Mathematical Methods for Physicists

Mathematical Methods for Physicists

3rd Edition - January 1, 1985

Write a review

  • Author: George Arfken
  • eBook ISBN: 9781483277820

Purchase options

Purchase options
DRM-free (PDF)
Sales tax will be calculated at check-out

Institutional Subscription

Free Global Shipping
No minimum order

Description

Mathematical Methods for Physicists, Third Edition provides an advanced undergraduate and beginning graduate study in physical science, focusing on the mathematics of theoretical physics. This edition includes sections on the non-Cartesian tensors, dispersion theory, first-order differential equations, numerical application of Chebyshev polynomials, the fast Fourier transform, and transfer functions. Many of the physical examples provided in this book, which are used to illustrate the applications of mathematics, are taken from the fields of electromagnetic theory and quantum mechanics. The Hermitian operators, Hilbert space, and concept of completeness are also deliberated. This book is beneficial to students studying graduate level physics, particularly theoretical physics.

Table of Contents


  • Chapter 1 Vector Analysis

    1.1 Definitions, Elementary Approach

    1.2 Advanced Definitions

    1.3 Scalar or Dot Product

    1.4 Vector or Cross Product

    1.5 Triple Scalar Product, Triple Vector Product

    1.6 Gradient

    1.7 Divergence

    1.8 Curl

    1.9 Successive Applications of V

    1.10 Vector Integration

    1.11 Gauss's Theorem

    1.12 Stokes's Theorem

    1.13 Potential Theory

    1.14 Gauss's Law, Poisson's Equation

    1.15 Helmholtz's Theorem

    Chapter 2 Coordinate Systems

    2.1 Curvilinear Coordinates

    2.2 Differential Vector Operations

    2.3 Special Coordinate Systems—Rectangular Cartesian Coordinates

    2.4 Circular Cylindrical Coordinates (p,φ,z)

    2.5 Spherical Polar Coordinates (r,0,φ)

    2.6 Separation of Variables

    Chapter 3 Tensor Analysis

    3.1 Introduction, Definitions

    3.2 Contraction, Direct Product

    3.3 Quotient Rule

    3.4 Pseudotensors, Dual Tensors

    3.5 Dyadics

    3.6 Theory of Elasticity

    3.7 Lorentz Co variance of Maxwell's Equations

    3.8 Noncartesian Tensors, Co variant Differentiation

    3.9 Tensor Differential Operations

    Chapter 4 Determinants, Matrices, and Group Theory

    4.1 Determinants

    4.2 Matrices

    4.3 Orthogonal Matrices

    4.4 Oblique Coordinates

    4.5 Hermitian Matrices, Unitary Matrices

    4.6 Diagonalization of Matrices

    4.7 Eigenvectors, Eigenvalues

    4.8 Introduction to Group Theory

    4.9 Discrete Groups

    4.10 Continuous Groups

    4.11 Generators

    4.12 SU(2), SU(3), and Nuclear Particles

    4.13 Homogeneous Lorentz Group

    Chapter 5 Infinite Series

    5.1 Fundamental Concepts

    5.2 Convergence Tests

    5.3 Alternating Series

    5.4 Algebra of Series

    5.5 Series of Functions

    5.6 Taylor's Expansion

    5.7 Power Series

    5.8 Elliptic Integrals

    5.9 Bernoulli Numbers, Euler-Maclaurin Formula

    5.10 Asymptotic or Semiconvergent Series

    5.11 Infinite Products

    Chapter 6 Functions of a Complex Variable I

    6.1 Complex Algebra

    6.2 Cauchy-Riemann Conditions

    6.3 Cauchy's Integral Theorem

    6.4 Cauchy's Integral Formula

    6.5 Laurent Expansion

    6.6 Mapping

    6.7 Conformal Mapping

    Chapter 7 Functions of a Complex Variable II: Calculus of Residues 396

    7.1 Singularities

    7.2 Calculus of Residues

    7.3 Dispersion Relations

    7.4 The Method of Steepest Descents

    Chapter 8 Differential Equations

    8.1 Partial Differential Equations of Theoretical Physics

    8.2 First-Order Differential Equations

    8.3 Separation of Variables—Ordinary Differential Equations

    8.4 Singular Points

    8.5 Series Solutions—Frobenius Method

    8.6 A Second Solution

    8.7 Nonhomogeneous Equation—Green's Function

    8.8 Numerical Solutions

    Chapter 9 Sturm-Liouville Theory - Orthogonal Functions

    9.1 Self-Adjoint Differential Equations

    9.2 Hermitian (Self-Adjoint) Operators

    9.3 Gram-Schmidt Orthogonalization

    9.4 Completeness of Eigenfunctions

    Chapter 10 The Gamma Function (Factorial Function)

