Mathematical Methods For Physicists International Student Edition

Mathematical Methods For Physicists International Student Edition

6th Edition - June 3, 2005

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  • Authors: George Arfken, Hans Weber
  • eBook ISBN: 9780080470696
  • Paperback ISBN: 9780120885848

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Description

This best-selling title provides in one handy volume the essential mathematical tools and techniques used to solve problems in physics. It is a vital addition to the bookshelf of any serious student of physics or research professional in the field. The authors have put considerable effort into revamping this new edition.

Key Features

  • Updates the leading graduate-level text in mathematical physics
  • Provides comprehensive coverage of the mathematics necessary for advanced study in physics and engineering
  • Focuses on problem-solving skills and offers a vast array of exercises
  • Clearly illustrates and proves mathematical relations

New in the Sixth Edition:

  • Updated content throughout, based on users' feedback
  • More advanced sections, including differential forms and the elegant forms of Maxwell's equations
  • A new chapter on probability and statistics
  • More elementary sections have been deleted

Readership

A reference and as a textbook for aspiring and practicing physicists. As a text it functions best at the graduate level, although it’s recommended often as a reference to an undergrad course, almost always in physics departments

Table of Contents

  • PREFACE

    CHAPTER 1. VECTOR ANALYSIS

    1.1 DEFINITIONS, ELEMENTARY APPROACH

    1.2 ROTATION OF THE COORDINATE AXES3

    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 ∇

    1.10 VECTOR INTEGRATION

    1.11 Gauss’ THEOREM

    1.12 STOKES’ THEOREM

    1.13 POTENTIAL THEORY

    1.14 Gauss’ LAW, POISSON’s EQUATION

    1.15 DIRAC DELTA FUNCTION

    1.16 HELMHOLTZ’S THEOREM

    Additional Readings

    CHAPTER 2. VECTOR ANALYSIS IN CURVED COORDINATES AND TENSORS

    2.1 ORTHOGONAL COORDINATES IN 3

    2.2 DIFFERENTIAL VECTOR OPERATORS

    2.3 SPECIAL COORDINATE SYSTEMS: INTRODUCTION

    2.4 CIRCULAR CYLINDER COORDINATES

    2.5 SPHERICAL POLAR COORDINATES

    2.6 TENSOR ANALYSIS

    2.7 CONTRACTION, DIRECT PRODUCT

    2.8 QUOTIENT RULE

    2.9 PSEUDOTENSORS, DUAL TENSORS

    2.10 GENERAL TENSORS

    2.11 TENSOR DERIVATIVE OPERATORS

    Additional Readings

    CHAPTER 3. DETERMINANTS AND MATRICES

    3.1 DETERMINANTS

    3.2 MATRICES

    3.3 ORTHOGONAL MATRICES

    3.4 HERMITIAN MATRICES, UNITARY MATRICES

    3.5 DIAGONALIZATION OF MATRICES

    3.6 NORMAL MATRICES

    Additional Readings

    CHAPTER 4. GROUP THEORY

    4.1 INTRODUCTION TO GROUP THEORY

    4.2 GENERATORS OF CONTINUOUS GROUPS

    4.3 ORBITAL ANGULAR MOMENTUM

    4.4 ANGULAR MOMENTUM COUPLING

    4.5 HOMOGENEOUS LORENTZ GROUP

    4.6 LORENTZ COVARIANCE OF MAXWELL’S EQUATIONS

    4.7 DISCRETE GROUPS

    4.8 DIFFERENTIAL FORMS

    Additional Readings

    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 SERIES

    5.11 INFINITE PRODUCTS

    Additional Readings

    CHAPTER 6. FUNCTIONS OF A COMPLEX VARIABLE I ANALYTIC PROPERTIES, MAPPING

    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 SINGULARITIES

    6.7 MAPPING

    6.8 CONFORMAL MAPPING

    Additional Readings

    CHAPTER 7. FUNCTIONS OF A COMPLEX VARIABLE II

    7.1 CALCULUS OF RESIDUES

    7.2 DISPERSION RELATIONS

    7.3 METHOD OF STEEPEST DESCENTS

    Additional Readings

    CHAPTER 8. THE GAMMA FUNCTION (FACTORIAL FUNCTION)

