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Wyld H.W. Mathematical Methods for Physics
Wyld H.W.  Mathematical Methods for Physics









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: Mathematical Methods for Physics

: Wyld H.W.

:

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.


: en

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ed2k: ed2k stats

: 1999

: 656

: 06.07.2008

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Aerodynamics      7 9
Analytic continuation      435440
Analytic continuation, of Fourier integrals      581587 596ff.
Analytic continuation, of gamma function      440442
Analytic continuation, of hypergeometric function      528531
Analytic functiony definition      386
Asymptotic expansions      513516
Asymptotic expansions, for $P_L(x)$      83
Asymptotic expansions, for $Q_L(x)$      91
Asymptotic expansions, for Bankel functions      133 215 552560
Asymptotic expansions, for Bessel functions of imaginary argument      135
Asymptotic expansions, for Bessel functions.      133 215 552560
Asymptotic expansions, for exponential integral      514515
Asymptotic expansions, for gamma function      516519
Asymptotic expansions, for hypergeometric function      531
Asymptotic expansions, for Neumann functions      133 215 552560
Asymptotic expansions, for spherical Bessel, Neumann, and Hankel functions      183184 216
Ausstrahlungsbedingimg      see Radiation condition
Bernoulli numbers      443
Bessel functions      34 36 123126 214 541552
Bessel functions, asymptotic expansions      133 135 215 556560
Bessel functions, generating functions for      152 547
Bessel functions, identities for      152
Bessel functions, integral representation for      550
Bessel functions, of imaginary argument      134135
Bessel functions, series for      125 552
Bessel functions, small argument expansions      132 214
Bessel functions, Sommerfelds integral representation for      546
Bessel functions, spherical Bessel functions      178184 215216
Bessels equation      3334 36 123 214 542
beta function      509510
Boundary conditions for Bessel functions      139
Boundary conditions for dielectrics      227229
Boundary conditions for diffusion equation      155 210 319 320 322
Boundary conditions for drumhead      163
Boundary conditions for Helmholtz equation      156157 210
Boundary conditions for inhomogeneous ordinary differential equations      261262 270
Boundary conditions for Laplaces equation      110113 211212
Boundary conditions for Legendre polynomials      77
Boundary conditions for magnetic media      246
Boundary conditions for Poissons equation      273 274
Boundary conditions for spherical Bessel functions      184
Boundary conditions for spherical harmonics      96
Boundary conditions for Sturm Llouville equation      4950
Boundary conditions for wave equation      159 210 300 303 Radiation
Branch point      405 409 410 412 414 416
Cauchy Riemann equations      392
Cauchys integral formula      426428
Cauchys Theorem      421423 423425
Cerenkov effect      315
Circle chain method      436439
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      417421 448465
Convergence, absolute      395
Convergence, Cauchy criterion      395
Convergence, of power series      398400
Convergence, of series      395ff.
Convergence, ratio test for      396
Convergence, uniform      428
Cut in complex plane      406 407 409 410 412 414 416 486487 530531 534535 538539 601 606
Differential equations, ordinary      3857
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      4349 7580 123126
Differential equations, ordinary, singular points      39 75 123 519522
Differential equations, ordinary, with constant coefficients      588590
Differential equations, ordinary, with three regular singular points      519ff.
Differential equations, ordinary, Wronskian      4042 47 152 288
Differential equations, partial      see Diffusion equation Helmholtz Klein Laplaces Poissons Wave
Diffusion equation      24 29 155 166168 209 319326
Dipole moment      105106 223
Diracs formula      479
Discontinuity problem      479481
dispersion relation      481492
Dispersion relation, subtracted      490491
Eigenfunctions, eigenvalues, for angular part of Laplaclan      96
Eigenfunctions, eigenvalues, for Helmholtz equation      156158 210
Eigenfunctions, eigenvalues, for integral equations      341 343 346 354 361363 368374
Eigenfunctions, eigenvalues, for Legendres equation      83 93
Eigenfunctions, eigenvalues, for particle in cylindrical box      168
