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Wyld H.W. — Mathematical Methods for Physics

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Название: Mathematical Methods for Physics

Автор: Wyld H.W.

Аннотация:

Mathematical Methods for Physics is a classic text for advanced undergraduate and beginning graduate students. It concentrates on fundamental mathematical methods used in physics and engineering. The topics are discussed in depth at an elementary level.

Язык:

Рубрика: Физика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1999

Количество страниц: 656

Добавлена в каталог: 06.07.2008

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Предметный указатель

Aerodynamics      7 9
Analytic continuation      435—440
Analytic continuation, of Fourier integrals      581—587 596ff.
Analytic continuation, of gamma function      440—442
Analytic continuation, of hypergeometric function      528—531
Analytic functiony definition      386
Asymptotic expansions      513—516
Asymptotic expansions, for       83
Asymptotic expansions, for       91
Asymptotic expansions, for Bankel functions      133 215 552—560
Asymptotic expansions, for Bessel functions of imaginary argument      135
Asymptotic expansions, for Bessel functions.      133 215 552—560
Asymptotic expansions, for exponential integral      514—515
Asymptotic expansions, for gamma function      516—519
Asymptotic expansions, for hypergeometric function      531
Asymptotic expansions, for Neumann functions      133 215 552—560
Asymptotic expansions, for spherical Bessel, Neumann, and Hankel functions      183—184 216
Ausstrahlungsbedingimg      see “Radiation condition”
Bernoulli numbers      443
Bessel functions      34 36 123—126 214 541—552
Bessel functions, asymptotic expansions      133 135 215 556—560
Bessel functions, generating functions for      152 547
Bessel functions, identities for      152
Bessel functions, integral representation for      550
Bessel functions, of imaginary argument      134—135
Bessel functions, series for      125 552
Bessel functions, small argument expansions      132 214
Bessel functions, Sommerfeld’s integral representation for      546
Bessel functions, spherical Bessel functions      178—184 215—216
Bessel’s equation      33—34 36 123 214 542
beta function      509—510
Boundary conditions for Bessel functions      139
Boundary conditions for dielectrics      227—229
Boundary conditions for diffusion equation      155 210 319 320 322
Boundary conditions for drumhead      163
Boundary conditions for Helmholtz equation      156—157 210
Boundary conditions for inhomogeneous ordinary differential equations      261—262 270
Boundary conditions for Laplace’s equation      110—113 211—212
Boundary conditions for Legendre polynomials      77
Boundary conditions for magnetic media      246
Boundary conditions for Poisson’s equation      273 274
Boundary conditions for spherical Bessel functions      184
Boundary conditions for spherical harmonics      96
Boundary conditions for Sturm Llouville equation      49—50
Boundary conditions for wave equation      159 210 300 303 “Radiation
Branch point      405 409 410 412 414 416
Cauchy — Riemann equations      392
Cauchy’s integral formula      426—428
Cauchy’s Theorem      421—423 423—425
Cerenkov effect      315
Circle chain method      436—439
Completeness relations for Fourier integrals      60 212
Completeness relations for Fourier — Bessel transforms      213
Completeness relations for Legendre polynomials      85
Completeness relations for spherical Bessel functions      187 214
Completeness relations for spherical harmonics      99
Completeness relations for Sturm Liouville problem      57
Contour integrals      417—421 448—465
Convergence, absolute      395
Convergence, Cauchy criterion      395
Convergence, of power series      398—400
Convergence, of series      395ff.
Convergence, ratio test for      396
Convergence, uniform      428
Cut in complex plane      406 407 409 410 412 414 416 486—487 530—531 534—535 538—539 601 606
Differential equations, ordinary      38—57
Differential equations, ordinary, indicial equation      45 76 123
Differential equations, ordinary, ordinary points      39
Differential equations, ordinary, second solution      42 47 88ff. 126ff.
Differential equations, ordinary, series solution      43—49 75—80 123—126
