Taylor M.E. — Partial Differential Equations. Basic theory (vol. 1) :: Электронная библиотека попечительского совета мехмата МГУ

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Taylor M.E. — Partial Differential Equations. Basic theory (vol. 1)

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Название: Partial Differential Equations. Basic theory (vol. 1)

Автор: Taylor M.E.

Язык:

Рубрика: Математика/Анализ/Дифференциальные уравнения/

Статус предметного указателя: Готов указатель с номерами страниц

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Количество страниц: 563

Добавлена в каталог: 06.11.2004

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

Absolute boundary conditions      361
Action integral      56
Adjoint      128 139 159 162
Airy function      458
Alaoglu's theorem      485
Analytic continuation      193 199 221
Anticommutation relation      66
Argument principle      324 374
Ascoli's theorem      110 496
Baire category theorem      297 489
Bairrer, local      332
Bairrer, week      320
Bairrer, week local      332
Banach algebra      487
Banach space      469
Barrier      329
Bessel function      226
Bessel's equation      227
beta function      265
Betti number      356
Boundary condition      119
Boundary condition, Dirichlet      143
Boundary condition, Neumann      143
Boundary conditions, absolute      429
Boundary conditions, relative      429
Boundary problem, regular      390
Bounded operator      487
Brouwer fixed point theorem      98
Calculus of variations      53
Campbell — Hausdorff formula      541
Canonical transformation      75 87 93
Cauchy integral formula      194
Cauchy integral theorem      194
Cauchy — Kowalewski theorem      430
Cauchy — Riemann equations      7 17 42 377
Cauchy's inequality      14 476
Caustic      449
Central force      88 91
Central limit theorem      202
Chain rule      3 65
Christoffel symbols      49
Clebsch — Gordon series      556
Closed graph theorem      490
Closed operator      510
Closed range theorem      491
Coercive estimate      382
Cohomology      368
Cohomology, deRham      103 354 369
Coisotropic      79
Compact operator      495
Conformal map      376
Conservation of matter      171
Conserved quantity      34
Contact form      76 538
Contraction mapping principle      8
Convolution      201 213
Cotangent bundle      158 537
Coulomb's law      165
Covariant derivative      48 130
Cramer's formula      7 26
Critical point      105
Curvature      136
Darboux's theorem      77
Deformation tensor      134 139 154 399
Degree      100 105
Delta function      205
Denjoy — Carleman theorem      225
Derivation      32 131 135
Derivative      2
Determinant      504
Diffeomorphism      535
Difference operator      254
Differential form      62
Differential form, closed      67 103 354
Differential form, exact      67 103 354
Differential operator      158 201 245
Dilation      239
Dirichlet boundary condition      235 415 417
Dirichlet condition      124
Dirichlet kernel      184
Dirichlet problem      188 323 325 376 390 397
Discrete Fourier Transform      251
distribution      213
Distribution, homogeneous      239
div-curl lemma      358
Divergence      123 125 150 160
Divergence theorem      127 146 155
Domain      510
Dominated Convergence Theorem      471
Dual      482
Duhamel's principle      21 25 280 523
Eigenfunction      304 306 615 345 352 415 417
Eigenvalue      17 309 498
Eigenvector      17 498
Eikonal equation      79 441
electromagnetic field      58 95 165 427
Elliptic      164 245 379
Elliptic regularity      247
Elliptic, properly      397
Elliptic, strongly      390
Energy      43 169 428
Energy conservation      143 146
Energy estimate      157 434
Euler characteristic      107 357 374 410
Euler product      238 266
Euler's constant      266
Exact sequence      409
Exact sequence, long      370
Exponential coordinate system      49
Exponential map      49 539
Exponential matrix      14
Exterior derivative      66 161 351
Exterior product      66 164
Faraday's law      165
Fejer kernel      186
FFT      258
Finite part      243
Finite propagation speed      146 157 222 419 424 439
Flow      32 125
Fourier inversion formula      178 197 206 220 223 251 264 272
Fourier series      177 214 248 282 479
Fourier series, Abel summability      180
Fourier transform      197 205 216 239 264
Frechet space      207 296 480
Fredholm      284 289 350 507
Fredholm alternative      499
Frenet — Serret formula      27
Friedrichs method      310
Frobenius's theorem      40 79 540
Fundamental solution      211 213 217 221 417
Fundamental theorem of algebra      18 105 210
Fundamental theorem of calculus      4
Gamma function      219 262 463
Gauss lemma      50
Gauss map      107
Gauss sums      255
Gauss' law      165
Gaussian      200 217 262
Generating function      87
Geodesic      45
Geodesic flow      51 88
Geometrical optics      443
Gevrey class      225
Gradient      123 128 160
Graph      510
Green function      323 331 340
Green — Stokes formula      160 162
Green's formula      129 143 194 361
Green's identities      138
Gronwall inequality      26 31