Eigenfunctions, eigenvalues, for spherical Bessel functions      184187
Eigenfunctions, eigenvalues, for Sturm Liouville problem      4957
Eigenfunctions, eigenvalues, for vibrating string      161162
Eigenfunctions, eigenvalues, for.vibrating drumhead      162166
Eigenfunctions, eigenvalues, numerical solution for      6466 354
electric field      15ff.
Electric field, macroscopic      219ff.
Electrodynamics      1421 298 313318
Electromagnetic field, due to point source      311318
Essential singularity      434
Eulers constant      129 132 512
Expansion theorems, for associated Legendre polynomials      93
Expansion theorems, for Bessel functions      140141 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      187189 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      189192 217 338
Expansion theorems, for Sturm Liouville problem      5557
Expansion theorems, Fourier Bessel transforms      150 213
Expansion theorems, Fourier integral theorem      60 212
Expansion theorems, Fourier series      59 212
Fourier Bessel transforms      149151 186 213 214
Fourier integral transforms      5960 212
Fourier series      5859 212
Fredholms solution of integral equation      356363
Fredholms solution of integral equation, conditions for validity of      363368
Gamma function      128130 440442 508512 516519
Gauge transformations      17 1920
Generating functions for Bessel functions      152 547
Generating functions for Legendre polynomials      86 217
Greens function, advanced      309
Greens function, expansion in eigenfunctions      269272 289291
Greens function, for bowed string      265268
Greens function, for diffusion equation      319326
Greens function, for Helmholtz equation      283291 566570
Greens function, for ingoing waves      293
Greens function, for Klein Gordon equation      573530
Greens function, for ordinary differential equations      260264
Greens function, for outgoing waves      293 337
Greens function, for Poissons equation      272283
Greens function, for scattering problem      337
Greens function, for wave, equation      291310 570572
Greens function, retarded      297 301ff. 304306 311
Greens Theorem      259 272 301 303 320 322
Hankel functions      133
Hankel functions, asymptotic expansions      133 215 556560
Hankel functions, Sommerfelds 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 156158 163 169 171 177
Helmholtz equation, as eigenvalue problem      156158
Helmholtz equation, eigenfunctions for      157
Hilbert transforms      483
Hilbert Schmidt theory      368374
Hydrodynamics      7ff. 11ff. 115117
Hypergeometric functions      402 519532
Hypergeometric functions, confluent      532
Hypergeometric functions, Legendre functions expressed as      537 541
Hysteresis      252
Identity theorem for analytic functions      436437
Images, for Qrefens function      276279
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 309310 571572
Integral equations, convolution equations      347348 590 591592
Integral equations, eigenvalue problem      341 343 345 354 361363 368374
Integral equations, first kind      341
Integral equations, for scattering problem      337 340 350
Integral equations, Fredholm formulas      356363
Integral equations, Hilbert Schmidt theory      368374
Integral equations, numerical solution      351356
Integral equations, second kind      341 342 344 347 349 353 356 361
Integral equations, separable kernels      342347
Integral equations, singular, with Cauchy kernels      499505
Integral equations, Volterra      341
Integral transforms, Fourier      60 212 565ff.
Integral transforms, Fourier Beaael      149151 186 213 214
Integral transforms, Fourier, ohe-sided      581587
Integral transforms, Hilbert      483
Integral transforms, Laplace      587590 593596
Integral transforms, Mellin      590592
Integrals, angular      462464
Integrals, evaluation      448465
Integrals, on range $(0, \infty)$      459462
Integrals, rational functions      451453
Integrals, transformation of contour      464465
Integrals, with exponential factors      453459
Irrotational flow      11 115117
Iteration of integral equation      see Liouville Neumann series
Jordans lemma      453455
Klein Gordon equation      573
Laplaces equation      108117 211
Laplaces equation, between two planes      147149 151
Laplaces equation, cylinder in external field      145147
Laplaces equation, exterior problem for cylinder      144
Laplaces equation, exterior problem for sphere      112
Laplaces equation, flow around sphere      115117
