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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
Abel's formula for the Wronskian      187
Absolutely continuous functions      307 532
Action of distribution      91
Adjoint for unbalanced problem      206 214
Adjoint, boundary conditions      198
Adjoint, boundary value problem      198
Adjoint, formal      100 167 170
Adjoint, Green's function      200
Adjoint, matrix      208
Adjoint, operator      313
Admissible pair      315
Algebraic independence      228 268 290
Alternative theorems for boundary value problems      210
Alternative theorems for integral equations      210 337
Alternative theorems in Euclidean space      208 321 323
Angular current density      26
Angular density      25
Arondszajn, N.      398
Arrhenius law      4 9
Ball, closed      1
Ball, open      1
Banach space      261
Band-limited functions      145 348 385
Base problem      566 591 594
Basis      228 297
Basis, dual      293
Basis, orthonormal      277 281—290 297
Basis, reciprocal      293
Basis, Schauder      277
Bazley, N.W.      348
Beam      63 70 83 553—557
Bessel equation      439 448
Bessel equation, modified      77
Bessel functions      288
Bessel's inequality      128 281
Bifurcation      see "Branching"
Bihaimonic operator      559
Bilinear form      274
Bilinear form, associated quadratic form      275
Bilinear form, coercive      525
Bilinear form, nonnegative      525
Bilinear form, positive      525
Bilinear form, symmetric      525
Blow-up      630
Boas, R.P.      122
Bolzano — Weierstrass theorem      335
Boundary      2
Boundary conditions for heat conduction      6
Boundary conditions in limit-circle case      447
Boundary conditions in recycling      13
Boundary conditions, adjoint      198 205
Boundary conditions, essential      535
Boundary conditions, for beam      18
Boundary conditions, natural      535 559
Boundary conditions, periodic      427 503
Boundary conditions, unilateral      536
Boundary conditions, unmixed      192
Boundary functional      192 204
Boundary value problems for second order equations      192
Boundary value problems, for equations of order p      203
Boundary value problems, regular      412
Boundary value problems, singular      412 438
Branch, Branch-point      583
Branching      575 582—591 603
Branching from infinity      618
Buckling      569
Capacity      550
Catastrophe theory      587
Cauchy data, Cauchy problem      469
Cauchy sequence      see "Fundamental sequence"
Cesaro sums      136 143
Characteristics      182 470
circle      1
Closed set      240
Closure      2 239
Codimension      309
Collision cross section      25
Compact operators      335 357
Compact set      240
Comparison theorem for diffusion      497
Compatibility      see "Solvability conditions"
completely continuous      see "Compact operators"; "Compact set"
Completeness relation      139
Conjunct      167
Connected      2
Consistency      see "Solvability conditions"
Constitutive relations      19
Continuous dependence for diffusion      497
Continuous dependence for wave equation      501
continuous dependence on data      57
Contraction      244 488
Convergence in space of test functions      89 154
Convergence of sequence of reals      31
Convergence, Cauchy criterion for      31
Convergence, distributional      107
Convergence, mean (or $L_{1}$)      34
Convergence, mean square (or $L_{2}$)      35 283
Convergence, pointwise      31 283
Convergence, uniform      32
Convergence, weak      339
Convex set      268 555
Convolution      104 163 363
DATA      42
Deficiency      325
Delta sequence      110 284
Dense set      240
Dependence and independence      186 227
Differential inequalities      64
Diffusion      71 73
Diffusion equation      7 475
Diffusion operator      170
Diffusion-reaction      612—621
Diffusivity      8
Dipole      509
Dipole layer      see "Double layer"
Dirac delta function      53
Dirichlet function      38
Dirichlet integral      561
Dirichlet kernel      113 114 121 133
Dirichlet problem      501—507 513—517
Dirichlet problem for disk      113
Dirichlet problem, exterior      515 550
Disk      1
Distance function      see "Metric"
Distributions      86—184
Distributions of slow growth      154
Distributions, action of      91
Distributions, complex-valued      137
Distributions, convergence of      107
Distributions, coordinate transformation of      120
Distributions, differentiation of      97
Distributions, dipole      95 97
Distributions, Dirac      94 98
Distributions, direct product of      122
Distributions, parametric differentiation of      115
Distributions, regular      93
Distributions, singular      93
Distributions, translation of      94
Domain      2 45
Domain of dependence      486—488
Domain of function or operator      222 295
Domain perturbation      599
Domination      66 497
Double layer      116 510
Drift      498
Duhamel's formula      45 488
Eigenfunctions      60
Eigenfunctions of compact, self-adjoint operator      373
Eigenfunctions, basis of      331
Eigenvalues      60 324 332
Eigenvalues of compact operators      357
Eigenvalues, degenerate      334
Eigenvalues, estimation of      392—409
Eigenvalues, geometric multiplicity of      325 357