Differential equations, ordinary, singular points      39 75 123 519—522
Differential equations, ordinary, with constant coefficients      588—590
Differential equations, ordinary, with three regular singular points      519ff.
Differential equations, ordinary, Wronskian      40—42 47 152 288
Differential equations, partial      see “Diffusion equation” “Helmholtz “Klein “Laplace’s “Poisson’s “Wave
Diffusion equation      2—4 29 155 166—168 209 319—326
Dipole moment      105—106 223
Dirac’s formula      479
Discontinuity problem      479—481
dispersion relation      481—492
Dispersion relation, subtracted      490—491
Eigenfunctions, eigenvalues, for angular part of Laplaclan      96
Eigenfunctions, eigenvalues, for Helmholtz equation      156—158 210
Eigenfunctions, eigenvalues, for integral equations      341 343 346 354 361—363 368—374
Eigenfunctions, eigenvalues, for Legendre’s equation      83 93
Eigenfunctions, eigenvalues, for particle in cylindrical box      168
Eigenfunctions, eigenvalues, for spherical Bessel functions      184—187
Eigenfunctions, eigenvalues, for Sturm Liouville problem      49—57
Eigenfunctions, eigenvalues, for vibrating string      161—162
Eigenfunctions, eigenvalues, for.vibrating drumhead      162—166
Eigenfunctions, eigenvalues, numerical solution for      64—66 354
electric field      15ff.
Electric field, macroscopic      219ff.
Electrodynamics      14—21 298 313—318
Electromagnetic field, due to point source      311—318
Essential singularity      434
Euler’s constant      129 132 512
Expansion theorems, for associated Legendre polynomials      93
Expansion theorems, for Bessel functions      140—141 213
Expansion theorems, for Legendre polynomials      84
Expansion theorems, for plane wave in cylindrical waves      152 547
Expansion theorems, for plane waves in spherical waves      187—189 217 338
Expansion theorems, for spherical Bessel functions      186 213
Expansion theorems, for spherical harmonics      99
Expansion theorems, for spherical waves in spherical waves about displaced center      189—192 217 338
Expansion theorems, for Sturm — Liouville problem      55—57
Expansion theorems, Fourier Bessel transforms      150 213
Expansion theorems, Fourier integral theorem      60 212
Expansion theorems, Fourier series      59 212
Fourier Bessel transforms      149—151 186 213 214
Fourier integral transforms      59—60 212
Fourier series      58—59 212
Fredholm’s solution of integral equation      356—363
Fredholm’s solution of integral equation, conditions for validity of      363—368
Gamma function      128—130 440—442 508—512 516—519
Gauge transformations      17 19—20
Generating functions for Bessel functions      152 547
Generating functions for Legendre polynomials      86 217
Green’s function, advanced      309
Green’s function, expansion in eigenfunctions      269—272 289—291
Green’s function, for bowed string      265—268
Green’s function, for diffusion equation      319—326
Green’s function, for Helmholtz equation      283—291 566—570
Green’s function, for ingoing waves      293
Green’s function, for Klein — Gordon equation      573—530
Green’s function, for ordinary differential equations      260—264
Green’s function, for outgoing waves      293 337
Green’s function, for Poisson’s equation      272—283
Green’s function, for scattering problem      337
Green’s function, for wave, equation      291—310 570—572
Green’s function, retarded      297 301ff. 304—306 311
Green’s Theorem      259 272 301 303 320 322
Hankel functions      133
Hankel functions, asymptotic expansions      133 215 556—560
Hankel functions, Sommerfeld’s integral representations for      544ff.
Hankel functions, spherical Bankel functions      182 183 215 216
Heat conduction equation      see “Diffusion equation”
Helmholtz equation      29 30 32 34 154 156—158 163 169 171 177
Helmholtz equation, as eigenvalue problem      156—158
Helmholtz equation, eigenfunctions for      157
Hilbert transforms      483
Hilbert — Schmidt theory      368—374
Hydrodynamics      7ff. 11ff. 115—117
Hypergeometric functions      402 519—532
Hypergeometric functions, confluent      532
Hypergeometric functions, Legendre functions expressed as      537 541
Hysteresis      252
Identity theorem for analytic functions      436—437
Images, for Qrefen’s function      276—279
Images, magnetostatics      253ff.

