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# Applied Mathematical Methods for Physicists by Arfken and Weber

by Greg Bernhardt
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 Admin P: 9,282 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:  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 
 P: 1,042 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.
 Sci Advisor PF Gold P: 2,056 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.
 P: 97 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.
 P: 437 A reference book, not great to learn from but good to recall
 P: 2,777 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)
P: 21,808
 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

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