Arfken / Weber Mathematical Methods for Physicists

4. Auflage 2013
ISBN: 978-1-4832-8806-2
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 1029 Seiten, Web PDF

This new and completely revised Fourth Edition provides thorough coverage of the important mathematics needed for upper-division and graduate study in physics and engineering. Following more than 28 years of successful class-testing, Mathematical Methods for Physicists is considered the standard text on the subject.A new chapter on nonlinear methods and chaos is included, as are revisions of the differential equations and complex variables chapters. The entire book has been made even more accessible, with special attention given to clarity, completeness, and physical motivation. It is an excellent reference apart from its course use.This revised Fourth Edition includes:Modernized terminologyGroup theoretic methods brought together and expanded in a new chapterAn entirely new chapter on nonlinear mathematical physicsSignificant revisions of the differential equations and complex variables chaptersMany new or improved exercisesForty new or improved figuresAn update of computational techniques for today's contemporary tools, such as microcomputers, Numerical Recipes, and Mathematica(r), among others

Autoren/Hrsg.

Arfken, George B.

Weber, Hans J.

Inhaltsverzeichnis

1;Front Cover;1
2;Mathematical Methods for Physicists;4
3;Copyright Page;5
4;Table of Contents;8
5;Dedication;6
6;PREFACE;16
7;INTRODUCTION;18
8;CHAPTER 1. VECTOR ANALYSIS;20
8.1;1.1 DEFINITIONS, ELEMENTARY APPROACH;20
8.2;1.2 ROTATION OF THE COORDINATE AXES;26
8.3;1.3 SCALAR OR DOT PRODUCT;32
8.4;1.4 VECTOR OR CROSS PRODUCT;37
8.5;1.5 TRIPLE SCALAR PRODUCT, TRIPLE VECTOR PRODUCT;45
8.6;1.6 GRADIENT;52
8.7;1.7 DIVERGENCE;57
8.8;1.8 CURL;61
8.9;1.9 SUCCESSIVE APPLICATIONS OF;67
8.10;1.10 VECTOR INTEGRATION;71
8.11;1.11 GAUSS'S THEOREM;77
8.12;1.12 STOKES'S THEOREM;81
8.13;1.13 POTENTIAL THEORY;85
8.14;1.14 GAUSS'S LAW, POISSON'S EQUATION;96
8.15;1.15 DIRAC DELTA FUNCTION;100
8.16;1.16 HELMHOLTZ'S THEOREM;111
8.17;ADDITIONAL READINGS;116
9;CHAPTER 2. VECTOR ANALYSIS IN CURVED COORDINATES AND TENSORS;118
9.1;2.1 ORTHOGONAL COORDINATES;119
9.2;2.2 DIFFERENTIAL VECTOR OPERATORS;123
9.3;2.3 SPECIAL COORDINATE SYSTEMS: INTRODUCTION;128
9.4;2.4 CIRCULAR CYLINDRICAL COORDINATES;129
9.5;2.5 SPHERICAL POLAR COORDINATES;136
9.6;2.6 TENSOR ANALYSIS;145
9.7;2.7 CONTRACTION, DIRECT PRODUCT;151
9.8;2.8 QUOTIENT RULE;153
9.9;2.9 PSEUDOTENSORS, DUAL TENSORS;154
9.10;2.10 NONCARTESIAN TENSORS,COVARIANT DIFFERENTIATION;164
9.11;2.11 TENSOR DIFFERENTIAL OPERATORS;171
9.12;ADDITIONAL READINGS;173
10;CHAPTER 3. DETERMINANTS AND MATRICES;175
10.1;3.1 DETERMINANTS;175
10.2;3.2 MATRICES;184
10.3;3.3 ORTHOGONAL MATRICES;200
10.4;3.4 HERMITIAN MATRICES, UNITARY MATRICES;213
10.5;3.5 DIAGONALIZATION OF MATRICES;220
