K. B. Vijaya Kumar, Antony P. Monteiro

Mathematica for Physicists and Engineers (eBook, ePUB)

• Format: ePub

Produktbeschreibung

Mathematica for Physicists and Engineers

Hands-on textbook for learning how to use Mathematica to solve real-life problems in physics and engineering

Mathematica for Physicists and Engineers provides the basic concepts of Mathematica for scientists and engineers, highlights Mathematica's several built-in functions, demonstrates mathematical concepts that can be employed to solve problems in physics and engineering, and addresses problems in basic arithmetic to more advanced topics such as quantum mechanics.

The text views mathematics and physics through the eye of computer programming, fulfilling the needs of students at master's levels and researchers from a physics and engineering background and bridging the gap between the elementary books written on Mathematica and the reference books written for advanced users.

Mathematica for Physicists and Engineers contains information on:

• Basics to Mathematica, its nomenclature and programming language, and possibilities for graphic output
• Vector calculus, solving real, complex and matrix equations and systems of equations, and solving quantum mechanical problems in infinite-dimensional linear vector spaces
• Differential and integral calculus in one and more dimensions and the powerful but elusive Dirac Delta function
• Fourier and Laplace transform, two integral transformations that are instrumental in many fields of physics and engineering for the solution of ordinary and partial differential equations

Serving as a complete first course in Mathematica to solve problems in science and engineering, Mathematica for Physicists and Engineers is an essential learning resource for students in physics and engineering, master's students in material sciences, geology, biological sciences theoretical chemists. Also lecturers in these and related subjects will benefit from the book.

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Produktdetails

• Verlag: Wiley-VCH
• Erscheinungstermin: 5. Juni 2023
• Englisch
• ISBN-13: 9783527843220
• Artikelnr.: 68207781

Autorenporträt

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.

Inhaltsangabe

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