1 Evaluation of the Limits Using L' Hospital?s Rule
10.2.2 Application of L' Hospital?s Rule for "Indeterminate Form
10.2.3 Evaluation of the Limit Using Taylor's Theorem of Me