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Stakgold I. — Boundary Value Problems of Mathematical Physics
Stakgold I. — Boundary Value Problems of Mathematical Physics



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Íàçâàíèå: Boundary Value Problems of Mathematical Physics

Àâòîð: Stakgold I.

Àííîòàöèÿ:

The present book is an outgrowth of a series of courses which I taught, first at Harvard and later at Northwestern, to classes consisting primarily of graduate students in engineering and in the physical sciences. Addressing myself to a similar audience, I have attempted here to present a modern, comprehensive treatment of boundary value problems. By definition, a boundary value problem consists of an ordinary or partial differential equation with associated boundary or initial conditions. When E. P. Wigner, a Nobel Laureate in Physics, spoke of "the unreasonable effectiveness of mathematics in the physical sciences," he must have had boundary value problemsinmind, for nearly every branch of the physical sciences has been enlightened by the mathematical theory of boundary value problems.


ßçûê: en

Ðóáðèêà: Ìàòåìàòèêà/

Ñòàòóñ ïðåäìåòíîãî óêàçàòåëÿ: Ãîòîâ óêàçàòåëü ñ íîìåðàìè ñòðàíèö

ed2k: ed2k stats

Ãîä èçäàíèÿ: 2000

Êîëè÷åñòâî ñòðàíèö: 408

Äîáàâëåíà â êàòàëîã: 30.06.2010

Îïåðàöèè: Ïîëîæèòü íà ïîëêó | Ñêîïèðîâàòü ññûëêó äëÿ ôîðóìà | Ñêîïèðîâàòü ID
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Ïðåäìåòíûé óêàçàòåëü
Addition theorem for cylindrical waves      268
Addition theorem for Legendre functions      398
Addition theorem for spherical waves      290
Adjoint      9 198
Admissible functions      332
Approximation in subspace      335—36
Aronszajn, N.      382
Asymptotic expansions for heat equation      206 222 236
Asymptotic expansions of eigenvalues of Laplacian      231—34
Asymptotic expansions of integrals      399—402
Asymptotic expansions,      239—40
Base operators      382
Bazley, N.W.      382
Bessel equation      242 268—70 295
Biharmonic equation      40 105 365
Boundary conditions, essential      353
Boundary conditions, natural      352—55
Boundary value problem      88
Boundary value problem, well-posed      89
Capacity      171—74 350—52
Cauchy data      74
Cauchy problem      73
Causal function      (see “Right-sided function”)
Causal fundamental solution      (see “Fundamental solution”)
Characteristic      74
Characteristic of wave equation      46
Characteristic, surface      74
Classification of partial differential equations      73—87
Comparison theorem      377
Composite medium      183 234—293
Conductor      171—83
Consistency condition      171
continuous dependence on data      89 91
Continuous dependence on data,      95 102—103 226
Convolution      18—20 49
Cylindrical wave      267—68
Damped wave equation      65—69 257—59
Damped wave equation,      264
Delta function      5 20 27 34
Descent, method of      255
Diaz, J.      344
Difference kernel      311
Diffraction      (see “Scattering”)
Diffusion      230 240—41 329
Dipole      6 111 201
Dipole layer      12 113
Dirac      5
Dirac of slow growth      31 37
Dirac, direct product of      17
Dirac, partial differential equations for      39
Dirac, product of functions and      7
Dirac, regular      5
Dirac, singular      5
Dirac, translation of      5
Dirac, values of      9
Dirichlet problem      90—103 122—25 135 142 172 296 348
Dissipative wave equation      (see “Damped wave equation”)
Distributions, action of      4
Distributions, convergence of      10—16
Distributions, convolution of      18
Distributions, definition of      4 31 37
Distributions, differentiation of      7
Distributions, dipole      6 8
Divergence theorem      89
D’Alembert’s formula      85
Eigenfunction expansion for heat-conduction equation      213—18
Eigenfunction expansion for Laplace’s equation      153—64
Eigenfunction expansion for wave equation      248 252
Eigenvalues of negative Laplacian      136—42
Eigenvalues, asymptotic distribution of      231 239—40
Eigenvalues, comparison theorem for      377
Eigenvalues, extremal principles for      369—92
Eigenvalues, lower bounds to      381—92
Elliptic equations      80
Energy flux      262 303
Energy inner product      342
Energy integral for heat conduction      225
Energy integral for wave equation      244 261—62
