Mathematical methods of physics:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York
Benjamin
1970
|
| Ausgabe: | 2. ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIII, 501 S. Tab. |
Internformat
MARC
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Datensatz im Suchindex
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|---|---|
| adam_text | Contents
PREFACE iii
CHAPTER 1 ORDINARY DIFFERENTIAL
EQUATIONS 1
1-1 Solution in Closed Form 1
1-2 Power-Series Solutions 13
1-3 Miscellaneous Approximate Methods 22
1-4 The WKB Method 27
References 37
Problems 38
CHAPTER 2 INFINITE SERIES 44
2-1 Convergence 44
2-2 Familiar Series 48
2-3 Transformation of Series 50
References 55
Problems 56
CHAPTER 3 EVALUATION OF INTEGRALS 58
3-1 Elementary Methods 58
3-2 Use of Symmetry Arguments 62
3-3 Contour Integration 65
3-4 Tabulated Integrals 75
3-5 Approximate Expansions 80
3-6 Saddle-Point Methods 82
References 90
Problems 91
v
i
vi Contents
CHAPTER 4 INTEGRAL TRANSFORMS 96
4-1 Fourier Series 96
4-2 Fourier Transforms 101
4-3 Laplace Transforms 107
4-4 Other Transform Pairs 109
4-5 Applications of Integral Transforms 110
References 119
Problems 120
CHAPTER 5 FURTHER APPLICATIONS OF COMPLEX
VARIABLES 123
5-1 Conformal Transformations 123
5-2 Dispersion Relations 129
References 135
Problems 135
CHAPTER 6 VECTORS AND MATRICES *19
6-1 Linear Vector Spaces 139
6-2 Linear Operators 141
6-3 Matrices 143
6-4 Coordinate Transformations 146
6-5 Eigenvalue Problems 150
6-6 Diagonalization of Matrices 158
6-7 Spaces of Infinite Dimensionality 160
References 163
Problems 163
CHAPTER 7 SPECIAL FUNCTIONS 167
7-1 Legendre Functions 167
7-2 Bessel Functions 178
7-3 Hypergeometric Functions 187
7-4 Confluent Hypergeometric Functions 194
7-5 Mathieu Functions 198
7-6 Elliptic Functions 204
References 210
Problems 210
Contents vii
CHAPTER 8 PARTIAL DIFFERENTIAL EQUATIONS 217
8-1 Examples 217
8-2 General Discussion 219
8-3 Separation of Variables 226
8-4 Integral Transform Methods 239
8-5 Wiener-Hopf Method 245
References 252
Problems 253
CHAPTER 9 EIGENFUNCTIONS, EIGENVALUES, AND
GREEN S FUNCTIONS 260
9-1 Simple Examples of Eigenvalue Problems 260
9-2 General Discussion • 263
9-3 Solutions of Boundary-Value Problems as
Eigenfunction Expansions 266
9-4 Inhomogeneous Problems. Green s Functions 267
9-5 Green s Functions in Electrodynamics 277
References 282
Problems 282
CHAPTER 10 PERTURBATION THEORY 286
10-1 Conventional Nondegenerate Theory 286
10-2 A Rearranged Series 292
10-3 Degenerate Perturbation Theory 293
References 296
Problems 296
CHAPTER 11 INTEGRAL EQUATIONS 299
11-1 Gasification 299
11-2 Degenerate Kernels 300
11-3 Neumann and Fredholm Series 302
11-4 Schmidt-Hilbert Theory 305
11-5 Miscellaneous Devices 311
11-6 Integral Equations in Dispersion Theory 316
References 318
Problems 318
v iii Contents
CHAPTER 12 CALCULUS OF VARIATIONS 322
12-1 Euler-Lagrange Equation 322
12-2 Generalizations of the Basic Problem 327
12-3 Connections between Eigenvalue Problems and
the Calculus of Variations 333
References 341
Problems 341
CHAPTER 13 NUMERICAL METHODS 345
13-1 Interpolation 345
13-2 Numerical Integration 349
13-3 Numerical Solution of Differential Equations 353
13-4 Roots of Equations 358
13-5 Summing Series 363
References 368
Problems 368
CHAPTER 14 PROBABILITY AND STATISTICS 372
14-1 Introduction 372
14-2 Fundamental Probability Laws 373
14-3 Combinations and Permutations 375
14-4 The Binomial, Poisson, and Gaussian
Distributions 377
14-5 General Properties of Distributions 380
14-6 Multivariate Gaussian Distributions 384
14-7 Fitting of Experimental Data 387
References 395
Problems 396
CHAPTER 15 TENSOR ANALYSIS AND DIFFERENTIAL
GEOMETRY 402
15-1 Cartesian Tensors in Three-Space 403
15-2 Curves in Three-Space ;Frenet Formulas 408
15-3 General Tensor Analysis 416
References 421
Problems 421
Contents ix
CHAPTER 16 INTRODUCTION TO GROUPS AND GROUP
REPRESENTATIONS 424
16-1 Introduction; Definitions 424
16-2 Subgroups and Classes 426
16-3 Group Representations 430
16-4 Characters 433
16-5 Physical Applications 440
16-6 Infinite Groups 449
16-7 Irreducible Representations of SU(2), SU(3),
and O(3) 457
References 467
Problems 468
APPENDIX SOME PROPERTIES OF FUNCTIONS OF A
COMPLEX VARIABLE 471
A-l Functions of a Complex Variable. Mapping 471
A-2 Analytic Functions 477
References 483
Problems 483
BIBLIOGRAPHY 485
INDEX 493
|
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| language | English |
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| physical | XIII, 501 S. Tab. |
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| spelling | Mathews, Jon Verfasser aut Mathematical methods of physics Jon Mathews ; Robert L. Walker* 2. ed. New York Benjamin 1970 XIII, 501 S. Tab. txt rdacontent n rdamedia nc rdacarrier Mathematische Physik Mathematical physics Mathematische Physik (DE-588)4037952-8 gnd rswk-swf Mathematische Methode (DE-588)4155620-3 gnd rswk-swf Physik (DE-588)4045956-1 gnd rswk-swf Physik (DE-588)4045956-1 s Mathematische Methode (DE-588)4155620-3 s DE-604 Mathematische Physik (DE-588)4037952-8 s 1\p DE-604 Walker, Robert Lee Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001257001&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Mathews, Jon Walker, Robert Lee Mathematical methods of physics Mathematische Physik Mathematical physics Mathematische Physik (DE-588)4037952-8 gnd Mathematische Methode (DE-588)4155620-3 gnd Physik (DE-588)4045956-1 gnd |
| subject_GND | (DE-588)4037952-8 (DE-588)4155620-3 (DE-588)4045956-1 |
| title | Mathematical methods of physics |
| title_auth | Mathematical methods of physics |
| title_exact_search | Mathematical methods of physics |
| title_full | Mathematical methods of physics Jon Mathews ; Robert L. Walker* |
| title_fullStr | Mathematical methods of physics Jon Mathews ; Robert L. Walker* |
| title_full_unstemmed | Mathematical methods of physics Jon Mathews ; Robert L. Walker* |
| title_short | Mathematical methods of physics |
| title_sort | mathematical methods of physics |
| topic | Mathematische Physik Mathematical physics Mathematische Physik (DE-588)4037952-8 gnd Mathematische Methode (DE-588)4155620-3 gnd Physik (DE-588)4045956-1 gnd |
| topic_facet | Mathematische Physik Mathematical physics Mathematische Methode Physik |
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