10.6;3.6 NORMAL MATRICES;232
10.7;ADDITIONAL READINGS;241
11;CHAPTER 4. GROUP THEORY;242
11.1;4.1 INTRODUCTION TO GROUP THEORY;242
11.2;4.2 GENERATORS OF CONTINUOUS GROUPS;246
11.3;4.3 ORBITAL ANGULAR MOMENTUM;262
11.4;4.4 ANGULAR MOMENTUM COUPLING;266
11.5;4.5 HOMOGENEOUS LORENTZ GROUP;277
11.6;4.6 LORENTZ COVARIANCE OF MAXWELL'S EQUATIONS;281
11.7;4.7 DISCRETE GROUPS;288
11.8;ADDITIONAL READINGS;301
12;CHAPTER 5. INFINITE SERIES;303
12.1;5.1 FUNDAMENTAL CONCEPTS;303
12.2;5.2 CONVERGENCE TESTS;307
12.3;5.3 ALTERNATING SERIES;321
12.4;5.4 ALGEBRA OF SERIES;323
12.5;5.5 SERIES OF FUNCTIONS;328
12.6;5.6 TAYLOR'S EXPANSION;332
12.7;5.7 POWER SERIES;343
12.8;5 . 8 ELLIPTIC INTEGRALS;350
12.9;5.9 BERNOULLI NUMBERS, EULER–MACLAURIN FORMULA;356
12.10;5.10 ASYMPTOTIC OR SEMICONVERGENT SERIES;368
12.11;5.11 INFINITE PRODUCTS;376
12.12;ADDITIONAL READINGS;380
13;CHAPTER 6. FUNCTIONS OF ACOMPLEX VARIABLE 1;382
13.1;6.1 COMPLEX ALGEBRA;383
13.2;6.2 CAUCHY-RIEMANN CONDITIONS;391
13.3;6.3 CAUCHY'S INTEGRAL THEOREM;396
13.4;6.4 CAUCHY'S INTEGRAL FORMULA;403
13.5;6.5 LAURENT EXPANSION;408
13.6;6.6 MAPPING;417
13.7;6.7 C0NF0RMAL MAPPING;425
13.8;ADDITIONAL READINGS;427
14;CHAPTER 7. FUNCTIONS OF ACOMPLEX VARIABLE II;429
14.1;7.1 SINGULARITIES;429
14.2;7.2 CALCULUS OF RESIDUES;433
14.3;7.3 DISPERSION RELATIONS;458
14.4;7.4 THE METHOD OF STEEPEST DESCENTS;465
14.5;ADDITIONAL READINGS;474
15;CHAPTER 8. DIFFERENTIALEQUATIONS;475
15.1;8.1 PARTIAL DIFFERENTIAL EQUATIONS,CHARACTERISTICS, AND BOUNDARY CONDITIONS;475
15.2;8.2 FIRST-ORDER DIFFERENTIAL EQUATIONS;482
15.3;8.3 SEPARATION OF VARIABLES;490
15.4;8.4 SINGULAR POINTS;499
15.5;8.5 SERIES SOLUTIONS-FROBENIUS' METHOD;502
15.6;8.6 A SECOND SOLUTION;516
15.7;8.7 NONHOMOGENEOUS EQUATION-GREEN'S FUNCTION;529
15.8;8.8 NUMERICAL SOLUTIONS;548
15.9;ADDITIONAL READINGS;553
16;CHAPTER 9. STURM–LIOUVILLE THEORY–ORTHOGONAL FUNCTIONS;556
16.1;9.1 SELF-ADJOINT DIFFERENTIAL EQUATIONS;556
16.2;9.2 HERMITIAN OPERATORS;570
16.3;9.3 GRAM–SCHMIDT ORTHOGONALIZATION;577
16.4;9.4 COMPLETENESS OF EIGENFUNCTIONS;584
16.5;9.5 GREEN'S FUNCTION—EIGENFUNCTION EXPANSION;596
16.6;ADDITIONAL READINGS;609
17;CHAPTER 10. THE GAMMA FUNCTION (FACTORIAL FUNCTION);610
17.1;10.1 DEFINITIONS, SIMPLE PROPERTIES;610
17.2;10.2 DIGAMMA AND POLYGAMMA FUNCTIONS;621
17.3;10.3 STIRLING'S SERIES;627
17.4;10.4 THE BETA FUNCTION;632
17.5;10.5 THE INCOMPLETE GAMMA FUNCTIONS AND RELATED FUNCTIONS;638
17.6;ADDITIONAL READINGS;645
18;11. BESSEL FUNCTIONS;646
18.1;11.1 BESSEL FUNCTIONS OF THE FIRST KIND;646
18.2;11.2 ORTHOGONALITY;664
18.3;11.3 NEUMANN FUNCTIONS, BESSEL FUNCTIONS OF THE SECOND KIND;670
18.4;11.4 HANKEL FUNCTIONS;677
18.5;11.5 MODIFIED BESSEL FUNCTIONS, Iv(x) and Kv( x );683
18.6;11.6 ASYMPTOTIC EXPANSIONS;690
18.7;11.7 SPHERICAL BESSEL FUNCTIONS;696
18.8;ADDITIONAL READINGS;711
19;12. LEGENDRE FUNCTIONS;712
19.1;12.1 GENERATING FUNCTION;712