    10.1 Definitions, Simple Properties

    10.2 Digamma and Polygamma Functions

    10.3 Stirling's Series

    10.4 The Beta Function

    10.5 The Incomplete Gamma Functions and Related Functions

    Chapter 11 Bessel Functions

    11.1 Bessel Functions of the First Kind, Jv(x)

    11.2 Orthogonality

    11.3 Neumann Functions, Bessel Functions of the Second Kind, Nv(x)

    11.4 Hankel Functions

    11.5 Modified Bessel Functions, Iv(x) and Kv(x)

    11.6 Asymptotic Expansions

    11.7 Spherical Bessel Functions

    Chapter 12 Legendre Functions

    12.1 Generating Function

    12.2 Recurrence Relations and Special Properties

    12.3 Orthogonality

    12.4 Alternate Definitions of Legendre Polynomials

    12.5 Associated Legendre Functions

    12.6 Spherical Harmonics

    12.7 Angular Momentum Ladder Operators

    12.8 The Addition Theorem for Spherical Harmonics

    12.9 Integrals of the Product of Three Spherical Harmonics

    12.10 Legendre Functions of the Second Kind, Qn(x)

    12.11 Vector Spherical Harmonics

    Chapter 13 Special Functions

    13.1 Hermite Functions

    13.2 Laguerre Functions

    13.3 Chebyshev (Tschebyscheff) Polynomials

    13.4 Chebyshev Polynomials—Numerical Applications

    13.5 Hypergeometric Functions

    13.6 Confluent Hypergeometric Functions

    Chapter 14 Fourier Series

    14.1 General Properties

    14.2 Advantages, Uses of Fourier Series

    14.3 Applications of Fourier Series

    14.4 Properties of Fourier Series

    14.5 Gibbs Phenomenon

    14.6 Discrete Orthogonality—Discrete Fourier Transform

    Chapter 15 Integral Transforms

    15.1 Integral Transforms

    15.2 Development of the Fourier Integral

    15.3 Fourier Transforms—Inversion Theorem

    15.4 Fourier Transform of Derivatives

    15.5 Convolution Theorem

    15.6 Momentum Representation

    15.7 Transfer Functions

    15.8 Elementary Laplace Transforms

    15.9 Laplace Transform of Derivatives

    15.10 Other Properties

    15.11 Convolution or Faltung Theorem

    15.12 Inverse Laplace Transformation

    Chapter 16 Integral Equations

    16.1 Introduction

    16.2 Integral Transforms, Generating Functions

    16.3 Neumann Series, Separable (Degenerate) Kernels

    16.4 Hilbert-Schmidt Theory

    16.5 Green's Functions—One Dimension

    16.6 Green's Functions—Two and Three Dimensions

    Chapter 17 Calculus of Variations

    17.1 One-Dependent and One-Independent Variable

    17.2 Applications of the Euler Equation

    17.3 Generalizations, Several Dependent Variables

    17.4 Several Independent Variables

    17.5 More Than One Dependent, More than One Independent Variable

    17.6 Lagrangian Multipliers

    17.7 Variation Subject to Constraints

    17.8 Rayleigh-Ritz Variational Technique

    Appendix 1 Real Zeros of a Function

    Appendix 2 Gaussian Quadrature

    General References

    Index


Product details

  • No. of pages: 1008
  • Language: English
  • Copyright: © Academic Press 1985
  • Published: January 1, 1985
  • Imprint: Academic Press
  • eBook ISBN: 9781483277820

About the Author

George Arfken

Affiliations and Expertise

Miami University, Oxford, Ohio, USA

Ratings and Reviews

Write a review

There are currently no reviews for "Mathematical Methods for Physicists"