    8.1 DEFINITIONS, SIMPLE PROPERTIES

    8.2 DIGAMMA AND POLYGAMMA FUNCTIONS

    8.3 STIRLING’S SERIES

    8.4 THE BETA FUNCTION

    8.5 THE INCOMPLETE GAMMA FUNCTIONS AND RELATED FUNCTIONS

    Additional Readings

    CHAPTER 9. DIFFERENTIAL EQUATIONS

    9.1 Partial Differential Equations

    9.2 First-Order Differential Equations

    9.3. SEPARATION OF VARIABLES

    9.4 Singular Points

    9.5 Series Solutions—Frobenius’ Method

    9.8 Heat Flow, or Diffusion, PDE

    Additional Readings

    CHAPTER 10. STURM-LIOUVILLE THEORY—ORTHOGONAL FUNCTIONS

    10.1 SELF-ADJOINT ODES

    10.2 HERMITIAN OPERATORS

    10.3 GRAM–SCHMIDT ORTHOGONALIZATION

    10.4 COMPLETENESS OF EIGENFUNCTIONS

    10.5 GREEN’S FUNCTION—EIGENFUNCTION EXPANSION

    Additional Readings

    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

    11.4 HANKEL FUNCTIONS

    11.5 MODIFIED BESSEL FUNCTIONS, Iv(x) AND Kv(x)

    11.6 ASYMPTOTIC EXPANSIONS

    11.7 SPHERICAL BESSEL FUNCTIONS

    Additional Readings

    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 ORBITAL ANGULAR MOMENTUM OPERATORS

    12.8 THE ADDITION THEOREM FOR SPHERICAL HARMONICS

    12.9 INTEGRALS OF PRODUCTS OF THREE SPHERICAL HARMONICS

    12.10 LEGENDRE FUNCTIONS OF THE SECOND KIND

    12.11 VECTOR SPHERICAL HARMONICS

    Additional Readings

    CHAPTER 13. MORE SPECIAL FUNCTIONS

    13.1 HERMITE FUNCTIONS

    13.2 LAGUERRE FUNCTIONS

    13.3 CHEBYSHEV POLYNOMIALS

    13.4 HYPERGEOMETRIC FUNCTIONS

    13.5 CONFLUENT HYPERGEOMETRIC FUNCTIONS

    13.6 MATHIEU FUNCTIONS

    Additional Readings

    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 FOURIER TRANSFORM

    14.7 FOURIER EXPANSIONS OF MATHIEU FUNCTIONS

    Additional Readings

    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. LAPLACE TRANSFORMS

    15.9. LAPLACE TRANSFORM OF DERIVATIVES

    15.10. OTHER PROPERTIES

    15.11. CONVOLUTION (FALTUNGS) THEOREM

    15.12. INVERSE LAPLACE TRANSFORM

    Additional Readings

    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

    Additional Readings

    CHAPTER 17. CALCULUS OF VARIATIONS

    17.1 A DEPENDENT AND AN INDEPENDENT VARIABLE

    17.2 APPLICATIONS OF THE EULER EQUATION

    17.3 SEVERAL DEPENDENT VARIABLES

    17.4 SEVERAL INDEPENDENT VARIABLES

    17.5 SEVERAL DEPENDENT AND INDEPENDENT VARIABLES

    17.6 LAGRANGIAN MULTIPLIERS

    17.7 VARIATION WITH CONSTRAINTS

    17.8 RAYLEIGH–RITZ VARIATIONAL TECHNIQUE

    Additional Readings

    CHAPTER 18. NONLINEAR METHODS AND CHAOS

    18.1 INTRODUCTION

    18.2 THE LOGISTIC MAP

    18.3 SENSITIVITY TO INITIAL CONDITIONS AND PARAMETERS

    18.4 NONLINEAR DIFFERENTIAL EQUATIONS

    Additional Readings

    CHAPTER 19. PROBABILITY

    19.1 DEFINITIONS, SIMPLE PROPERTIES

    19.2 RANDOM VARIABLES

    19.3 BINOMIAL DISTRIBUTION

    19.4 POISSON DISTRIBUTION

    19.5 GAUSS’ NORMAL DISTRIBUTION

    19.6 STATISTICS

    Additional Readings

    INDEX

Product details

  • No. of pages: 1
  • Language: English
  • Copyright: © Academic Press 2005
  • Published: June 3, 2005
  • Imprint: Academic Press
  • eBook ISBN: 9780080470696
  • Paperback ISBN: 9780120885848

About the Authors

George Arfken

Affiliations and Expertise

Miami University, Oxford, Ohio, USA

Hans Weber

Affiliations and Expertise

University of Virginia, USA

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