Energy norm      343
Entire functions      315
Extremal principles for capacity      350—52
Extremal principles for eigenvalues in Hilbert space      372
Extremal principles for eigenvalues in n space      369—72
Extremal principles for functionals      337 40 352—55 358-361
Extremal principles for torsional rigidity      346—48
Extremal principles,      392
Extremal principles, complementary      344—52
Fluid flow      185—90
Fokker — Planck equation      230
Fourier integral theorem      23
Fourier transforms and Wiener — Hopf equations      311—31
Fourier transforms of distributions      30—39
Fourier transforms of functions      23
Fourier transforms of test function      31
Fox, D. W.      382
Free boundary      237
Friedrichs, K. O.      344
Functionals      3 332
Functionals, continuity of      3
Fundamental solution      48
Fundamental solution of damped wave equation      65—69
Fundamental solution of heat-conduction equation      58—60
Fundamental solution of Helmholtz’s equation      53—58 266-267
Fundamental solution of Laplace’s equation      49—53
Fundamental solution of wave equation      61—65 249 253—56
Fundamental solution, on Riemann surface      270—72
Fundamental solution, pole of      48
Generalized functions      (see “Distributions”)
Generalized solution      42 (see also “Fundamental solution”)
Green’s function; see also Fundamental for heat conduction      198 204 209—18
Green’s function; see also Fundamental for Helmholtz’s equation      265—90
Green’s function; see also Fundamental for Laplace’s equation      130—71
Green’s function; see also Fundamental for wave equation      246—52
Green’s Theorem      40 89
Hadamard, J.      255
Hankel functions      (see “Bessel equation”)
Hankel transform      275—80
Harmonic functions, maximum principle for      101
Harmonic functions, mean value theorem for      99
Heat-conduction equation      81 194—243
Heat-conduction equation,      280—81
Heat-conduction equation, backward      229
Heat-conduction equation, causal fundamental solution      58—60
Heat-conduction equation, causal Green’s function for      197—222
Heat-conduction equation, energy integral for      223
Heat-conduction equation, Green’s theorem for      41 196
Heat-conduction equation, ill-posed problems for      229
Heat-conduction equation, in composite medium      234—37
Heat-conduction equation, maximum principle for      224—25
Heat-conduction equation, Stefan problem for      237—38
Heat-conduction equation, uniqueness for      225—26
Helmholtz’s equation, fundamental solution of      53—58
Helmholtz’s equation, Green’s function for      265—85
Helmholtz’s equation, half-plane problem for      281—90 321—27
Helmholtz’s equation, in exterior domain      294—311
Helmholtz’s equation, in wedge      272—73
Helmholtz’s equation, mean value property      105
Hilbert — Schmidt kernels      135 375
Huyghens’ principle      256
Hyperbolic equations      80—85
Images      149 166—69 204 209 211 251
Images,      252
Incident field      299
Initial data      72
Initial value problem      73
Integral equations for capacity      172—74 351
Integral equations for scattering problems      301
Integral equations of potential theory      122—30 146 171
Integral equations of Wiener — Hopf type      311—31
Integral equations with difference kernel      311—31
Integral equations,      193
Integrodifferential equation      366—67 389-390
Interior operator      74
Intermediate problems      382
Jones, D. S.      368
Kantorovich — Lebedev transform      273
Kirchhoif s formula      263
Klein — Gordon equation      70
Laplace’s equation      40 49—53 88—192
Laplace’s equation, eigenvalue problem for      136—42 231
Laplace’s equation, exterior Dirichlet problem for      123 129 142
Laplace’s equation, fundamental solution of      49—53
Laplace’s equation, Green’s function for      130—71
Laplace’s equation, Green’s theorem for      40
Laplace’s equation, interior Dirichlet problem for      122 128
Least squares      361—63
Left-side function      28
Legendre functions      393—98
Levine, H.      283 311 340 357
Limiting absorption      259—61
Locally integrable      2
Macdonald function      266 279 321
Mapping function      164
Maximin theorem      371
Mehler’s integral representation      284
Mellin transform      167 169
Minimax theorem      371
