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## Mathematical Methods for Physicists by Arfken and Weber

Code:
 Preface
Vector Analysis Definitions, Elementary Approach
Rotation of the Coordinate Axes
Scalar or Dot Product
Vector or Cross Product
Triple Scalar Product, Triple Vector Product
Divergence, ∇
Curl, ∇x
Successive Applications of ∇
Vector Integration
Gauss' Theorem
Stokes' Theorem
Potential Theory
Gauss' Law, Poisson's Equation
Dirac Delta Function
Helmholtz's Theorem

Vector Analysis in Curved Coordinates and Tensors Orthogonal Coordinates in R^3
Differential Vector Operators
Special Coordinate Systems: Introduction
Circular Cylinder Coordinates
Spherical Polar Coordinates
Tensor Analysis
Contraction, Direct Product
Quotient Rule
Pseudotensors, Dual Tensors
General Tensors
Tensor Derivative Operators

Determinants and Matrices Determinants
Matrices
Orthogonal Matrices
Hermitian Matrices, Unitary Matrices
Diagonalization of Matrices
Normal Matrices

Group Theory Introduction to Group Theory
Generators of Continuous Groups
Orbital Angular Momentum
Angular Momentum Coupling
Homogeneous Lorentz Group
Lorentz Covariance of Maxwell's Equations
Discrete Groups
Differential Forms

Infinite Series Fundamental Concepts
Convergence Tests
Alternating Series
Algebra of Series
Series of Functions
Taylor's Expansion
Power Series
Elliptic Integrals
Bernoulli Numbers, Euler-Maclaurin Formula
Asymptotic Series
Infinite Products

Functions of a Complex Variable I Analytic Properties, Mapping Complex Algebra
Cauchy-Riemann Conditions
Cauchy's Integral Theorem
Cauchy's Integral Formula
Laurent Expansion
Singularities
Mapping
Conformal Mapping

Functions of a Complex Variable II Calculus of Residues
Dispersion Relations
Method of Steepest Descents

The Gamma Function (Factorial Function) Definitions, Simple Properties
Digamma and Polygamma Functions
Stirling's Series
The Beta Function
Incomplete Gamma Function

Differential Equations Partial Differential Equations
First-Order Differential Equations
Separation of Variables
Singular Points
Series Solutions—Frobeniusy Method
A Second Solution
Nonhomogeneous Equation—Green's Function
Heat Flow, or Diffusion, PDF

Hermitian Operators
Gram-Schmidt Orthogonalization
Completeness of Eigenfunctions
Green's Function—Eigenfunction Expansion

Bessel Functions Bessel Functions of the First Kind, J_v(x)
Orthogonality
Neumann Functions
Hankel Functions
Modified Bessel Functions, I_v(x) and K_v(x)
Asymptotic Expansions
Spherical Bessel Functions

Legendre Functions Generating Function
Recurrence Relations
Orthogonality
Alternate Definitions
Associated Legendre Functions
Spherical Harmonics
Orbital Angular Momentum Operators
Integrals of Three Y's
Legendre Functions of the Second Kind
Vector Spherical Harmonics

More Special Functions Hermite Functions
Laguerre Functions
Chebyshev Polynomials
Hypergeometric Functions
Confluent Hypergeometric Functions
Mathieu Functions

Fourier Series General Properties
Applications of Fourier Series
Properties of Fourier Series
Gibbs Phenomenon
Discrete Fourier Transform
Fourier Expansions of Mathieu Functions

Integral Transforms Integral Transforms
Development of the Fourier Integral
Fourier Transforms—Inversion Theorem
Fourier Transform of Derivatives
Convolution Theorem
Momentum Representation
Transfer Functions
Laplace Transforms
Laplace Transform of Derivatives
Other Properties
Convolution (Faltungs) Theorem
Inverse Laplace Transform

Integral Equations Introduction
Integral Transforms, Generating Functions
Neumann Series, Separable (Degenerate) Kernels
Hilbert-Schmidt Theory

Calculus of Variations A Dependent and an Independent Variable
Applications of the Euler Equation
Several Dependent Variables
Several Independent Variables
Several Dependent and Independent Variables
Lagrangian Multipliers
Variation with Constraints
Rayleigh-Ritz Variational Technique

Nonlinear Methods and Chaos Introduction
The Logistic Map
Sensitivity to Initial Conditions and Parameters
Nonlinear Differential Equations

Probability Definitions, Simple Properties
Random Variables
Binomial Distribution
Poisson Distribution
Gauss'Normal Distribution
Statistics

General References
Index


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 Recognitions: Gold Member I actually think Arfken & Weber is a very good book. It's not a 'mathematical physics' book aiming to teach the structure of physical theories - it's just a methods text. If you need to do an integral and forgot a method, look it up in here, and to that end, I think it serves its purpose well.
 Recognitions: Science Advisor I also like Arfken. It's a good reference book, and because examples are taken from all areas of physics, I always learn something new when I use it.

## Mathematical Methods for Physicists by Arfken and Weber

It probably works well if you already know/knew the material. From experience, I don't recommend trying to learn the techniques for the first time with this book. The explanations are too brief.

 A reference book, not great to learn from but good to recall
 I've found some mistakes in the book, but one of which stumped me for a awhile: chapter 1 vector diagram showing the three axes of XYZ space and a vector with a projection onto the XY plane and with three arcs to indicate the vector cosines. The mistake is one arc goes from the x axis to the dashlined vector projection and not to the vector itself. Earlier editions had two diagrams here so some copyeditor/artist combined them and introduced the mistake (I think from 4th edition to the present, I haven't seen the 7th edition yet)

 Quote by jedishrfu I've found some mistakes in the book, but one of which stumped me for a awhile: chapter 1 vector diagram showing the three axes of XYZ space and a vector with a projection onto the XY plane and with three arcs to indicate the vector cosines. The mistake is one arc goes from the x axis to the dashlined vector projection and not to the vector itself. Earlier editions had two diagrams here so some copyeditor/artist combined them and introduced the mistake (I think from 4th edition to the present, I haven't seen the 7th edition yet)
The figure (1.5 in 6th edition) is fixed in the 7th edition (Figure 1.9), at least according to the book review on Google books.

The 7th edition has been restructured as follows:

1 Mathematical Preliminaries
1.1 Infinite Series
1.2 Series of Functions
1.3 Binomial Theorm
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 Matrices and Determinants
2.1 Determinants
2.2 Matrices

3 Vector Analysis

4 Tensors and Differential Forms

5 Vector Spaces

6 Eigenvalue Problems

7 Ordinary Differential Equations

8 Sturm-Liouville Theory

9 Partial Differential Equations

10 Green's Functions

11 Complex Variable Theory

12 Further Topics in Analysis

13 Gamma Function

14 Bessel Functions

15 Legendre Functions

16 Angular Momentum

17 Group Theory

18 More Special Functions

19 Fourier Series

20 Integral Transforms

21 Integral Equations

22 Calculus of Variations

23 Probability and Statistics

Index