Mathematical Methods for Physicists A Comprehensive Guide 7th edition by Arfken, Weber, Harris 0123846544 9780123846549

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ISBN 10: 0123846544

ISBN 13: 9780123846549

Author: Arfken, Weber, Harris

Now in its 7th edition, Mathematical Methods for Physicists continues to provide all the mathematical methods that aspiring scientists and engineers are likely to encounter as students and beginning researchers. This bestselling text provides mathematical relations and their proofs essential to the study of physics and related fields. While retaining the key features of the 6th edition, the new edition provides a more careful balance of explanation, theory, and examples. Taking a problem-solving-skills approach to incorporating theorems with applications, the book’s improved focus will help students succeed throughout their academic careers and well into their professions. Some notable enhancements include more refined and focused content in important topics, improved organization, updated notations, extensive explanations and intuitive exercise sets, a wider range of problem solutions, improvement in the placement, and a wider range of difficulty of exercises.

Mathematical Methods for Physicists A Comprehensive Guide 7th Table of contents:

1. Mathematical Preliminaries
   1.1 Infinite Series
   1.2 Series of Functions
   1.3 Binomial Theorem
   1.4 Mathematical Induction
   1.5 Operations on Series Expansions of Functions
   1.6 Some Important Series
   1.7 Vectors
   1.8 Complex Numbers and Functions
   1.9 Derivatives and Extrema
   1.10 Evaluation of Integrals
   1.11 Dirac Delta Function

2. Determinants and Matrices
   2.1 Determinants
   2.2 Matrices

3. Vector Analysis
   3.1 Review of Basic Properties
   3.2 Vectors in 3-D Space
   3.3 Coordinate Transformations
   3.4 Rotations in R3
   3.5 Differential Vector Operators
   3.6 Differential Vector Operators: Further Properties
   3.7 Vector Integration
   3.8 Integral Theorems
   3.9 Potential Theory
   3.10 Curvilinear Coordinates

4. Tensors and Differential Forms
   4.1 Tensor Analysis
   4.2 Pseudotensors, Dual Tensors
   4.3 Tensors in General Coordinates
   4.4 Jacobians
   4.5 Differential Forms
   4.6 Differentiating Forms
   4.7 Integrating Forms

5. Vector Spaces
   5.1 Vectors in Function Spaces
   5.2 Gram-Schmidt Orthogonalization
   5.3 Operators
   5.4 Self-Adjoint Operators
   5.5 Unitary Operators
   5.6 Transformations of Operators
   5.7 Invariants
   5.8 Summary—Vector Space Notation

6. Eigenvalue Problems
   6.1 Eigenvalue Equations
   6.2 Matrix Eigenvalue Problems
   6.3 Hermitian Eigenvalue Problems
   6.4 Hermitian Matrix Diagonalization
   6.5 Normal Matrices

7. Ordinary Differential Equations
   7.1 Introduction
   7.2 First-Order Equations
   7.3 ODEs with Constant Coefficients
   7.4 Second-Order Linear ODEs
   7.5 Series Solutions—Frobenius’ Method
   7.6 Other Solutions
   7.7 Inhomogeneous Linear ODEs
   7.8 Nonlinear Differential Equations

8. Sturm-Liouville Theory
   8.1 Introduction
   8.2 Hermitian Operators
   8.3 ODE Eigenvalue Problems
   8.4 Variation Method
   8.5 Summary, Eigenvalue Problems

9. Partial Differential Equations
   9.1 Introduction
   9.2 First-Order Equations
   9.3 Second-Order Equations
   9.4 Separation of Variables
   9.5 Laplace and Poisson Equations
   9.6 Wave Equation
   9.7 Heat-Flow, or Diffusion PDE
   9.8 Summary

10. Green’s Functions
    10.1 One-Dimensional Problems
    10.2 Problems in Two and Three Dimensions

11. Complex Variable Theory
    11.1 Complex Variables and Functions
    11.2 Cauchy-Riemann Conditions
    11.3 Cauchy’s Integral Theorem
    11.4 Cauchy’s Integral Formula
    11.5 Laurent Expansion
    11.6 Singularities
    11.7 Calculus of Residues
    11.8 Evaluation of Definite Integrals
    11.9 Evaluation of Sums
    11.10 Miscellaneous Topics

12. Further Topics in Analysis
    12.1 Orthogonal Polynomials
    12.2 Bernoulli Numbers
    12.3 Euler-Maclaurin Integration Formula
    12.4 Dirichlet Series
    12.5 Infinite Products
    12.6 Asymptotic Series
    12.7 Method of Steepest Descents
    12.8 Dispersion Relations

13. Gamma Function
    13.1 Definitions, Properties
    13.2 Digamma and Polygamma Functions
    13.3 The Beta Function
    13.4 Stirling’s Series
    13.5 Riemann Zeta Function
    13.6 Other Related Functions

14. Bessel Functions
    14.1 Bessel Functions of the First Kind, Jν(x)
    14.2 Orthogonality
    14.3 Neumann Functions, Bessel Functions of the Second Kind
    14.4 Hankel Functions
    14.5 Modified Bessel Functions, Iν(x) and Kν(x)
    14.6 Asymptotic Expansions
    14.7 Spherical Bessel Functions

15. Legendre Functions
    15.1 Legendre Polynomials
    15.2 Orthogonality
    15.3 Physical Interpretation of Generating Function
    15.4 Associated Legendre Equation
    15.5 Spherical Harmonics
    15.6 Legendre Functions of the Second Kind

16. Angular Momentum
    16.1 Angular Momentum Operators
    16.2 Angular Momentum Coupling
    16.3 Spherical Tensors
    16.4 Vector Spherical Harmonics

17. Group Theory
    17.1 Introduction to Group Theory
    17.2 Representation of Groups
    17.3 Symmetry and Physics
    17.4 Discrete Groups
    17.5 Direct Products
    17.6 Symmetric Group
    17.7 Continuous Groups
    17.8 Lorentz Group
    17.9 Lorentz Covariance of Maxwell’s Equations
    17.10 Space Groups

18. More Special Functions
    18.1 Hermite Functions
    18.2 Applications of Hermite Functions
    18.3 Laguerre Functions
    18.4 Chebyshev Polynomials
    18.5 Hypergeometric Functions
    18.6 Confluent Hypergeometric Functions
    18.7 Dilogarithm
    18.8 Elliptic Integrals

19. Fourier Series
    19.1 General Properties
    19.2 Applications of Fourier Series
    19.3 Gibbs Phenomenon

20. Integral Transforms
    20.1 Introduction
    20.2 Fourier Transform
    20.3 Properties of Fourier Transforms
    20.4 Fourier Convolution Theorem
    20.5 Signal-Processing Applications
    20.6 Discrete Fourier Transform
    20.7 Laplace Transforms
    20.8 Properties of Laplace Transforms
    20.9 Laplace Convolution Theorem
    20.10 Inverse Laplace Transform

21. Integral Equations
    21.1 Introduction
    21.2 Some Special Methods
    21.3 Neumann Series
    21.4 Hilbert-Schmidt Theory

22. Calculus of Variations
    22.1 Euler Equation
    22.2 More General Variations
    22.3 Constrained Minima/Maxima
    22.4 Variation with Constraints

23. Probability and Statistics
    23.1 Probability: Definitions, Simple Properties
    23.2 Random Variables
    23.3 Binomial Distribution
    23.4 Poisson Distribution
    23.5 Gauss’ Normal Distribution
    23.6 Transformations of Random Variables
    23.7 Statistics

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