Hunter J.K., Nachtergaele B. — Applied Analysis :: Электронная библиотека попечительского совета мехмата МГУ

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Hunter J.K., Nachtergaele B. — Applied Analysis

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Название: Applied Analysis

Авторы: Hunter J.K., Nachtergaele B.

Аннотация:

This book provides an introduction to those parts of analysis that are most useful in applications for graduate students. The material is selected for use in applied problems, and is presented clearly and simply but without sacrificing mathematical rigour. The text is accessible to students from a wide variety of backgrounds, including undergraduate students entering applied mathematics from non-mathematical fields and graduate students in the sciences and engineering who want to learn analysis. A basic background in calculus, linear algebra and ordinary differential equations, as well as some familiarity with functions and sets, should be sufficient.

Язык:

Рубрика: Математика/Анализ/Учебники по элементарному анализу/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2000

Количество страниц: 439

Добавлена в каталог: 20.10.2004

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Предметный указатель

-semigroup      114 163
norm      4
spaces      351
spaces, local      362
$L^{\infty}$ norm      5
$\epsilon$ -net      24
$\sigma$ -algebra      335
$\sigma$ -algebra, Borel      336 338
$\sigma$ -finite      337
Absolute convergence      8
Absolute convergence in a normed linear space      33
action      419
Activator      409
Adjoint of a bounded operator      193
Adjoint of an unbounded operator      246
Advection-diffusion equation      279
Airy's equation      329
Algebra      109
Almost everywhere      15 340
Almost periodic function      135
Analytic      220
Annihilation operator      147
Antilinear      126
Approximate identity      151
Approximate spectrum      241
Approximation scheme      114
Approximation scheme, consistent      114
Approximation scheme, convergent      114
Approximation scheme, stable      115
Arzela — Ascoli theorem      45
Asymptotically stable      235 404
Averaging kernel      260
Backwards heat equation      164
Baker — Campbell — Hausdorff formula      123
Ball, closed      14
Ball, open      14
Ball, unit      4
Banach algebra      39
Banach space      8 91
Banach space of linear operators      110
Banach — Alaoglu theorem      119 208
Banach — Steinhaus theorem      204
Base of open sets      84
Basis, Hamel      94
Basis, orthonormal      133
Basis, Schauder      94
Bernstein polynomials      40
Bessel function, spherical      279
Bessel's inequality      137
Bifurcation equation      425
Bifurcation theory      399
Biot — Savart law      284
Birkhoff ergodic theorem      204
Bolzano — Weierstrass theorem      23
Borel $\sigma$ -algebra      336 338
Borel set      336
Born approximation      69
Boundary      88
boundary conditions      250
Boundary value problem      69 249
Bounded from above      9
Bounded from below      9
Bounded function      11
Bounded linear operator      95
Bounded linear transformation theorem      100
Bounded set      9
Brachistochrone problem      413
Brownian motion      327
Calculus of variations      410 420
Cantor function      32
Cantor set      16
Cartesian product      3
Cauchy sequence      7
Cauchy unordered sum      136
Cauchy — Schwarz inequality      128 357
Central limit theorem      320
Chain rule      388
Characteristic function of a random variable      323
Characteristic function of a set      343
Characteristic polynomial      217
Circle map      172
Classical solution      370
Closed ball      14
Closed operator      247
Closed set      15
Closure      16 88
Closure, sequential      86
Cluster point      31
Codimension      187 212
Coercive      34 211
Commutator      109
Compact metric space      25
Compact operator      110
Compact relatively      27
Compact resolvent      227
Compact support      39
Compact topological space      83
Complete measure space      339
Complete metric space      8
Complete metric space of continuous functions      38
Complete orthonormal set      139
Completion of a measure space      339
Completion of a metric space      19
Complex measure      337
Conjugate exponent, Sobolev      366
Conjugate linear      126
Connected      89
Continuous extension      100
Continuous function      12
Continuous in       376
Continuous random variable      320
Continuous spectrum      219
Continuous topological space      83
Continuous uniformly      13 27
Contraction      61
Contraction mapping theorem      62
Convergence of a sequence      6
Convergence of series      8
Convergence, absolute      8
Convergence, pointwise      35
Convergence, topological space      82
Convergence, unconditional      136
Convergence, uniform      36
Convergence, weak in Hilbert space      204
Convex function      209
Convex set      4
Convolution      150 298 359
Convolution operator      329
Convolution theorem      154 309
Countable      30
Countably additive      335
Counting measure      337
Covariance matrix of a Gaussian      330
Cover      24
Creation operator      147
Critical point      381 410
Cylinder set      85
d'Alembert's solution      185
Deficiency index      268
Delta function      253 291
Delta function, derivative of      296
Delta sequence      299
Dense      16
Derivative, distributional      295
Derivative, Frechet      386
Derivative, functional      415
Derivative, Gateaux      389
Derivative, variational      415
Derivative, weak      158 295 362
Devil's staircase      32

