Mathematical methods of physics:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Menlo Park, Calif. [u.a.]
Benjamin/Cummings
1970
|
| Ausgabe: | 2. ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIII, 501 S. graph. Darst. |
| ISBN: | 0805370021 |
Internformat
MARC
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| 245 | 1 | 0 | |a Mathematical methods of physics |c Jon Mathews ; R. L. Walker |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Menlo Park, Calif. [u.a.] |b Benjamin/Cummings |c 1970 | |
| 300 | |a XIII, 501 S. |b graph. Darst. | ||
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Datensatz im Suchindex
| _version_ | 1804128734134927360 |
|---|---|
| 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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| indexdate | 2024-07-09T18:53:57Z |
| institution | BVB |
| isbn | 0805370021 |
| language | English |
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| physical | XIII, 501 S. graph. Darst. |
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| spelling | Mathews, Jon Verfasser aut Mathematical methods of physics Jon Mathews ; R. L. Walker 2. ed. Menlo Park, Calif. [u.a.] Benjamin/Cummings 1970 XIII, 501 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathematische Physik (DE-588)4037952-8 gnd rswk-swf Physik (DE-588)4045956-1 gnd rswk-swf Mathematische Methode (DE-588)4155620-3 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=009505910&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 (DE-588)4037952-8 gnd Physik (DE-588)4045956-1 gnd Mathematische Methode (DE-588)4155620-3 gnd |
| subject_GND | (DE-588)4037952-8 (DE-588)4045956-1 (DE-588)4155620-3 |
| 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 ; R. L. Walker |
| title_fullStr | Mathematical methods of physics Jon Mathews ; R. L. Walker |
| title_full_unstemmed | Mathematical methods of physics Jon Mathews ; R. L. Walker |
| title_short | Mathematical methods of physics |
| title_sort | mathematical methods of physics |
| topic | Mathematische Physik (DE-588)4037952-8 gnd Physik (DE-588)4045956-1 gnd Mathematische Methode (DE-588)4155620-3 gnd |
| topic_facet | Mathematische Physik Physik Mathematische Methode |
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