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Stakgold I. — Green's Functions and Boundary Value Problems
Stakgold I. — Green's Functions and Boundary Value Problems



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Название: Green's Functions and Boundary Value Problems

Автор: Stakgold I.

Аннотация:

Presents a down-to-earth approach to using differential and integral equations when tackling significant problems in the physical sciences, engineering, and applied mathematics. The author incorporates developments that have altered the field of applied mathematics in recent decades< — >particularly in areas of modeling, Fourier analysis, fixed-point theorems, inverse problems, asymptotics, and nonlinear methods. The second edition retains popular features such as chapter introductions, clear explanations of basic concepts, and plentiful exercises


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1979

Количество страниц: 638

Добавлена в каталог: 10.12.2009

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Matrix      297
Maximum principle      64 498 593 610
Maximum principle for diffusion      495
Maximum Principle for harmonic functions      66 507
Mean value property      507
Measurable      37
Measure      37
Mellin transform      466 519
Mercer's theorem      376
Method of continuity      567
Metric      234
Metric spaces      233—243
Metric spaces, complete      235
Metric spaces, completion of      238 241
Metric, $L_{2}$      238
Metric, equivalent      242
Metric, natural      260
Metric, uniform      238
Minimum potential energy      522
Minimum principle      see "Maximum principle"
Monotone iteration      581 593 608—621 627
Multi-index      89
Multiplication factor      25 620
Multiplicity      325
Neumann problem      519
Neumann series      249 378—380
Neutron diffusion      30 84
Neutron transport      25 355 620
Newton's law of cooling      6
Newton's method      563
Norm      259
Normalization of eigenfunctions      418 434
Null sequence      90 154 161
Null space      208
One-sided functions      150
One-to-one      223
Onto      222
Open set      1
Operators      295 see
Operators with closed range      320
Operators, adjoint of      313 315
Operators, bounded      295
Operators, bounded away from zero      308
Operators, bounded below or above      342 433
Operators, closable      304
Operators, closed      305 310
Operators, closure of      305
Operators, coercive      342
Operators, compact      335 345
Operators, continuous      296
Operators, differentiation      301
Operators, domain of      295
Operators, extension of      304
Operators, extremal properties of      339—346
Operators, Frechet derivative of      579
Operators, indefinite      374
Operators, inverse      308
Operators, linearization of      578
Operators, nonnegative      342 374
Operators, norm of      296
Operators, null space of      295 306
Operators, positive      342 374
Operators, range of      295
Operators, regular      309
Operators, self-adjoint      315
operators, shift      302
Operators, state of      309
Operators, strictly positive      342
Operators, symmetric      315
Operators, unbounded      296
Order interval      581
Orthogonal      208 264
Orthogonal complement      266
Orthogonal with weight      285
Orthogonality condition      see "Solvability conditions"
Orthonormal basis      269
Orthonormal set      127 264
Orthonormal set, complete      269
Orthonormal set, maximal      282
Parabolic equations      475 488—498
Parallelogram law      264 274
Parseval's identity      129 134 282
Partial differential equations, Cauchy problem      468 469 476
Partial differential equations, classification      467—482
Partial differential equations, elliptic      475 501
Partial differential equations, hyperbolic      475 482
Partial differential equations, parabolic      475
Partial differential equations, semilinear      472 474
Payne — Rayner inequality      562
Peclet number      12
Perturbation methods      569 591—602
Poincare maximin theorem      397
Poincare — Keller method      607
Poisson equation      505 546
Poisson kernel      113 121 122 504
Poisson summation formula      140 492
Polar identity      275
Pole      94 177
Pollack, H.O.      387
Polya's isoperimetric inequality      549
Potential theory      see "Laplace's equation"
Principal part of operator      468
Principal value of square root      62 420
Principle of linearized stability      623
Projection      265 266
Projection theorem      266 281
Pseudo function      102
Pseudo inverse      218 595 598 605
RANGE      222
Rayleigh quotient      339 392
Reciprocity principle      200
Reciprocity relation      526
Relatively compact set      241 335
Representative sequence      528
Resolvent set      324
Resonance index      382
Riemann integral      36
Riemann — Lebesgue lemma      108 122 129 133
Riesz representation theorem      292 294
Riesz — Fisher theorem      278
Ritz — Rayleigh approximation      394 539
Rods      14
Sampling formula      146
Scattering      27
Schwarz inequality      262 263 271 272 525
Schwarz iteration      400 405
Schwinger — Levine principle      539
Self-adjoint      315 354
Self-adjoint, boundary value problem      198 205
Self-adjoint, formally      100 168 170
Sifting property      54
Similarity solution      499 500
Simple layer      96 509
Singular point      185 467
Slepian, D.      387
Sobolev spaces      272 532
Solutions, classical      46 172
Solutions, distributional      173
Solutions, lower      504
Solutions, maximal      565
Solutions, upper      564
Solutions, weak      173 176 524
Solvability conditions      208 320—323 382
Span, algebraic      229 276
Span, closed      276
Spanning set      276 277
Specific heat      3
Spectrum      324
Spectrum of compact, self-adjoint operator      369—375
Spectrum, approximate      325
Spectrum, compression      325
Spectrum, continuous      325 451
Spectrum, point      324
Sphere      1
Stability      621—631
Stefan — Boltzmann law      254
Step response      191
strings      14
Strong $L_{2}$ derivative      532
Successive approximations      243
Superposition principle      42 193 201
Support      90 164
Supremum      2
Surface layers      508—513
Symmetrization      561
Symmetry of compact operator      354
Symmetry of kernel      315
Symmetry of matrix      315
Symmetry of operator in Hilbert space      315
Test functions of compact support      87
Test functions of rapid decay      153 161
thermal conductivity      3
Thermal diffusivity      4
Theta function      492
Torsional rigidity      546
Trace inequality      377
Transformations      223 224 see
Transformations, continuous      241
Transformations, linear      225
Transposed matrix      see "Adjoint matrix"
Transversal      181
Triangle inequality      234
Unforced      583
Unilateral constraints      552—558
Uniqueness      56 193 244 495 499
Variance      400
Variational equation      524 526
Variational inequality      554 557
Variational principles for inhomogeneous problems      520—562
Variational principles for operators      339—346 392—399
Variational principles, complementary      545
Variational principles, Schwinger — Levine      539
Vector space      see "Linear space"
Vibrations, of rod      14 24
Vibrations, of string      20 24
Volterra integral equation      249 388
Wave equation      175 475 481
Wave operator      171
Weber transform      465
Weierstrass approximation theorem      113 120 240 284 289
Weinstein, A.      398
Well posed      58 482
Weyl — Courant minimax theorem      393 434
Weyl's theorem      438
Wiener — Hopf method      350
wronskian      187
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