Problems of Mathematical Physics (Selected Russian Publications in the Mathematical Sciences)

Series......Page 2
Title......Page 3
Publication Data......Page 4
Author’s Preface......Page 5
Translator’s Preface......Page 7
Contents......Page 9
Part 1: Problems......Page 13
1. Mechanics......Page 15
2. Heat Conduction......Page 21
3. Electricity and Magnetism......Page 23
1. Hyperbolic Equations......Page 31
2. Elliptic Equations: The Green’s Function Method......Page 39
3. Elliptic Equations: The Method of Conformal Mapping......Page 45
3 – Steady-State Harmonic Oscillations......Page 54
1. Elastic Bodies: Free Oscillations......Page 55
2. Elastic Bodies: Forced Oscillations......Page 58
3. Electromagnetic Oscillations......Page 61
4 – The Fourier Method......Page 67
1. Mechanics: Vibrating Systems, Acoustics......Page 72
2. Mechanics: Statics of Deformable Media, Fluid Dynamics......Page 85
3. Heat Conduction: Non stationary Problems......Page 89
4. Heat Conduction: Stationary Problems......Page 95
5. Electricity and Magnetism......Page 103
5 – The Eigenfunction Method for Solving Inhomogenous Problems......Page 115
1. Mechanics: Vibrating Systems......Page 119
2. Mechanics: Statics of Deformable Media......Page 126
3. Heat Conduction: Nonstationary Problems......Page 131
4. Heat Conduction: Stationary Problems......Page 136
5. Electricity and Magnetism......Page 143
6 – Integral Transforms......Page 155
1. The Fourier Transform......Page 158
2. The Hankel Transform......Page 172
3. The Laplace Transform......Page 181
4. The Mellin Transform......Page 201
5. Integral Transforms Involving Cylinder Functions of Imaginary Order......Page 206
7 – Curvilinear Coordinates......Page 215
1. Elliptic Coordinates......Page 216
2. Parabolic Coordinates......Page 222
3. Two-Dimensional Bipolar Coordinates......Page 224
4. Spheroidal Coordinates......Page 231
5. Paraboloidal Coordinates......Page 243
6. Toroidal Coordinates......Page 245
7. Three-Dimensional Bipolar Coordinates......Page 254
8. Some General Problems on Separation of Variables......Page 259
8 – Integral Equations......Page 265
1. Diffraction Theory......Page 266
2. Electrostatics......Page 271
Part 2: Solutions......Page 285
1. Special Functions Appearing in the Text......Page 393
2. Some Expansions in Series of Orthogonal Functions......Page 396
3. Some Definite Integrals Frequently Encountered in the Applications......Page 398
4. Expansion of Some Differential Operators in Orthogonal Curvilinear Coordinates......Page 400
Supplement: Variational and Related Methods......Page 403
1.1. Formulation of Variational Problems......Page 404
1.2. The Ritz Method......Page 408
1.3. Kantorovich’s Method......Page 413
2.1. Galerkin’s Method......Page 416
2.2. Collocation......Page 419
2.3. Least Squares......Page 423
3. References......Page 424
A-B-C......Page 427
D-E-F-G......Page 428
H-J-K......Page 429
L......Page 430
M-N-O-P-R......Page 431
S......Page 432
T-U-V-W......Page 433
A-B-C-D-E-F-G-H......Page 435
I-J-K-L-M-N-O-P-R-S......Page 436
T-U-V-W......Page 437
A-B-C-D-E-F......Page 439
G-H-I-J-K-L-M-N-P-R-S......Page 440
T-V-W......Page 441