Laplaces equation, for dielectric sphere      233235
Laplaces equation, interior problem for cylinder      136139 141143
Laplaces equation, Interior problem for sphere      110
Laplaces equation, sphere in external field      113115
Laurent expansion      433
Legendre functions $P_L(z)$      533537
Legendre functions $Q_L(z)$      37 8892 497/538541
Legendre functions $Q_L(z)$, identity for      562
Legendre polynomials $P_L(x)$      37 7887
Legendre polynomials $P_L(x)$, formulas      80 81
Legendre polynomials $P_L(x)$, generating function for      86
Legendre polynomials $P_L(x)$, identities for      86 87 92 119
Legendre polynomials $P_L(x)$, normalization      81 84
Legendre polynomials, associated, $P_L^m(x)$      9295
Legendre polynomials, formulas      93 95 217
Legendre polynomials, normalization      95
Legendres equation      37 75 77 88 533
Liouville Neumann series      348351
Liouville Neumann series, convergence of      365
Liouyilles theorem      445
Magnetic field      15ff.
Magnetic field, macroscopic      241ff.
magnetic moment      240
Magnetic pole density      250
magnetization      244 247ff. 250ff.
Magnetization, current      241245 248249
Maximum modulus theorem      445
Maxwells equations      15
Mean value theorem      444
Morera s theorem      421423
Multipole expansion for scalar potential      103108
Multipole expansion for vector potential      236240
Natural boundary in complex plane      439
Neumann functions      34 36 126131 214 546
Neumann functions, series for      131
Neumann functions, spherical Neumann functions      178184 215
Normal modes, for acoustic resonant cavity      168170
Normal modes, for acoustic wave guide      170173
Normal modes, for vibrating drumhead      162166
Normal modes, for vibrating string      161162
Numerical solution, integral equations      351356
Numerical solution, ordinary differential equations      6166
Omnes equation      500ff.
Partial fraction expansions      466470
Plasma dispersion function      497499
Plemelj formulas      476479
Poissons solution of Dirichlet problem for circle      446447
Polarization      224 226
Polarization, charge      220227 229 232 235
Pole in complex plane      39 390 434
Polssons equation, scalar      16 103 272283
Polssons equation, vector      17
Potential, scalar      15 19 103 219ff.
Potential, vector      16 18 236ff.
Power series      43ff. 78 123 397402
Product expansions for $\Gamma(z)$      512
Product expansions for $\sin\pi z$      470
Quadrupole moment      106) 223
Radiation condition      195 294 310 336337 568570 605
Rational functions      389
Regular function      see Analytic function
Residue theorem      448451
Riemann sheets      407 408 409 412 415 417 492
Rlemann P symbol      522ff.
Rodrlgues formula      80
Runge Kutta numerical integration      62f f.
Scattering, in quantum mechanics      336340 550351
Scattering, of waves by sphere      197203
Schrodingers equation      4 160 168
Schwartz reflection principle      487489
Separation of variables      2938 207269
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, Laplaces 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      96103 104ff. 109ff. 178 189 192 194ff. 198ff. 216217
Spherical harmonics, addition theorem      99103 217
Spherical harmonics, completeness      99
Spherical harmonics, formulas      9698 216217
Spherical harmonics, normalization      9899
Steepest descents, method of      516519 552560
Stirlings formula      518 519
Sturm Liouville problem      4957
Sturm Liouville problem, completeness of solutions      5457
Sturm Liouville problem, for associated Legendre polynomials      9395
Sturm Liouville problem, for Bessel functions      139141
Sturm Liouville problem, for legendre polynomials      8384
Sturm Liouville problem, for spherical Bessel functions      184187
Sturm Liouville problem, orthogonality of solutions      54
Sturm Liouville problem, relation to Greens function      269272
Taylor expansion      430
Wave equation      159 209 291310
Wave equation, acoustic      9 168170 170173
Wave equation, for electromagnetic fields      18
Wave equation, for membranes      6 162166
Wave equation, for scalar potential      20 298
Wave equation, for strings      5 161162
Wave equation, for vector potential      20 298
Wave guide, acoustic      170173
Waves, acoustic      9 168170 170173
Waves, diffraction by knife edge      604617
Waves, due to point source      311318
Waves, emission of spherical wave      192197
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