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Mathematical Methods for Physicists,9780120598762
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Mathematical Methods for Physicists

by ;
Edition:
6th
ISBN13:

9780120598762

ISBN10:
0120598760
Format:
Hardcover
Pub. Date:
6/21/2005
Publisher(s):
Elsevier Science & Technology
List Price: $137.60

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Summary

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. * 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

Table of Contents

Preface xi
Vector Analysis
1(102)
Definitions, Elementary Approach
1(6)
Rotation of the Coordinate Axes
7(5)
Scalar or Dot Product
12(6)
Vector or Cross Product
18(7)
Triple Scalar Product, Triple Vector Product
25(7)
Gradient
32(6)
Divergence
38(5)
Curl, x
43(6)
Successive Applications
49(5)
Vector Integration
54(6)
Gauss' Theorem
60(4)
Stokes' Theorem
64(4)
Potential Theory
68(11)
Gauss' Law, Poisson's Equation
79(4)
Dirac Delta Function
83(12)
Helmholtz's Theorem
95(8)
Additional Readings
101(2)
Vector Analysis in Curved Coordinates and Tensors
103(62)
Orthogonal Coordinates in R3
103(7)
Differential Vector Operators
110(4)
Special Coordinate Systems: Introduction
114(1)
Circular Cylinder Coordinates
115(8)
Spherical Polar Coordinates
123(10)
Tensor Analysis
133(6)
Contraction, Direct Product
139(2)
Quotient Rule
141(1)
Pseudotensors, Dual Tensors
142(9)
General Tensors
151(9)
Tensor Derivative Operators
160(5)
Additional Readings
163(2)
Determinants and Matrices
165(76)
Determinants
165(11)
Matrices
176(19)
Orthogonal Matrices
195(13)
Hermitian Matrices, Unitary Matrices
208(7)
Diagonalization of Matrices
215(16)
Normal Matrices
231(10)
Additional Readings
239(2)
Group Theory
241(80)
Introduction to Group Theory
241(5)
Generators of Continuous Groups
246(15)
Orbital Angular Momentum
261(5)
Angular Momentum Coupling
266(12)
Homogeneous Lorentz Group
278(5)
Lorentz Covariance of Maxwell's Equations
283(8)
Discrete Groups
291(13)
Differential Forms
304(17)
Additional Readings
319(2)
Infinite Series
321(82)
Fundamental Concepts
321(4)
Convergence Tests
325(14)
Alternating Series
339(3)
Algebra of Series
342(6)
Series of Functions
348(4)
Taylor's Expansion
352(11)
Power Series
363(7)
Elliptic Integrals
370(6)
Bernoulli Numbers, Euler--Maclaurin Formula
376(13)
Asymptotic Series
389(7)
Infinite Products
396(7)
Additional Readings
401(2)
Functions of a Complex Variable I Analytic Properties, Mapping
403(52)
Complex Algebra
404(9)
Cauchy--Riemann Conditions
413(5)
Cauchy's Integral Theorem
418(7)
Cauchy's Integral Formula
425(5)
Laurent Expansion
430(8)
Singularities
438(5)
Mapping
443(8)
Conformal Mapping
451(4)
Additional Readings
453(2)
Functions of a Complex Variable II
455(44)
Calculus of Residues
455(27)
Dispersion Relations
482(7)
Method of Steepest Descents
489(10)
Additional Readings
497(2)
The Gamma Function (Factorial Function)
499(36)
Definitions, Simple Properties
499(11)
Digamma and Polygamma Functions
510(6)
Stirling's Series
516(4)
The Beta Function
520(7)
Incomplete Gamma Function
527(8)
Additional Readings
533(2)
Differential Equations
535(86)
Partial Differential Equations
535(8)
First-Order Differential Equations
543(11)
Separation of Variables
554(8)
Singular Points
562(3)
