Mathematical Methods for Physicists

by Arfken, George B.; Weber, Hans J.

• ISBN13: 9780120598250
• ISBN10: 0120598256
• Edition: 5th
• Format: Hardcover
• Copyright: 2000-10-01
• Publisher: Academic Pr

Summary

Through four editions, Arfken and Weber's best-selling Mathematical Methods for Physicists has provided upper-level undergraduate and graduate students with the paramount coverage of the mathematics necessary for advanced study in physics and engineering. It provides the essential mathematical methods that aspiring physicists are likely to encounter as students or beginning researchers. Appropriate for a physics service course, as well as for more advanced coursework, this is the book of choice in the field. * Provides the essential mathematical methods that aspiring physicists are likely to encounter as students or beginning researchers * * Serves as both text and useful reference for students of physics and applied mathematics * * Throughout the text the physical relevance of the mathematics is constantly reinforced

Table of Contents

Preface	xiii
Vector Analysis	1	(102)
Definitions, Elementary Approach	1	(7)
Rotation of the Coordinate Axes	8	(5)
Scalar or Dot Product	13	(6)
Vector or Cross Product	19	(8)
Triple Scalar Product, Triple Vector Product	27	(8)
Gradient, ▿	35	(5)
Divergence, ▿	40	(4)
Curl, ▿x	44	(7)
Successive Applications of ▿	51	(4)
Vector Integration	55	(6)
Gauss's Theorem	61	(4)
Stokes's Theorem	65	(4)
Potential Theory	69	(11)
Gauss's Law, Poisson's Equation	80	(4)
Dirac Delta Function	84	(12)
Helmholtz's Theorem	96	(7)
Curved Coordinates, Tensors	103	(62)
Orthogonal Coordinates	103	(5)
Differential Vector Operators	108	(5)
Special Coordinate Systems: Introduction	113	(1)
Circular Cylindrical Coordinates	114	(7)
Spherical Polar Coordinates	121	(10)
Tensor Analysis	131	(6)
Contraction, Direct Product	137	(2)
Quotient Rule	139	(2)
Pseudotensors, Dual Tensors	141	(9)
Non-Cartesian Tensors	150	(10)
Tensor Derivative Operators	160	(5)
Determinants and Matrices	165	(72)
Determinants	165	(9)
Matrices	174	(18)
Orthogonal Matrices	192	(14)
Determinants Matrices, Unitary Matrices	206	(7)
Diagonalization of Matrices	213	(14)
Normal Matrices	227	(10)
Group Theory	237	(66)
Introduction to Group Theory	237	(5)
Generators of Continuous Groups	242	(16)
Orbital Angular Momentum	258	(5)
Angular Momentum Coupling	263	(12)
Homogeneous Lorentz Group	275	(3)
Lorentz Covariance of Maxwell's Equations	278	(8)
Discrete Groups	286	(17)
Infinite Series	303	(86)
Fundamental Concepts	303	(3)
Convergence Tests	306	(16)
Alternating Series	322	(3)
Algebra of Series	325	(4)
Series of Functions	329	(5)
Taylor's Expansion	334	(12)
Power Series	346	(8)
Elliptic Integrals	354	(6)
Bernoulli Numbers, Euler-Maclaurin Formula	360	(13)
Asymptotic Series	373	(8)
Infinite Products	381	(8)
Functions of a Complex Variable I	389	(50)
Complex Algebra	390	(9)
Cauchy-Riemann Conditions	399	(5)
Cauchy's Integral Theorem	404	(7)
Cauchy's Integral Formula	411	(5)
Laurent Expansion	416	(9)
Mapping	425	(9)
Conformal Mapping	434	(5)
Functions of a Complex Variable II	439	(48)
Singularities	439	(5)
Calculus of Residues	444	(25)
Dispersion Relations	469	(8)
