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| Авторизация |
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| Bateman H. — Partial Differential Equations of Mathematical Physics |
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| Предметный указатель |
Abel’s theorem for power series 243
Absorption of sound 336
Adiabatic flow 171 509
Aerofoils, of small thickness 313
Aerofoils, of small thickness thin (Mnnk’s theory) 259
Aeroplane, fall of 492
Air waves in a pipe 227
Alternating process, Schwarz’s 247
Associated Legendre functions 359
Beam, bending of a 16
Bessel functions 229 385 398
Bicharacteristics 133
Bilinear transformation 270
Bipolar co-ordinates 260
Blasius, formulae of 310
Boss, hemispherical 437
boundary conditions 2
Bowl, potential of a spherical 468
Brill’s theorem 161
Cable, theory of unloaded 74 221
Cesaro’s method of summation 10 513
Characteristics 101 132
Circuit theory 54
Circular cylinder flow round 249
Circular cylinder flow round, disc in any field of force 474
Classification of partial differential equations of second order 134
Combination tones 499
Compound pendulum 34
Compressible fluid, motion of 171 509
Con focal co-ordinates 421
Conduction of Heat, equation of 118
Conduction of heat, equation of in a moving medium 218
Conduction of heat, equation of some problems in 338
Confluent hypergeoinetric function 457
Conformal representation 266
Conformal representation of a circle on a half plane 273
Conical harmonics 382
Conjugate Fourier series 242
Conjugate Fourier series functions 73
Conservation of energy and momentum in an electromagnetic field 180
Continued fractions, use of 432 442
Continuity bit by bit (piecewise continuity) 12
Conway’s formula 359 362
Cooling of a spherical solid 353
Cubical compression 163
Curl of a vector 115
Curvature, principal radii of 170
Curves, types of 278
Damped vibrations, equation of 47
Daniell’s orthogonal polynomials 325
Derivative of a normalised mapping function 283
Diffracted wave 485
Diffusion from cylindrical rod 398
Diffusion in two dimensions 398
Diffusion of smoke 345
Diffusion, equation of 121 398
Diffusion, modified equation of 129
Dilatation 163
Dipoles, moving electric and magnetic 199
Discontinuity, moving surface of 196
Dissipation function 52
Distortion theorem 284
Diverging waves 387
Doublet, instantaneous 343
Doubly carpeted region, mapping of 285
Drying of wood 121
Du Bois — Reymond’s lemma 153
Eddy conductivity 219
Eigenfunktion (eif) 6
Eigenwert (eit) 6
Elastic equilibrium, equations of 162
Electric filter 233
Electric pole, moving 197
Electromagnetic equations 177
Electromagnetic equations, waves 178
Elementary solutions (simple solutions) in polar co-ordinates 351
Ellipsoid, potential of 425
Ellipsoidal co-ordinates (confocal coordinates) 421
Elliptic coordinates 254
Elliptic coordinates type, equations of 134 135
Equation of continuity 117
Equation of continuity of three moments 21
Equicontinuity 287
Eulerian rule in Calculus of Variations 155
Euler’s critical load 21
Euler’s critical load, formula 21
Fatou’s theorem 243
Field, electromagnetic 179
Field, electromagnetic of functions 154
Field, electromagnetic, vectors 178 179
Filter, electric 233
Fluctuating temperatures 214
Force, lines of 84
Forced oscillations 40
Fourier’s constants 9
Fourier’s constants, inversion formula 207
Fourier’s series 15
Fourier’s series, theorem 7
Fundamental Lemma of Calculus of Variations 154
Gauss’s mean value theorem 369
Generalisation of solutions 205
Green’s functions 4 140
Green’s functions for beam 18
Green’s functions for circular disc 465
Green’s functions for parallel planes 414
Green’s functions for semi-infinite plane 473
Green’s functions for spherical bowl 468
Green’s functions for wedge 472
Group velocity 231
Half plane, diffraction by 476
Hamack’s Theorem 246
Hankel’s cylindrical functions 387 403
Hankel’s cylindrical functions, inversion formula 411
Heaviside’s expansion 59
Helmholtz’s formula 189
Hemispherical boss 437
Hermite’s polynomial 454
Hermitian forms 39
Hertzian vectors 179
Hobson’s formulae for Legendre functions 357 376
Hobson’s formulae for Legendre functions, theorem 355
Homoeoid, potential of 427
Hydrodynamics, applications of Conformal representation 309
Images, use of method of 85 212 250 469
INDEX 521
Induced charge density 257
Inequalities 149
Inequalities, satisfied by a mapping function 283
Inequalities, Schwarz’s 150 151 317
Influence lines 20
Integral equations 142
Integral equations of electromagnetism 193
Integral equations, use of 131 444
Inversion, method of 85
Inviscid fluid, equations of motion of 164
Isotropic elastic solid 163
Jacobians, use of 107
Jacobi’s polynomials 392
Jacobi’s polynomials, polynomial expansion 390 512
Jacobi’s polynomials, theorem 97
Jacobi’s polynomials, transformation 463
Jordan curves 278 287 324 327
Kinetic potential 165
Kirchhoff’s formula 184
Koshliakov’s theorem 223
Lagrange’s equations of motion 30
Lagrange’s equations of motion, expansion, use of 358
