Mathematical Methods for Physicists

Name: Mathematical Methods for Physicists
Price: 59.25 USD
Availability: InStock
ISBN: 9780120598250

ISBN-10: 0120598256

ISBN-13: 9780120598250

Edition: 5th 2001

Authors: George B. Arfken, Hans J. Weber

List price: $104.95

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Description:

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…

Book details

List price: $104.95
Edition: 5th
Copyright year: 2001
Publisher: Elsevier Science & Technology Books
Publication date: 10/18/2000
Binding: Hardcover
Pages: 1112
Size: 6.50" wide x 9.25" long x 1.75" tall
Weight: 3.542
Language: English

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