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Mathematical methods for physicists.

Author: George B Arfken; Hans-Jurgen Weber
Publisher: San Diego : Harcourt/Academic Press, ©2001.
Edition/Format:   eBook : Document : English : 5th ed.
Summary:

This volume contains the essential mathematical tools and techniques used to solve problems in physics. A useful textbook for all serious undergraduate students of physics.

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Additional Physical Format: Print version:
Arfken, George B. (George Brown), 1922-
Mathematical methods for physicists.
San Diego : Harcourt/Academic Press, ©2001
(DLC) 00108275
(OCoLC)45705658
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: George B Arfken; Hans-Jurgen Weber
OCLC Number: 872634373
Reproduction Notes: Electronic reproduction. [S.l.] : HathiTrust Digital Library, 2011. MiAaHDL
Description: 1 online resource (xiv, 1112 pages) : illustrations
Details: Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002.
Contents: 1 Vector Analysis 1 --
1.2 Rotation of the Coordinate Axes 8 --
1.3 Scalar or Dot Product 13 --
1.4 Vector or Cross Product 19 --
1.5 Triple Scalar Product, Triple Vector Product 27 --
1.6 Gradient, [down triangle, open] 35 --
1.7 Divergence, [down triangle, open] 40 --
1.8 Curl, [down triangle, open] x 44 --
1.9 Successive Applications of [down triangle, open] 51 --
1.10 Vector Integration 55 --
1.11 Gauss's Theorem 61 --
1.12 Stokes's Theorem 65 --
1.13 Potential Theory 69 --
1.14 Gauss's Law, Poisson's Equation 80 --
1.15 Dirac Delta Function 84 --
1.16 Helmholtz's Theorem 96 --
2 Curved Coordinates, Tensors 103 --
2.1 Orthogonal Coordinates 103 --
2.2 Differential Vector Operators 108 --
2.3 Special Coordinate Systems: Introduction 113 --
2.4 Circular Cylindrical Coordinates 114 --
2.5 Spherical Polar Coordinates 121 --
2.6 Tensor Analysis 131 --
2.7 Contraction, Direct Product 137 --
2.8 Quotient Rule 139 --
2.9 Pseudotensors, Dual Tensors 141 --
2.10 Non-Cartesian Tensors 150 --
2.11 Tensor Derivative Operators 160 --
3 Determinants and Matrices 165 --
3.1 Determinants 165 --
3.2 Matrices 174 --
3.3 Orthogonal Matrices 192 --
3.4 Hermitian Matrices, Unitary Matrices 206 --
3.5 Diagonalization of Matrices 213 --
3.6 Normal Matrices 227 --
4 Group Theory 237 --
4.1 Introduction to Group Theory 237 --
4.2 Generators of Continuous Groups 242 --
4.3 Orbital Angular Momentum 258 --
4.4 Angular Momentum Coupling 263 --
4.5 Homogeneous Lorentz Group 275 --
4.6 Lorentz Covariance of Maxwell's Equations 278 --
4.7 Discrete Groups 286 --
5 Infinite Series 303 --
5.2 Convergence Tests 306 --
5.3 Alternating Series 322 --
5.4 Algebra of Series 325 --
5.5 Series of Functions 329 --
5.6 Taylor's Expansion 334 --
5.7 Power Series 346 --
5.8 Elliptic Integrals 354 --
5.9 Bernoulli Numbers, Euler-Maclaurin Formula 360 --
5.10 Asymptotic Series 373 --
5.11 Infinite Products 381 --
6 Functions of a Complex Variable I 389 --
6.1 Complex Algebra 390 --
6.2 Cauchy-Riemann Conditions 399 --
6.3 Cauchy's Integral Theorem 404 --
6.4 Cauchy's Integral Formula 411 --
6.5 Laurent Expansion 416 --
6.6 Mapping 425 --
6.7 Conformal Mapping 434 --
7 Functions of a Complex Variable II 439 --
7.1 Singularities 439 --
7.2 Calculus of Residues 444 --
7.3 Dispersion Relations 469 --
7.4 Method of Steepest Descents 477 --
8 Differential Equations 487 --
8.1 Partial Differential Equations 487 --
8.2 First-Order Differential Equations 496 --
8.3 Separation of Variables 506 --
