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Mathematical Methods for Physicists

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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…    
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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

Prefacep. xiii
Vector Analysisp. 1
Definitions, Elementary Approachp. 1
Rotation of the Coordinate Axesp. 8
Scalar or Dot Productp. 13
Vector or Cross Productp. 19
Triple Scalar Product, Triple Vector Productp. 27
Gradient, [down triangle, open]p. 35
Divergence, [down triangle, open]p. 40
Curl, [down triangle, open] xp. 44
Successive Applications of [down triangle, open]p. 51
Vector Integrationp. 55
Gauss's Theoremp. 61
Stokes's Theoremp. 65
Potential Theoryp. 69
Gauss's Law, Poisson's Equationp. 80
Dirac Delta Functionp. 84
Helmholtz's Theoremp. 96
Curved Coordinates, Tensorsp. 103
Orthogonal Coordinatesp. 103
Differential Vector Operatorsp. 108
Special Coordinate Systems: Introductionp. 113
Circular Cylindrical Coordinatesp. 114
Spherical Polar Coordinatesp. 121
Tensor Analysisp. 131
Contraction, Direct Productp. 137
Quotient Rulep. 139
Pseudotensors, Dual Tensorsp. 141
Non-Cartesian Tensorsp. 150
Tensor Derivative Operatorsp. 160
Determinants and Matricesp. 165
Determinantsp. 165
Matricesp. 174
Orthogonal Matricesp. 192
Hermitian Matrices, Unitary Matricesp. 206
Diagonalization of Matricesp. 213
Normal Matricesp. 227
Group Theoryp. 237
Introduction to Group Theoryp. 237
Generators of Continuous Groupsp. 242
Orbital Angular Momentump. 258
Angular Momentum Couplingp. 263
Homogeneous Lorentz Groupp. 275
Lorentz Covariance of Maxwell's Equationsp. 278
Discrete Groupsp. 286
Infinite Seriesp. 303
Fundamental Conceptsp. 303
Convergence Testsp. 306
Alternating Seriesp. 322
Algebra of Seriesp. 325
Series of Functionsp. 329
Taylor's Expansionp. 334
Power Seriesp. 346
Elliptic Integralsp. 354
Bernoulli Numbers, Euler-Maclaurin Formulap. 360
Asymptotic Seriesp. 373
Infinite Productsp. 381
Functions of a Complex Variable Ip. 389
Complex Algebrap. 390
Cauchy-Riemann Conditionsp. 399
Cauchy's Integral Theoremp. 404
Cauchy's Integral Formulap. 411
Laurent Expansionp. 416
Mappingp. 425
Conformal Mappingp. 434
Functions of a Complex Variable IIp. 439
Singularitiesp. 439
Calculus of Residuesp. 444
Dispersion Relationsp. 469
Method of Steepest Descentsp. 477
Differential Equationsp. 487
Partial Differential Equationsp. 487
First-Order Differential Equationsp. 496
Separation of Variablesp. 506
Singular Pointsp. 516
Series Solutions--Frobenius's Methodp. 518
A Second Solutionp. 533
Nonhomogeneous Equation--Green's Functionp. 548
Numerical Solutionsp. 567
Sturm-Liouville Theoryp. 575
Self-Adjoint ODEsp. 575
Hermitian Operatorsp. 588
Gram-Schmidt Orthogonalizationp. 596
Completeness of Eigenfunctionsp. 604
Green's Function--Eigenfunction Expansionp. 616
Gamma-Factorial Functionp. 631
Definitions, Simple Propertiesp. 631
Digamma and Polygamma Functionsp. 643
Stirling's Seriesp. 649
The Beta Functionp. 654
Incomplete Gamma Functionp. 660
Bessel Functionsp. 669
Bessel Functions of the First Kind J[subscript v](x)p. 669
Orthogonalityp. 688
Neumann Functions, Bessel Functions of the Second Kindp. 694
Hankel Functionsp. 702
Modified Bessel Functions I[subscript v](x) and K[subscript v](x)p. 709
Asymptotic Expansionsp. 716
Spherical Bessel Functionsp. 722
Legendre Functionsp. 739
Generating Functionp. 739
Recurrence Relationsp. 748
Orthogonalityp. 755
Alternate Definitionsp. 767
Associated Legendre Functionsp. 771
Spherical Harmonicsp. 786
Orbital Angular Momentum Operatorsp. 792
The Addition Theorem for Spherical Harmonicsp. 796
Integrals of Three Ysp. 802
Legendre Functions of the Second Kindp. 806
Vector Spherical Harmonicsp. 813
Special Functionsp. 817
Hermite Functionsp. 817
Laguerre Functionsp. 828
Chebyshev Polynomialsp. 839
Hypergeometric Functionsp. 850
Confluent Hypergeometric Functionsp. 855
Fourier Seriesp. 863
General Propertiesp. 863
Advantages, Uses of Fouries Seriesp. 870
Applications of Fourier Seriesp. 874
Properties of Fourier Seriesp. 886
Gibbs Phenomenonp. 893
Discrete Fourier Transformp. 898
Integral Transformsp. 905
Integral Transformsp. 905
Development of the Fourier Integralp. 909
Fourier Transforms--Inversion Theoremp. 911
Fourier Transform of Derivativesp. 920
Convolution Theoremp. 924
Momentum Representationp. 928
Transfer Functionsp. 935
Laplace Transformsp. 938
Laplace Transform of Derivativesp. 946
Other Propertiesp. 953
Convolution or Faltungs Theoremp. 965
Inverse Laplace Transformp. 969
Integral Equationsp. 983
Introductionp. 983
Integral Transforms, Generating Functionsp. 991
Neumann Series, Separable Kernelsp. 997
Hilbert-Schmidt Theoryp. 1009
Calculus of Variationsp. 1017
A Dependent and an Independent Variablep. 1018
Applications of the Euler Equationp. 1023
Several Dependent Variablesp. 1031
Several Independent Variablesp. 1036
Several Dependent and Independent Variablesp. 1038
Lagrangian Multipliersp. 1039
Variation With Constraintsp. 1045
Rayleigh-Ritz Variational Techniquep. 1052
Nonlinear Methods and Chaosp. 1059
Introductionp. 1059
The Logistic Mapp. 1060
Sensitivity to Initial Conditionsp. 1064
Nonlinear Differential Equationsp. 1068
Real Zeros of a Functionp. 1085
Gaussian Quadraturep. 1089
Indexp. 1097
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