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

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

Предметный указатель

Simple eigenvalue      236
Simple function      343
Sine function      300 308
Sine-Gordon equation      421
Singular distribution      292
Singular integral operator      316
Skew-adjoint operator      200
Sobolev conjugate      366
Sobolev embedding theorem      160 266 366—368
Sobolev space      93 128 158 362 363
Space filling curve      89
Spectral gap      164
Spectral mapping theorem      234 285
Spectral radius      97 220
Spectral theorem for Sturm-Liouville operators      268
Spectral theorem, compact operator      225
Spectrum      218
Spectrum of a linear operator      218
Spectrum of a matrix      216
Spectrum point      219
Spectrum residual      219
Spectrum, approximate      241
Spectrum, continuous      219
Spherical Bessel function      279
Spherical harmonics      279
Stability      404
Stable      404
Standard deviation      321
Stationary point      410
Stationary solution      380
Step function      254
Strang splitting      123
Strictly convex function      209
Strong convergence      111
Strong operator topology      111
Structure theorem for distributions      295
Sturm — Liouville operator      252
Sturm — Liouville operator, spectral theorem for      268
Sturm — Liouville problem, regular      271
Sturm — Liouville problem, singular      271
Subsequence      6
subspace      5
Sum norm      4
Sum, unordered      136
Summable function      345
Support      39
Support line      375
Supremum      9 28 29
Supremum, essential      340
Symbol      314
Symmetric form      197
Symmetric matrix      197
Symmetric operator      247
Tchebyshev polynomials      146
Tchebyshev's inequality      359
Tempered distributions      291
Test function      288 362
Theta function      319
Toda lattice      242
Topological linear space      86
Topological space      81
Topological space, dual      116
topology      81

Topology, discrete      82
Topology, indiscrete      82
Topology, induced      82
Topology, operator      109
Topology, relative      82
Topology, strong operator      111
Topology, trivial      82
Topology, uniform      109
Topology, weak      119 204
Topology, weak-*      299
Totally bounded metric space      24
Trace class operator      231
Trace theorem for Sobolev functions      369
Trajectory      172
Translation invariant operator      313
Translation operator      297
Transonic small disturbance equation      396
Triangle inequality      2 4
Triangle inequality for the norm      358
Tricomi equation      397
Trigonometric polynomials      150
Trivial topology      82
Turing instability      408
Ultradistribution      310
Ultrametric      3
Unconditionally convergent      136
Uncorrelated random variables      143
Uncountable      30
Uniform boundedness theorem      204
Uniformly continuous group      113
Uniformly convex      417
Unit ball      4
Unitary      199
Unstable      404
Upper bound      9
Upper semicontinuous      14
Urysohn's lemma      32
Variance      321
Variational derivative      415
Vector-valued measure      337
Volterra integral operator      104
von Neumann ergodic theorem      201
Wave, dispersive      170
Wave, equation      167
Wavelets      175
Weak convergence in       361
Weak convergence in Banach space      119
Weak convergence in Hilbert space      204
Weak convergence of operators      112
Weak convergence of probability distributions      327
Weak derivative      158 295 362
Weak solution      163 370
Weak topology      119 204
Weak topology on       361
Weak-* convergence      119
Weak-* topology      299
Weierstrass approximation theorem      40
Weighted norm      59
Weyl ergodic theorem      173
Wiener process      327
Wigner distribution      332
wronskian      256
Young's inequality      154 359
Zorn's lemma      140

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