Eigenvectors      324
Elements of finite energy      528
Energy inner product      524 525 537 554
Energy norm      524 525 537
Equality almost everywhere      92
Error function      457
Euclidean space      264
Euler — Bernoulli law      571
Euler — Lagrange equation      524
Expansion theorem      372
Fejer kernel      112 143
Finite part of divergent integrals      102 106
Fission      27
Fixed points      243 563 596
Forced problem      583
Forcing function      42
Fourier coefficients      128 279
Fourier integral theorem      145
Fourier series of distributions      137
Fourier series, convergence of      132
Fourier series, convolution      143 384
Fourier series, Dirichlet conditions for      130
Fourier series, full-range      287
Fourier series, general      281
Fourier series, half-range      287
Fourier series, mean-square convergence of      128
Fourier sine transform      453
Fourier sum      279
Fourier transform      140 144 148 365 462
Fourier — Bessel series      450
Fourier's law      3
Fox, D.W.      398
Frechet derivative      579
Fredholm alternative      see "Alternative theorems"
Fredholm integral equations      247 248 356
Fredholm integral equations of potential theory      514 516
Friedrichs' inequality      537
Functionals      87 224
Functionals, bounded      291
Functionals, continuous      291
Functionals, critical point of      580
Functionals, linear      290
Functionals, norm of      291
Functionals, quadratic      525
Functionals, stationary      525
Functions of slow growth      1 52
Fundamental sequence      31 234
Fundamental solution, casual      178 180 484 485 see
Fundamental solution, pole of      177
Galerkin equation      395 540
Gauss kernel      113
Generalized functions      see "Distributions"
Gibbs phenomenon      134
Gradient operator      580
Gram — Schmidt process      268
Green's formula      168 169
Green's function      43 194 259 see
Green's function for Bessel's equation      423 462
Green's function for diffusion      488 493
Green's function for first-order BVP      431
Green's function for periodic problem      428
Green's function for semi-infinite strip      454
Green's function for unit disk      506
Green's function for wave equation      485
Green's function in limit-circle case      444
Green's function in limit-point case      441
Green's function, adjoint      200
Green's function, bilinear series      61 415
Green's function, causal      69
Green's function, direct      200
Green's function, modified      215 217 520
Green's function, relation to eigenfunctions      416
Hankel transform      459
Harmonic functions      502
Harmonic functions, maximum principle for      66 507
Harmonic functions, mean value theorem for      507
Heat conduction      2 See
Heaviside function      47 93 159
Heisenberg's uncertainty principle      146
Hermite equation      439
Hermite polynomials      288 391
Hilbert space      263
Hilbert space, separable      276
Hilbert — Schmidt kernels      see "Kernel"
Hyperbolic equations      475 482—488
Images      72 459 491 493
Indicator function      93 100
Infimum      2
Initial value problem      68 186
Inner product      208 261 262
Inner product space, complex      262
Inner product space, real      261
Integral equations      61 210 247
Integral equations for capacity      552
Integral equations for Dirichlet problem      513—517
Integral equations, Abel      347 390
Integral equations, eigenvalue problem for      369
Integral equations, Fredholm      247 248 356
Integral equations, inhomogeneous      378—391
Integral equations, Volterra      249 388
Integral operator      248 300 351
Integral operator, Hammerstein      577
Integral operator, Hilbert — Schmidt      352
Integrodifferential equations      28 405—409 560
Interface condition      78 81 82
Jensen's inequality      631
Jordan — von Neumann theorem      274
Kernel      248 300
Kernel, bilinear expansion of      276
Kernel, difference      367 384
Kernel, Hilbert — Schmidt      300 352 360 447
Kernel, Holmgren      303 352 362 443
Kernel, iterated      355
kernel, Poisson      113 121 122 384
kernel, resolvent      382
Kernel, separable      352
Kohn — Kato method      402
Lagrange identity      168 169
Landau, H.J.      387
Laplace transform      163 487
Laplace's equation      176 475 481 502—520 See
Laplacian      44 169
Least squares      558
Lebesgue dominated convergence theorem      33 34 40
Lebesgue integral      36
Legendre equation      440
Legendre polynomials      271 286
Level line coordinates      548 560
Lewis number      12
Liapunov — Schmidt method      605
Limit-circle      437 438 444
Limit-point      437 438 440
Linear dependence      see "Dependence and independence"
Linear independence      see "Algebraic independence"; "Dependence and independence"
Linear manifold      229 264
Linear space      226
Linear space, basis for      228
Linear space, complex      226
Linear space, dimension of      228
Linear space, normed      259
Linear space, real      226
Linearization      578
Lipschitz continuous      244 247 249
Locally integrable      91
Macdonald function      462
Mapping      see "Transformations"
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