Series Solutions---Frobenius' Method
565(13)
A Second Solution
578(14)
Nonhomogeneous Equation---Green's Function
592(19)
Heat Flow, or Diffusion, PDE
611(10)
Additional Readings
618(3)
Sturm--Liouville Theory---Orthogonal Functions
621(54)
Self-Adjoint ODEs
622(12)
Hermitian Operators
634(8)
Gram-Schmidt Orthogonalization
642(7)
Completeness of Eigenfunctions
649(13)
Green's Function---Eigenfunction Expansion
662(13)
Additional Readings
674(1)
Bessel Functions
675(66)
Bessel Functions of the First Kind, Jv(x)
675(19)
Orthogonality
694(5)
Neumann Functions
699(8)
Hankel Functions
707(6)
Modified Bessel Functions, Iv(x) and Kv(x)
713(6)
Asymptotic Expansions
719(6)
Spherical Bessel Functions
725(16)
Additional Readings
739(2)
Legendre Functions
741(76)
Generating Function
741(8)
Recurrence Relations
749(7)
Orthogonality
756(11)
Alternate Definitions
767(4)
Associated Legendre Functions
771(15)
Spherical Harmonics
786(7)
Orbital Angular Momentum Operators
793(4)
Addition Theorem for Spherical Harmonics
797(6)
Integrals of Three Y's
803(3)
Legendre Functions of the Second Kind
806(7)
Vector Spherical Harmonics
813(4)
Additional Readings
816(1)
More Special Functions
817(64)
Hermite Functions
817(20)
Laguerre Functions
837(11)
Chebyshev Polynomials
848(11)
Hypergeometric Functions
859(4)
Confluent Hypergeometric Functions
863(6)
Mathieu Functions
869(12)
Additional Readings
879(2)
Fourier Series
881(50)
General Properties
881(7)
Advantages, Uses of Fourier Series
888(4)
Applications of Fourier Series
892(11)
Properties of Fourier Series
903(7)
Gibbs Phenomenon
910(4)
Discrete Fourier Transform
914(5)
Fourier Expansions of Mathieu Functions
919(12)
Additional Readings
929(2)
Integral Transforms
931(74)
Integral Transforms
931(5)
Development of the Fourier Integral
936(2)
Fourier Transforms---Inversion Theorem
938(8)
Fourier Transform of Derivatives
946(5)
Convolution Theorem
951(4)
Momentum Representation
955(6)
Transfer Functions
961(4)
Laplace Transforms
965(6)
Laplace Transform of Derivatives
971(8)
Other Properties
979(11)
Convolution (Faltungs) Theorem
990(4)
Inverse Laplace Transform
994(11)
Additional Readings
1003(2)
Integral Equations
1005(32)
Introduction
1005(7)
Integral Transforms, Generating Functions
1012(6)
Neumann Series, Separable (Degenerate) Kernels
1018(11)
Hilbert--Schmidt Theory
1029(8)
Additional Readings
1036(1)
Calculus of Variations
1037(42)
A Dependent and an Independent Variable
1038(6)
Applications of the Euler Equation
1044(8)
Several Dependent Variables
1052(4)
Several Independent Variables
1056(2)
Several Dependent and Independent Variables
1058(2)
Lagrangian Multipliers
1060(5)
Variation with Constraints
1065(7)
Rayleigh--Ritz Variational Technique
1072(7)
Additional Readings
1076(3)
Nonlinear Methods and Chaos
1079(30)
Introduction
1079(1)
The Logistic Map
1080(5)
Sensitivity to Initial Conditions and Parameters
1085(3)
Nonlinear Differential Equations
1088(21)
Additional Readings
1107(2)
Probability
1109(44)
Definitions, Simple Properties
1109(7)
Random Variables
1116(12)
Binomial Distribution
1128(2)
Poisson Distribution
1130(4)
Gauss' Normal Distribution
1134(4)
Statistics
1138(15)
Additional Readings
1150(1)
General References
1150(3)
Index 1153


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