Lagrange’s equations of motion, method of variable multiplier 160
Laplace’s equation 90
Laplace’s equation, formula for a potential function symmetrical about an axis 405
| Laplace’s equation, functions (surface harmonics) 371 514
Laplace’s equation, in m+2 variables 385 422
Legendre constants 364
Legendre constants, functions, expressions for 354 360 376
Legendre constants, integral relations 362
Legendre constants, properties of 364
Legendre’s expansion 372
Lemniscates 269 270
Lens, stream function for a 471
Lerch’s theorem 365
Lightning conductor 436
Lines of force 87 494
Lines of force of shearing stress 173
Liouville’s equation 167
Love-waves in stratified medium 329
Mapping, doubly carpeted region 285
Mapping, doubly carpeted region for a polygon 296
Mapping, doubly carpeted region for the region outside a polygon 305
Mapping, doubly carpeted region, function, approximation to the 322
Mapping, problem, normalisation of the 281
Mapping, unit circle on itself 280
Mapping, wing profile on a nearly circular curve 311
Mathieu functions 430
Mathieu’s equation 430
Mathieu’s equation, modified 430
Mean value theorem and Poisson’s formula 272 368
Mean value theorem and Poisson’s formula, circle 418
Mehler’s functions 382
Membrane, vibration of 176 401
Minimal surface, differential equation 169 501
Moments, equation of three 21
Momentum 180
Mound, effect on electrical potential 261
Moving medium, conduction of heat 218
Munk’s theory of thin aerofoils 259
Neumann’s formula 412
Newtonian potential 82
Non-linear equations 491 497
Normal vibrations 33
Normalisation of mapping problem 281
Oblate spheroid 435
Orthogonal polynomials 317 325
Orthogonal polynomials, relations xviii 213 362 388 392 453
Orthogonal polynomials, set of functions xviii
Parabolic coordinates 486
Paraboloidal coordinates 449
Parseval’s theorem 12
Partial difference equations 76 144
Pits and projections, effect on electric potential 439 522
Plateau’s problem 503
Point charge, electric 197
Poisson’s formula 368
Poisson’s formula, identity 217
Poisson’s formula, integral 239
Poisson’s formula, ratio 163
Polar coordinates 351
Pole, electric 197
Porous body, heating of a 123
Potential function on a spherical surface 366
Potential function with assigned values on a circle 236
Potentials 77
Potentials, retarded 197
Primary solutions 95
Primitive solutions 106
Prism, torsion of 172
Progressive waves 61
Prolate spheroid 433
Quadratic forms 33
Quadratic forms and partial difference equations 145 147
Quadratic forms, non-negative 37
Rayleigh’s reciprocal theorem 53
Rays 110
Rays and bicharacteristics 103
Reciprocal relations 20 203 379
Reciprocal relations, theorem of wireless telegraphy 201
Reduction to algebraic equations 47
Reflection of waves 331
Refraction of waves 331
Regions, properties of 277
Residual oscillations 43
Resisted motion 45 491
Retarded potentials 197
Riccati’s equation 491
Riemann’s method 126
Riemann’s method, problem 275
Riemann’s method, surfaces 269
Rigidity, modulus of 163
Ring, potential of 410 416 418
Ring, potential of, stream function 417
Rodrigues’s formula 369 361
Rotation theorem 285
Schwarz’s alternating process 247
Schwarz’s alternating process, inequality 150 151 317 281
Schwarz’s alternating process, lemma 294
Schwarz’s alternating process, method (Plateau’s problem) 504
Selection theorem 287
Simple solutions and their generalisation 329
Soap film, equilibrium of 169
Solid angle, extension 386
Solid angle, friction 499
Sommerfeld’s formula 410
Sommerfeld’s formula, solution of diffraction problem 479 485
Sonine’s polynomials, definition 451
Sonine’s polynomials, recurrence relations 452
Sonine’s polynomials, roots 452
Spherical harmonics 371
Spherical lens 468
Spheroidal co-ordinates 440
Spheroidal co-ordinates, harmonics 441
Spheroidal co-ordinates, wave-functions 442
standing waves 330
Stieltjes, method of 389
Stokes’s theorem 115
Stone’s theorem 365
Strain, components of 163
Stream functions 79
Stress, components of 163
Successive approximations 497
Surface harnjonics 371
Systems of equations 73 92
Telegraphic equation 75
Temperatures, fluctuations 214
Toroidal co-ordinates 461
Toroidal co-ordinates, Laplace’s equation in 461
Torsion of a prism 172
Torsional oscillations of a shaft 235
Transcendental equation, roots of a 223
Transformation, conformal 266
Transformation, Eulerian equations 157
Transformation, Laplace’s equation 158
Transformation, wave-equation 409
Uniformly bounded sequences 287
Unit circle, mapped on itself 280
Variational Principle 152
Variational principle, problems, regular 157
Velocity potential 79
Velocity, group 231
Vertical wall, effect on electric potential 263
Vibrations of a disc 400
Vibrations, damped 49
Vibrations, forced 41
Vibrations, loaded string 229
Vibrations, membrane 330 401
Vibrations, of a building 66
Vibrations, string 65
Vibrations, torsional 67
Vibrations, transmission of 63
Viscosity, effect on sound waves 226
Viscous flow 171
Viscous flow, fluid, two-dimensional motion 345
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