19.2;12.2 RECURRENCE RELATIONS AND SPECIAL PROPERTIES;720
19.3;12.3 ORTHOGONALITY;727
19.4;12.4 ALTERNATE DEFINITIONS OF LEGENDRE POLYNOMIALS;738
19.5;12.5 ASSOCIATED LEGENDRE FUNCTIONS;741
19.6;12.6 SPHERICAL HARMONICS;755
19.7;12.7 ORBITAL ANGULAR MOMENTUM OPERATORS;761
19.8;12.8 THE ADDITION THEOREM FOR SPHERICAL HARMONICS;765
19.9;12.9 INTEGRALS OF THE PRODUCT OF THREE SPHERICAL HARMONICS;770
19.10;12.10 LEGENDRE FUNCTIONS OF THE SECOND KIND, Qn(X) ;774
19.11;12.11 VECTOR SPHERICAL HARMONICS;781
19.12;ADDITIONAL READINGS;784
20;CHAPTER 13. SPECIAL FUNCTIONS;785
20.1;13.1 HERMITE FUNCTIONS;785
20.2;13.2 LAGUERRE FUNCTIONS;795
20.3;13.3 CHEBYSHEV (TSCHEBYSCHEFF) POLYNOMIALS;805
20.4;13.4 HYPERGEOMETRIC FUNCTIONS;815
20.5;13.5 CONFLUENT HYPERGEOMETRIC FUNCTIONS;820
20.6;ADDITIONAL READINGS;826
21;CHAPTER 14. FOURIER SERIES;827
21.1;14.1 GENERAL PROPERTIES;827
21.2;14.2 ADVANTAGES, USES OF FOURIER SERIES;834
21.3;14.3 APPLICATIONS OF FOURIER SERIES;837
21.4;14.4 PROPERTIES OF FOURIER SERIES;848
21.5;14.5 GIBBS PHENOMENON;855
21.6;14.6 DISCRETE ORTHOGONALITY–DISCRETE FOURIER TRANSFORM;859
21.7;ADDITIONAL READINGS;864
22;CHAPTER 15. INTEGRAL TRANSFORMS;865
22.1;15.1 INTEGRAL TRANSFORMS;865
22.2;15.2 DEVELOPMENT OF THE FOURIER INTEGRAL;869
22.3;15.3 FOURIER TRANSFORMS–INVERSION THEOREM;871
22.4;15.4 FOURIER TRANSFORM OF DERIVATIVES;879
22.5;15.5 CONVOLUTION THEOREM;882
22.6;15.6 MOMENTUM REPRESENTATION;887
22.7;15.7 TRANSFER FUNCTIONS;893
22.8;15.8 ELEMENTARY LAPLACE TRANSFORMS;896
22.9;15.9 LAPLACE TRANSFORM OF DERIVATIVES;904
22.10;15.10 OTHER PROPERTIES;911
22.11;15.11 CONVOLUTION OR FALTUNG THEOREM;923
22.12;15.12 INVERSE LAPLACE TRANSFORMATION;927
22.13;ADDITIONAL READINGS;937
23;CHAPTER 16. INTEGRAL EQUATIONS;939
23.1;16.1 INTRODUCTION;939
23.2;16.2 INTEGRAL TRANSFORMS, GENERATING FUNCTIONS;946
23.3;16.3 NEUMANN SERIES, SEPARABLE (DEGENERATE) KERNELS;952
23.4;16.4 HUBERT—SCHMIDT THEORY;963
23.5;ADDITIONAL READINGS;970
24;CHAPTER 17. CALCULUS OF VARIATIOS;971
24.1;17.1 ONE-DEPENDENT AND ONE-INDEPENDENT VARIABLE;972
24.2;17.2 APPLICATIONS OF THE EULER EQUATION;976
24.3;17.3 GENERALIZATIONS, SEVERAL DEPENDENT VARIABLES;984
24.4;17.4 SEVERAL INDEPENDENT VARIABLES;989
24.5;17.5 MORE THAN ONE DEPENDENT, MORE THAN ONE INDEPENDENT VARIABLE;991
24.6;17.6 LAGRANGIAN MULTIPLIERS;992
24.7;17.7 VARIATION SUBJECT TO CONSTRAINTS;997
24.8;17.8 RAYLEIGH–RITZ VARIATIONAL TECHNIQUE;1005
24.9;ADDITIONAL READINGS;1009
25;CHAPTER 18. NONLINEAR METHODS AND CHAOS;1011
25.1;18.1 INTRODUCTION;1011
25.2;18.2 THE LOGISTIC MAP;1012
25.3;18.3 SENSITIVITY TO INITIAL CONDITIONS AND PARAMETERS;1016
25.4;18.4 NONLINEAR DIFFERENTIAL EQUATIONS;1018
25.5;ADDITIONAL READINGS;1023
26;APPENDIX 1: Real Zeros of a Function;1024
26.1;ADDITIONAL READINGS;1027
27;APPENDIX 2: Gaussian Quadrature;1028
27.1;ADDITIONAL READINGS;1034
28;GENERAL REFERENCES;1035
29;INDEX;1036