Images, method of electrostatics      230ff.
Initial conditions for diffusion equation      155 210 319 320 322 323 326
Initial conditions for Klein — Gordon equation      574
Initial conditions for vibrating membrane      165
Initial conditions for vibrating string      162
Initial conditions for wave equation      159 211 300 301 303 304 309—310 571—572
Integral equations, convolution equations      347—348 590 591—592
Integral equations, eigenvalue problem      341 343 345 354 361—363 368—374
Integral equations, first kind      341
Integral equations, for scattering problem      337 340 350
Integral equations, Fredholm formulas      356—363
Integral equations, Hilbert — Schmidt theory      368—374
Integral equations, numerical solution      351—356
Integral equations, second kind      341 342 344 347 349 353 356 361
Integral equations, separable kernels      342—347
Integral equations, singular, with Cauchy kernels      499—505
Integral equations, Volterra      341
Integral transforms, Fourier      60 212 565ff.
Integral transforms, Fourier Beaael      149—151 186 213 214
Integral transforms, Fourier, ohe-sided      581—587
Integral transforms, Hilbert      483
Integral transforms, Laplace      587—590 593—596
Integral transforms, Mellin      590—592
Integrals, angular      462—464
Integrals, evaluation      448—465
Integrals, on range $(0, \infty)$       459—462
Integrals, rational functions      451—453
Integrals, transformation of contour      464—465
Integrals, with exponential factors      453—459
Irrotational flow      11 115—117
Iteration of integral equation      see “Liouville — Neumann series”
Jordan’s lemma      453—455
Klein — Gordon equation      573
Laplace’s equation      108—117 211
Laplace’s equation, between two planes      147—149 151
Laplace’s equation, cylinder in external field      145—147
Laplace’s equation, exterior problem for cylinder      144
Laplace’s equation, exterior problem for sphere      112
Laplace’s equation, flow around sphere      115—117
Laplace’s equation, for dielectric sphere      233—235
Laplace’s equation, interior problem for cylinder      136—139 141—143
Laplace’s equation, Interior problem for sphere      110
Laplace’s equation, sphere in external field      113—115
Laurent expansion      433
Legendre functions       533—537
Legendre functions       37 88—92 497/538—541
Legendre functions , identity for      562
Legendre polynomials       37 78—87
Legendre polynomials , formulas      80 81
Legendre polynomials , generating function for      86
Legendre polynomials , identities for      86 87 92 119
Legendre polynomials , normalization      81 84
Legendre polynomials, associated,       92—95
Legendre polynomials, formulas      93 95 217
Legendre polynomials, normalization      95
Legendre’s equation      37 75 77 88 533
Liouville — Neumann series      348—351
Liouville — Neumann series, convergence of      365
Liouyille’s theorem      445
Magnetic field      15ff.
Magnetic field, macroscopic      241ff.
magnetic moment      240
Magnetic pole density      250
magnetization      244 247ff. 250ff.
Magnetization, current      241—245 248—249
Maximum modulus theorem      445
Maxwell’s equations      15
Mean value theorem      444
Morera’ s theorem      421—423
Multipole expansion for scalar potential      103—108
Multipole expansion for vector potential      236—240
Natural boundary in complex plane      439
Neumann functions      34 36 126—131 214 546
Neumann functions, series for      131
Neumann functions, spherical Neumann functions      178—184 215
Normal modes, for acoustic resonant cavity      168—170
Normal modes, for acoustic wave guide      170—173
Normal modes, for vibrating drumhead      162—166
Normal modes, for vibrating string      161—162
Numerical solution, integral equations      351—356
Numerical solution, ordinary differential equations      61—66
Omnes’ equation      500ff.
Partial fraction expansions      466—470
Plasma dispersion function      497—499
Plemelj formulas      476—479
Poisson’s solution of Dirichlet problem for circle      446—447
Polarization      224 226
Polarization, charge      220—227 229 232 235
Pole in complex plane      39 390 434
Polsson’s equation, scalar      16 103 272—283
Polsson’s equation, vector      17
Potential, scalar      15 19 103 219ff.
Potential, vector      16 18 236ff.
Power series      43ff. 78 123 397—402
Product expansions for $\Gamma(z)$       512
Product expansions for $\sin\pi z$       470
Quadrupole moment      106) 223
Radiation condition      195 294 310 336—337 568—570 605
Rational functions      389
Regular function      see “Analytic function”
Residue theorem      448—451
Riemann sheets      407 408 409 412 415 417 492
Rlemann P symbol      522ff.
Rodrlgue’s formula      80
Runge — Kutta numerical integration      62f f.
Scattering, in quantum mechanics      336—340 550—351
Scattering, of waves by sphere      197—203
Schrodinger’s equation      4 160 168
Schwartz reflection principle      487—489
Separation of variables      29—38 207—269
Separation of variables, Helmholtz equation, cartesian coordinates      30
Separation of variables, Helmholtz equation, cylindrical coordinates      32
Separation of variables, Helmholtz equation, spherical coordinates      34
Separation of variables, Laplace’s equation      34 36
Separation of variables, spherical harmonica      75
Separation of variables, time dependence      29 156 160
Small argument expansions for Bessel functions      132 214
Small argument expansions for Bessel functions of imaginary argument      135
Small argument expansions for Neumann functions      132 214
Small argument expansions for spherical Bessel and Neumann functions      183 216
Sommerfeld — Watson transformation      471
Spectral representation      484
Spherical harmonics      96—103 104ff. 109ff. 178 189 192 194ff. 198ff. 216—217
Spherical harmonics, addition theorem      99—103 217
Spherical harmonics, completeness      99
Spherical harmonics, formulas      96—98 216—217
Spherical harmonics, normalization      98—99
Steepest descents, method of      516—519 552—560
Stirling’s formula      518 519
Sturm — Liouville problem      49—57
Sturm — Liouville problem, completeness of solutions      54—57
Sturm — Liouville problem, for associated Legendre polynomials      93—95
Sturm — Liouville problem, for Bessel functions      139—141
Sturm — Liouville problem, for legendre polynomials      83—84
Sturm — Liouville problem, for spherical Bessel functions      184—187
Sturm — Liouville problem, orthogonality of solutions      54
Sturm — Liouville problem, relation to Green’s function      269—272
Taylor expansion      430
Wave equation      159 209 291—310
Wave equation, acoustic      9 168—170 170—173
Wave equation, for electromagnetic fields      18
Wave equation, for membranes      6 162—166
Wave equation, for scalar potential      20 298
Wave equation, for strings      5 161—162
Wave equation, for vector potential      20 298
Wave guide, acoustic      170—173
Waves, acoustic      9 168—170 170—173
Waves, diffraction by knife edge      604—617
Waves, due to point source      311—318
Waves, emission of spherical wave      192—197

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