Method of Steepest Descents	477	(10)
Differential Equations	487	(88)
Partial Differential Equations	487	(9)
First-Order Differential Equations	496	(10)
Separation of Variables	506	(10)
Singular Points	516	(2)
Series Solutions---Frobenius's Method	518	(15)
A Second Solution	533	(15)
Nonhomogeneous Equation---Green's Function	548	(19)
Numerical Solutions	567	(8)
Sturm-Liouville Theory	575	(56)
Self-Adjoint ODEs	575	(13)
Hermitian Operators	588	(8)
Gram-Schmidt Orthogonalization	596	(8)
Completeness of Eigenfunctions	604	(12)
Green's Function---Eigenfunction Expansion	616	(15)
Gamma-Factorial Function	631	(38)
Definitions, Simple Properties	631	(12)
Digamma and Polygamma Functions	643	(6)
Stirling's Series	649	(5)
The Beta Function	654	(6)
Incomplete Gamma Function	660	(9)
Bessel Functions	669	(70)
Bessel Functions of the First Kind Jv(x)	669	(19)
Orthogonality	688	(6)
Neumann Functions, Bessel Functions of the Second Kind	694	(8)
Hankel Functions	702	(7)
Modified Bessel Functions Iv(x) and Kv(x)	709	(7)
Asymptotic Expansions	716	(6)
Spherical Bessel Functions	722	(17)
Legendre Functions	739	(78)
Generating Function	739	(9)
Recurrence Relations	748	(7)
Orthogonality	755	(12)
Alternate Definitions	767	(4)
Associated Legendre Functions	771	(15)
Spherical Harmonics	786	(6)
Orbital Angular Momentum Operators	792	(4)
The Addition Theorem for Spherical Harmonics	796	(6)
Integrals of Three Ys	802	(4)
Legendre Functions of the Second Kind	806	(7)
Vector Spherical Harmonics	813	(4)
Special Functions	817	(46)
Hermite Functions	817	(11)
Laguerre Functions	828	(11)
Chebyshev Polynomials	839	(11)
Hypergeometric Functions	850	(5)
Confluent Hypergeometric Functions	855	(8)
Fourier Series	863	(42)
General Properties	863	(7)
Advantages, Uses of Fourier Series	870	(4)
Applications of Fourier Series	874	(12)
Properties of Fourier Series	886	(7)
Gibbs Phenomenon	893	(5)
Discrete Fourier Transform	898	(7)
Integral Transforms	905	(78)
Integral Transforms	905	(4)
Development of the Fourier Integral	909	(2)
Fourier Transforms---Inversion Theorem	911	(9)
Fourier Transform of Derivatives	920	(4)
Convolution Theorem	924	(4)
Momentum Representation	928	(7)
Transfer Functions	935	(3)
Laplace Transforms	938	(8)
Laplace Transform of Derivatives	946	(7)
Other Properties	953	(12)
Convolution or Faltungs Theorem	965	(4)
Inverse Laplace Transform	969	(14)
Integral Equations	983	(34)
Introduction	983	(8)
Integral Transforms, Generating Functions	991	(6)
Neumann Series, Separable Kernels	997	(12)
Hilbert-Schmidt Theory	1009	(8)
Calculus of Variations	1017	(42)
A Dependent and an Independent Variable	1018	(5)
Applications of the Euler Equation	1023	(8)
Several Dependent Variables	1031	(5)
Several Independent Variables	1036	(2)
Several Dependent and Independent Variables	1038	(1)
Lagrangian Multipliers	1039	(6)
Variation With Constraints	1045	(7)
Rayleigh-Ritz Variational Technique	1052	(7)
Nonlinear Methods and Chaos	1059	(26)
Introduction	1059	(1)
The Logistic Map	1060	(4)
Sensitivity to Initial Conditions	1064	(4)
Nonlinear Differential Equations	1068	(17)
Appendix 1 Real Zeros of a Function	1085	(4)
Appendix 2 Gaussian Quadrature	1089	(8)
Index	1097