Diagonal argument      46
Diagonalizable matrix      216
Diagonally dominant matrix      79
Diameter      11
Diffeomorphism      393
Differentiable      31
Differentiable map      386
Differential equation, existence and uniqueness      73 74
Differential equation, existence of solutions      53
Differential equation, nonlinear      52
Differential operator      249
Diffusion equation      161
Diffusion-driven instability      408
Dini's monotone convergence theorem      60
Dirac delta function      253
Direct method in the calculus of variations      381
Direct sum      133 187
Directional derivative      389
Dirichlet boundary conditions      250
Dirichlet form      270 372
Dirichlet kernel      183
Discrete Laplacian operator      240
Dispersive waves      170
Distance      11
Distance function      1
Distribution function      340
Distributional derivative      295
Distributions      287 294
Distributions, tempered      291
Divergent series      8
Domain of a linear operator      245
Domain regular      365
Dominated Convergence Theorem      348
du Bois — Reymond lemma      412
Dual basis      117
Dual space of       361
Dual space, algebraic      116
Dual space, topological      116
Duality pairing      293
Duhamel's formula      425
Dynamical system      63
Eigenvalue      216
Eigenvalue of a linear operator      219
Eigenvalue problem, Laplace's equation      277
Eigenvalue problem, Sturm-Liouville      268
Eigenvector      216
Energy norm      373
Epigraph      33
Equicontinuous      44
Equilibrium solution      380
Equivalence relation      33
Equivalent norms      101
Ergodic map      203
Ergodic theorem      172
Ergodic theorem, Birkhoff      204
Ergodic theorem, von Neumann's mean      201
Ergodic theorem, Weyl      173
Essential supremum      340
Essentially self-adjoint      248
Euclidean norm      4
Euclidean norm of a matrix      97
Euclidean space      4
Euler operator      415
Euler-Lagrange equation      412
Even function      156
Event      341
Exponential      112
Extended real numbers      342
Extension of an operator      246
Fatou's lemma      347
Fejer kernel      183
Final conditions      250
Finite element method      373
Finite part distribution      293
First countable      84
Fixed point      62 380
Flow      113
Fourier basis      134
Fourier coefficients      153
Fourier cosine expansion      156
Fourier series      149
Fourier sine expansion      156
Fourier transform      301
Fourier transform of a characteristic function      308
Fourier transform of a convolution      304
Fourier transform of a delta function      307
Fourier transform of a derivative      301
Fourier transform of a distribution      306
Fourier transform of a Gaussian      302
Fourier transform of a rotationally invariant function      330
Fourier transform of a Schwartz function      301
Fourier transform of a tempered distribution      306
Fourier transform of a translated function      304
Fourier transform of an exponential function      308
Fourier transform of positive type      329
Fourier transform on       307
Fourier transform on       311
Fourier transform, eigenfunctions      312
Fourier transform, inverse transform      305
Fourier — Laplace transform      310
Fractal      16
Fredholm alternative      195
Fredholm integral equation      67
Fredholm integral operator      68
Fredholm operator      196
Free boundary conditions      416
Freshet derivative      386
Freshet space      289
Fubini's theorem      350
Function even, odd      156
Function of an operator      232
Functional      116
Functional calculus      232
Functional derivative      415
Functional, linear, on Hilbert space      190
Fundamental lemma of the calculus of variations      412
Fundamental theorem of calculus      384
Gamma function      276
Gateaux derivative      389
Gauss — Seidel method      79
Gaussian      302 321 341
Generalized Holder inequality      375
Generator      114
Gibbs phenomenon      155
Gradient      425
Gradient flow      77
Gradient mapping      417
Gram — Schmidt procedure      140
Graph of an operator      248
Green's function      70 245 253 254 316
Green's function of Laplace's equation      276
Green's function of the heat equation      163
Green's theorem      250 274
Gronwall's inequality      56
Haar measure      339
Haar scaling function      176
Haar wavelet basis      177
Hahn — Banach theorem      118
Hamel basis      94
Hamiltonian operator      147
Hamiltonian system      77 419
Hardy's inequality      284
Harmonic map      423
Hausdorff      82
Heat equation      69 161
Heat equation, Green's function      318
Heat equation, smoothing property      318
Heaviside step function      254
Heine — Borel theorem      23
Heisenberg uncertainty principle      332

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