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Cheney W. — Analysis for Applied Mathematics
Cheney W. — Analysis for Applied Mathematics

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Название: Analysis for Applied Mathematics

Автор: Cheney W.

Аннотация:

BLECK:

SIAM REVIEW "The book succeeds well in providing a sound basis in analysis beyond that which most students will have received as undergraduates...Overall, this text serves as a wonderful introduction to 'useful' analysis for new applied mathematicians."

BULLETIN OF MATHEMATICS BOOKS "This text is written with the usual elegance and orderly style that we have come to expect from this author. Topics are presented in a clear and logical manner, and the text is rich with important and interesting content...This text is well worth considering in any program in applied mathematics, and also by anyone seeking a valuable reference in analysis and its applications."

MATHEMATICAL REVIEWS "The author describes this marvelous book as designed for beginning graduate students in mathematics - in particular for those who intend to specialize in applied mathematics, and for graduate students in other disciplines such as engineering, physics and computer science...Those who are familiar with the author's earlier books will not be surprised by its excellence. It is business-like and will be found to be demanding, but it is user-friendly. It is the reviewer's opinion that it will be extremely useful and popular as a text; institutions that do not already require their students to take such a course no longer have an excuse, and should immediately organize one based on this book...The author gives a rigorous discussion of a very large number of topics. Careful definitions and clearly stated theorems are given...The writing in clear and readable throughout, with a pleasant and friendly style...it is the reviewer's view that the author has presented a rich harvest of useful and interesting analysis in a splendid manner."



Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2001

Количество страниц: 456

Добавлена в каталог: 15.02.2014

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$G_{\delta}$ set      46
A-orthogonal      233
A-orthonormal      233
Absolute continuity      413
Absolutely convergent      14 17
Accumulation point      12
Adjoint of an operator      50 82—83
Adjoint space      34
Affine map      120
Alaoglu theorem      370
Alexander's Theorem      365
Algebra of sets      421
Almost everywhere      396
Almost periodic functions      76 77
Almost uniformly      397
Angle between vectors      67
Annihilator      36
Approximate inverse      188
Arzela — Ascoli Theorems      347ff
Autocorrelation      293
Axiom of Choice      31
Babuska — Lax — Milgram Theorem      201
Baire theorem      40
Banach limits      37
Banach space      10
Banach — Alaoglu theorem      370
Banach — Steinhaus theorem      41
Bartle — Graves Theorem      342
Base      5
Base for a topology      362
Basin of attraction      135
Bernoulli, J.      153
Bessel functions      179
Bessel's inequality      72
Best approximation      192
Bilinear functional      201
Binomial coefficients      261
Binomial theorem      262
Biorthogonal system      82 192
Bohl's theorem      339
Borel sets      392
Borel sigma-algebra      384
Bounded above      6
Bounded functional      81
Bounded map      25
Bounded set      20 368
Brachistochrone problem      153 157ff
Brouwer's theorem      333
Calculus of variations      152
Canonical embedding      58
Cantor set      46
Caratheodory's theorem      387
Category      41
Category argument      45 46 47 48
Catenary      153 156 169
Cauchy sequence      10
Cauchy — Riemann equations      199
Cauchy — Schwarz inequality      62
Cesaro means      13
Chain      31
Chain rule      121
Characteristic function of a set      395
Characters      288
Chebyshev polynomials      214
Closed graph      47
Closed graph theorem      49
Closed mapping      47
Closed range theorem      50
Closed set      16
Closure of a set      16 363
Cluster point      12
Collocation methods      213ff
Compact operator      85 351
Compact set      8
Compactness      19 20 364
Compactness in the weak topologies      369
Complete measure space      387
Completeness      9 10 15 21
Completion of a space      15 60
Composition operator      252
Condensation of singularities      46
Conjugate direction methods      232
Conjugate gradient method      235
Conjugate space      34
Conjugate-linear map      90
Connectedness      124
Continuation methods      238
Continuity      15
Contraction      132 176
Contraction mapping theorem      177 333
Convergence      8 11 17
Convergence in measure      408
Convergence of distributions      257
Convergence of test functions      249
Convex functional      231
Convex hull      12
Convex set      6
Convolution      269ff 290ff
Convolution of distributions      285
Coset      29
Cosine transform      300 321
Countable additivity      386
Countably compact      227
Counting measure      382
Cycloid      153 158
Degenerate kernel      176 357
Dense set      14 28 36
Derivative of a distribution      253
Descent methods      225
Diaconis — Shahshahani Theorem      361
Diagonal dominance      172ff
Diameter of a set      185
Differentiable      115
Differential operator      24 273
Dini's theorem      350
Dirac distribution      250 256 260 268 283
Direct sum      80 143
Directed set      363
Directional derivative      227
Dirichlet problem      167 198
Discrete space      46
Discrete topology      362
Discretization      170
Distance function      9 19 23 34 64
Distributions      246 249
Dominate      32
Dominated Convergence Theorem      406
Dual space      34
Eberlein — Smulyan Theorem      59
Egorov's theorem      397
Eigenvalue      91
Eigenvector      92
Elliptic      211
Embedding theorems      330ff
Equimeasurable rearrangement      403
EQUIVALENCE      4
Equivalent norms      23 27 39
Essential supremum      409
Euclidean norm      4
Euler equation      155ff 164
Euler — Lagrange equation      155
Extended real number system      381
Extension of a function      31
Extremum problems      145
Fatou's lemma      403
Feasible set      243
Fermat's principle      162 164
Finite dimensional      5
Fixed point of Fourier transform      301
Fixed-point theorems      140 333
Formal adjoint      279 280
Fourier coefficients      72
Fourier projections      42
Fourier series      42 167
Fourier transform      24 287ff
Fourier transform table      292
Frechet derivative      115
Frechet — Kolmogorov Theorem      350
Fredholm alternative      351ff
Fredholm integral equation      175 178 190
Fredholm theory      356
Fubini Theorems      424 426 427
Fundamental set      36
Fundamental solution of an operator      273
Galerkin method      198
Game theory      345
Gamma function      293
Gateaux derivative      120 228
Gaussian elimination      172
Gaussian function      318
Gaussian quadrature      223
Generalized Cauchy — Schwarz inequality      84
Generalized function      246
Generalized sequence      364
Geodesic      13 164ff
Geometrical optics      162
Goedel's theorem      30
Goldschmidt solution      157
Gradient      117
Gram matrix      197
Gram — Schmidt process      75
Greatest lower bound      6
Green's functions      107ff 215
Green's identity      277
Green's theorem      161 200 203 205 210
Hahn decomposition      420
Hahn — Banach theorem      32
Half-space      38
Hamel base      32
Hammerstein equation      225
Harmonic function      199
Harmonic series      18
Hausdorff — Young theorem      309
Hausdprff space      362
Heat equation      318ff
Heaviside distribution      250 254 256 257 283
Heine — Borel theorem      19
Helmholtz equation      320
Hermite functions      309
Hermitian matrices      104
Hermitian operator      83
Hilbert cube      351
Hilbert space      61 63
Hilbert — Schmidt operator      83 96 98
Hoelder inequality      55 409
Homotopy      237ff
Hyperplane      38
Idempotent operator      189 191
Implicit function theorems      135ff
Infimum      6
Initial-value problem      179ff
Inner measure      390
Inner product      61
Integrable function      405
Integral equations      131 141 357
Integral operator      24
Integration      399ff
Interior mapping theorem      48
Interior of a set      363
Invariant measure      385 392
Inverse Fourier transform      301ff
Inverse Function Theorems      139 140
Invertible      28
Isolated point      47
Isometric      35
Isoperimetric problem      159 161
Iteration      176
Iterative refinement      187 188
Jacobian      118
James' theorem      60
Jordan decomposition      417
Kantorovich theorem      127 130
Kernel      26
Kharshiladze — Lozinski Theorem      377
Kuratowski — Ryll — Nardzewski theorem      342
Lagrange interpolation      193
Lagrange multipliers      145 148 152 159
Laplace transform      24 287
Laplacian      198 275 297
Laurent's theorem      315
Least upper bound      6
Lebesgue decomposition theorem      415
Lebesgue measurable set      389 391
Lebesgue measure      391
Lebesgue outer measure      382
Lebesgue space      4
Lebesgue — Stieltjes outer measure      382
Legendre polynomials      76 77 377
Leibniz formula      265
Limit in the mean      308
Linear functional      24
Linear independence      4
Linear inequalities      344
Linear mapping      24
Linear operator      24
Linear programming      243
Linear space      2
Linear topological spaces      367ff
Linear transformation      24
Lion      154
Lipschitz condition      120 178 180
Local integrability      251
Locally-convex space      370
Locally-finite covering      345
Lower semicontinuity      22 226 340
Lusin's theorem      408
Malgrange — Ehrenpreis theorem      273
Mathematica      126 205 230
Maximal element      32
Mazur's theorem      372
Mean-value theorem      122 123
Measurable functions      394ff
Measurable rectangle      421
Measurable sets      384
Measurable space      384
Measure      386
Measure space      386
Metric space      8 13
Meyers — Serrin Theorem      330
Michael selection theorem      341
Min-max theorem      346
Minimizing sequence      226
Minimum deviation      192
Minkowski functional      334 343
Minkowski inequality      55
Minkowski's inequality      410
Modifier      249
Monomial      6 261
Monotone class      422
Monotone Convergence Theorem      401
Monotone norm      14
Moore's theorem      373 375
Multi-index      246
Multinomial theorem      263
Multiplication operator      252 268
Multivariate interpolation      313
Mutually singular      415
Natural embedding      58
Neighborhood      17
Neighborhood base      367
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