Monochromatic excitation      259—61
Multiindex      2
Neumann problem      126 128 171 185
Neumann problem and fluid flow      185—91
Neumann problem for      126 128
Neumann problem for, double      12 113
Neumann problem for, in two dimensions      128
Neumann problem for, Laplace transform      38 206 218 236
Neumann problem for, simple      7 39 112
Neumann problem for, surface      7 12 110—121
Neumann problem, consistency condition for      171
Neumann problem, extremal principles for      363—64
Null sequences      3 30 36
One-sided functions      28
Operators, base      382
Operators, bounded above      372
Operators, bounded below      372
Operators, completely continuous      133—35 375
Operators, Hilbert — Schmidt      135 375
Operators, indefinite      355—57
Operators, integrodifferential      366 389—90
Operators, interior      74
Operators, nonnegative      336
Operators, nonsymmetric      355—57
Operators, positive      337 358
Operators, self-adjoint      9 376
Operators, semibounded      372
Operators, strongly positive      343 363
Operators, symmetric      337
Parabolic equations      80
Parseval formula      24
Partial differential equations      88—311
Partial differential equations for distributions      39—48
Partial differential equations of first order      76—79
Partial differential equations of second order      79—87
Partial differential equations, classification of      73—87
Partial differential equations, elliptic      80
Partial differential equations, fundamental solutions of      48—72
Partial differential equations, hyperbolic      80
Partial differential equations, parabolic      80
Plane wave      285—86 302
Poisson equation      103 345
Poisson kernel      95
Poisson sum formula      212
Pole of fundamental solution      48
Potential theory      88—193 267
Projection operator      335—36
Propagation of discontinuities      46 77
Radiation condition      297
Rayleigh quotient      369
Reciprocity principle      303 342 368
Rellich, F.      297
Retarded potential      254
Riemann mapping theorem      164
Riemann surface      270
Right-side function      28
Ritz — Rayleigh, equations      341 363 366—68
Ritz — Rayleigh, procedure      332 334 340—43 362 377-378
Scattered amplitude      304
Scattered field      300
Scattering      299—311 328
Scattering cross section      303
Scattering cross section, stationary principle for      309
Schwarz constants      380
Schwarz inequality      344
Schwinger — Levine principle      311 340 357
Self-adjoint      9 376
Semigroups of operators      227
Slow growth, distribution of      31 37
Slow growth, functions of      29
Sokolnikoff, I.S.      346
Sommerfeld, A.      277 297
Spherical harmonics      109 126 127 144
Spherical harmonics,      290 295 393—98
Spherical wave      267 290
Stationary principles for indefinite operators      356
Stationary principles for nonsymmetric operators      357 367—368
Stationary principles for scattering cross section      309—11
Steady heat conduction      88 183
Stefan Problem      237
Strict solution      42
Support      2
Symbolic functions      (see Distributions)
Tangential derivative      74
Telegraphy equation      65 258
Test functions      3
Test functions of rapid decay      30 36
Test functions, convergence of      3 30
Test functions, null sequences of      3 30 36
Theta function      212
Torsional rigidity      346—48
Transversal      41
Uniqueness theorem for heat conduction      225—26
Uniqueness theorem for Helmholtz’s equation      296—99
Uniqueness theorem for Laplace’s equation      102
Uniqueness theorem for wave equation      243
Variation-iteiation      380—81
Variational methods      (see Extremal principles and Stationary principles)
Wave equation      81 194 196—97 243—65
Wave equation, damped      65—69 257—59 264
Wave equation, d’Alembert’s solution of      85
Wave equation, fundamental solution of      61—65
Wave equation, generalized solution of      44
Wave equation, Green’s function of      246—56
Wave equation, Green’s theorem for      41 47 197
Wave equation, in composite medium      293
Wave equation, method of descent for      255—56
Wave guide      291
Weber transform      242
Weinstein, A.      382
Well-posed problem      89
Wiener — Hopf equation      311—31
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