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Bateman H. Partial Differential Equations of Mathematical Physics
Bateman H.  Partial Differential Equations of Mathematical Physics







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: Partial Differential Equations of Mathematical Physics

: Bateman H.

:

Harry Bateman (1882-1946) was an esteemed mathematician particularly known for his work on special functions and partial differential equations. This book, first published in 1932, has been reprinted many times and is a classic example of Bateman's work. Partial Differential Equations of Mathematical Physics was developed chiefly with the aim of obtaining exact analytical expressions for the solution of the boundary problems of mathematical physics.


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: 10.04.2010

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Abels theorem for power series      243
Absorption of sound      336
Adiabatic flow      171 509
Aerofoils, of small thickness      313
Aerofoils, of small thickness thin (Mnnks theory)      259
Aeroplane, fall of      492
Air waves in a pipe      227
Alternating process, Schwarzs      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
Brills theorem      161
Cable, theory of unloaded      74 221
Cesaros 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
Conways 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
Daniells 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 Reymonds 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
Eulers critical load      21
Eulers critical load, formula      21
Fatous 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
Fouriers constants      9
Fouriers constants, inversion formula      207
Fouriers series      15
Fouriers series, theorem      7
Fundamental Lemma of Calculus of Variations      154
Gausss mean value theorem      369
Generalisation of solutions      205
Greens functions      4 140
Greens functions for beam      18
Greens functions for circular disc      465
Greens functions for parallel planes      414
Greens functions for semi-infinite plane      473
Greens functions for spherical bowl      468
Greens functions for wedge      472
Group velocity      231
Half plane, diffraction by      476
Hamacks Theorem      246
Hankels cylindrical functions      387 403
Hankels cylindrical functions, inversion formula      411
Heavisides expansion      59
Helmholtzs formula      189
Hemispherical boss      437
Hermites polynomial      454
Hermitian forms      39
Hertzian vectors      179
Hobsons formulae for Legendre functions      357 376
Hobsons 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, Schwarzs      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
Jacobis polynomials      392
Jacobis polynomials, polynomial expansion      390 512
Jacobis polynomials, theorem      97
Jacobis polynomials, transformation      463
Jordan curves      278 287 324 327
Kinetic potential      165
Kirchhoffs formula      184
Koshliakovs theorem      223
Lagranges equations of motion      30
Lagranges equations of motion, expansion, use of      358
Lagranges equations of motion, method of variable multiplier      160
Laplaces equation      90
Laplaces equation, formula for a potential function symmetrical about an axis      405
Laplaces equation, functions (surface harmonics)      371 514
Laplaces 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
Legendres expansion      372
Lemniscates      269 270
Lens, stream function for a      471
Lerchs theorem      365
Lightning conductor      436
Lines of force      87 494
Lines of force of shearing stress      173
Liouvilles 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
Mathieus equation      430
Mathieus equation, modified      430
Mean value theorem and Poissons formula      272 368
Mean value theorem and Poissons formula, circle      418
Mehlers 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
Munks theory of thin aerofoils      259
Neumanns 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
Parsevals theorem      12
Partial difference equations      76 144
Pits and projections, effect on electric potential      439 522
Plateaus problem      503
Point charge, electric      197
Poissons formula      368
Poissons formula, identity      217
Poissons formula, integral      239
Poissons 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
Rayleighs 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
Riccatis equation      491
Riemanns method      126
Riemanns method, problem      275
Riemanns method, surfaces      269
Rigidity, modulus of      163
Ring, potential of      410 416 418
Ring, potential of, stream function      417
Rodriguess formula      369 361
Rotation theorem      285
Schwarzs alternating process      247
Schwarzs alternating process, inequality      150 151 317 281
Schwarzs alternating process, lemma      294
Schwarzs alternating process, method (Plateaus problem)      504
Selection theorem      287
Simple solutions and their generalisation      329
Soap film, equilibrium of      169
Solid angle, extension      386
Solid angle, friction      499
Sommerfelds formula      410
Sommerfelds formula, solution of diffraction problem      479 485
Sonines polynomials, definition      451
Sonines polynomials, recurrence relations      452
Sonines 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
Stokess theorem      115
Stones 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, Laplaces 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, Laplaces 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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