Haar measure      99 540
Hahn — Banach theorem      215 484
Hamilton's principle      56 116
Hamiltonian system      43 51 54
Hamiltonian vector field      43 73 145
Hankel function      230
Harmonic      188
Harmonic conjugate      323 340
Harmonic form      353
Harmonic function      378
Harmonic maps      145
harmonic oscillator      44
Hausdorff space      534
Heat equation      216 235 415 423
Heaviside function      205
hessian      132
Hilbert space      476
Hilbert — Schmidt      298
Hilbert — Schmidt kernel theorem      501
Hilbert — Schmidt operator      500
Hille — Yosida theorem      527
Hodge decomposition      353 367
Hodge laplacian      162 351 361
Hodge star operator      355 377
Hoelder space      272
Hoelder's inequality      472
Holmgren uniqueness theorem      433
Holomorphic      7 14 30 188 192 203 324 340
Homeomorphism      534
Homogeneous distribution      212
Homotopic      73 101
Hooke's law      116
Huygens principle      222
Hyperbolic equation      154 434
Hyperbolic system, symmetric      437 439
Implicit function theorem      13
INDEX      105 284 290 507
Infinitesimal generator      518
Initial condition      143 216 220 415 417
Initial conditions      118 124
Initial-value problem      11
Inner product      476
Integrable system      86
Integral curves      33
Integral equation      8
Integral manifold      39
Integrating factor      73
Interior product      66 162
Interpolation      276 282 285
Inverse function theorem      11 33 54
Involution      85
Involutive      40
Isothermal coordinates      376
Jacobi's trick      83
Jordan curve theorem      102
Jordan normal form      20 36
Jordan — Brouwer separation theorem      102 410
Kadlec's formula      340
Kepler problem      89 92
Killing field      133
Killing field, conformal      134
Killing field, timelike      150
kinetic energy      56 116 119
Korn's inequality      400
Kunneth formula      356
Lagrange's equation      54
Lagrangian      56 79 80 170 452
Lame constants      123
Laplace asymptotic method      267
Laplace operator      121 137 188 216 245 302
Laplace transform      475
Laplacian      123
Legendre symbol      257
Legendre transform      55 145
Lenz vector      90
Levi — Civita connection      48
Lie algebra      539
Lie bracket      36
Lie derivative      36 67 125
Lie group      357 539
Linear elsticity      123 148 161
Linearization      118
Liouville theorem      209
Liouville's theorem      75
Lipschitz      8
Locally convex space      481
Longitudinal wave      118
Lorentz force      58 95
Lorentz force law      172
Lorentz manifolds      149
Lorentz metric      94
MacDonald's function      233
Manifold      535
Maximum principle      191 277 416 420
Maximum principle, strong      313 328 332
Maximum principle, weak      311
Maxwell's equations      58 96 165 427 439
Mayer — Vietoris sequence      408
Mean-value property      190 318
Mellin transform      237 264
Meromorphic      243
Method of images      119 235
Metric space      530
Metric space, compact      530
Minkowski's inequality      472
Minkowsli spacetime      94 166
Monotone Convergence Theorem      471
Montel's theorem      343
Morse lemma      465
Negligible set      337
Neumann boundary condition      236
Neumann problem      196 288 344
Newton's law      43 57
Newton's method      14
Noncharacteristic      79
Norm      469
Normal coordinate system      49
Normal derivative      138
Oblique derivative problem      289 401
Open mapping theorem      490
Orbit      31
Orientable      64
Orientation      64
Orthonormal basis      478
Paley — Wiener theorem      203 216 225
Parametrix      246
Parseval identity      179
Partial derivative      3
Partition of unity      536
Pendulum      44 58
Peter — Weyl theorem      549
Phase function      441
Picard iteration      8
Picard's theorem      343
Plancherel formula      179 199
Plemelj jump relation      207 222
Poincare duality      356 370
Poincare lemma      69 98
Poisson bracket      43
Poisson integral      187 287
Poisson integral formula      322
Poisson kernel      255
Poisson summation formula      236
potential energy      43 56 116 119 141
Power series      192
Pressure waves      161
Principal value      207 241
Projection, orthogonal      478
Propagation of singularities      444
Propagation speed      118

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