8.4 Singular Points 516 --
8.5 Series Solutions--Frobenius's Method 518 --
8.6 A Second Solution 533 --
8.7 Nonhomogeneous Equation--Green's Function 548 --
8.8 Numerical Solutions 567 --
9 Sturm-Liouville Theory 575 --
9.1 Self-Adjoint ODEs 575 --
9.2 Hermitian Operators 588 --
9.3 Gram-Schmidt Orthogonalization 596 --
9.4 Completeness of Eigenfunctions 604 --
9.5 Green's Function--Eigenfunction Expansion 616 --
10 Gamma-Factorial Function 631 --
10.1 Definitions, Simple Properties 631 --
10.2 Digamma and Polygamma Functions 643 --
10.3 Stirling's Series 649 --
10.4 Beta Function 654 --
10.5 Incomplete Gamma Function 660 --
11 Bessel Functions 669 --
11.1 Bessel Functions of the First Kind J[subscript v](x) 669 --
11.2 Orthogonality 688 --
11.3 Neumann Functions, Bessel Functions of the Second Kind 694 --
11.4 Hankel Functions 702 --
11.5 Modified Bessel Functions I[subscript v](x) and K[subscript v](x) 709 --
11.6 Asymptotic Expansions 716 --
11.7 Spherical Bessel Functions 722 --
12 Legendre Functions 739 --
12.1 Generating Function 739 --
12.2 Recurrence Relations 748 --
12.3 Orthogonality 755 --
12.4 Alternate Definitions 767 --
12.5 Associated Legendre Functions 771 --
12.6G Spherical Harmonics 786 --
12.7 Orbital Angular Momentum Operators 792 --
12.8 Addition Theorem for Spherical Harmonics 796 --
12.9 Integrals of Three Ys 802 --
12.10 Legendre Functions of the Second Kind 806 --
12.11 Vector Spherical Harmonics 813 --
13 Special Functions 817 --
13.1 Hermite Functions 817 --
13.2 Laguerre Functions 828 --
13.3 Chebyshev Polynomials 839 --
13.4 Hypergeometric Functions 850 --
13.5 Confluent Hypergeometric Functions 855 --
14 Fourier Series 863 --
14.1 General Properties 863 --
14.2 Advantages, Uses of Fouries Series 870 --
14.3 Applications of Fourier Series 874 --
14.4 Properties of Fourier Series 886 --
14.5 Gibbs Phenomenon 893 --
14.6 Discrete Fourier Transform 898 --
15 Integral Transforms 905 --
15.1 Integral Transforms 905 --
15.2 Development of the Fourier Integral 909 --
15.3 Fourier Transforms--Inversion Theorem 911 --
15.4 Fourier Transform of Derivatives 920 --
15.5 Convolution Theorem 924 --
15.6 Momentum Representation 928 --
15.7 Transfer Functions 935 --
15.8 Laplace Transforms 938 --
15.9 Laplace Transform of Derivatives 946 --
15.10 Other Properties 953 --
15.11 Convolution or Faltungs Theorem 965 --
15.12 Inverse Laplace Transform 969 --
16 Integral Equations 983 --
16.2 Integral Transforms, Generating Functions 991 --
16.3 Neumann Series, Separable Kernels 997 --
16.4 Hilbert-Schmidt Theory 1009 --
17 Calculus of Variations 1017 --
17.1 A Dependent and an Independent Variable 1018 --
17.2 Applications of the Euler Equation 1023 --
17.3 Several Dependent Variables 1031 --
17.4 Several Independent Variables 1036 --
17.5 Several Dependent and Independent Variables 1038 --
17.6 Lagrangian Multipliers 1039 --
17.7 Variation With Constraints 1045 --
17.8 Rayleigh-Ritz Variational Technique 1052 --
18 Nonlinear Methods and Chaos 1059 --
18.2 Logistic Map 1060 --
18.3 Sensitivity to Initial Conditions 1064 --
18.4 Nonlinear Differential Equations 1068 --
Appendix 1 Real Zeros of a Function 1085 --
Appendix 2 Gaussian Quadrature 1089.

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"Praise for previous edition Many instructors have considered ... Arfken ... to be the best available compendium of the mathematics required for advanced study in science and engineering. -American Read more...

 
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