Applied Mathematical Methods for Physicists by Arfken and Weber

Greg Bernhardt

Author: George B. Arfken (Author), Hans J. Weber (Author), Frank E. Harris (Author)
Title: Mathematical Methods for Physicists
Amazon Link: http://www.amazon.com/Mathematical-M.../dp/0123846544
Prerequisities: Calculus 1,2,3

Table of Contents:

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
 Gradient, ∇
 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
 Additional Readings

 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
 Additional Readings

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

 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
 Additional Readings

 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
 Additional Readings

 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
 Additional Readings

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

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

 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
 Additional Readings

 Sturm-Liouville Theory—Orthogonal Functions Self-Adjoint ODEs
 Hermitian Operators
 Gram-Schmidt Orthogonalization
 Completeness of Eigenfunctions
 Green's Function—Eigenfunction Expansion
 Additional Readings

 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
 Additional Readings

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

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

 Fourier Series General Properties
 Advantages, Uses of Fourier Series
 Applications of Fourier Series
 Properties of Fourier Series
 Gibbs Phenomenon
 Discrete Fourier Transform
 Fourier Expansions of Mathieu Functions
 Additional Readings

 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
 Additional Readings

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

 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
 Additional Readings

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

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

 General References
 Index

Jorriss

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.

marcusl

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.

rhombusjr

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.

jesse73

A reference book, not great to learn from but good to recall

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)

Astronuc

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.

http://books.google.com/books?id=JOp...page&q&f=false

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

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Jorriss 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.

marcusl 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.

rhombusjr	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.

jesse73	A reference book, not great to learn from but good to recall