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Nikolsky S.M. — A Course of Mathematical Analysis (Vol. 2)

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Название: A Course of Mathematical Analysis (Vol. 2)

Автор: Nikolsky S.M.

Аннотация:

A textbook for university students (physicists and mathematicians) with special supplementary material on mathematical physics. Based on the course read by the author at the Moscow Engineering Physics Institute. Volume 2 contains multiple integrals, field theory, Fourier series and Fourier integral, differential manifolds and differential forms, and the Lebesgue integral.

Язык:

Рубрика: Математика/

Серия: Сделано в холле

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1977

Количество страниц: 440

Добавлена в каталог: 25.04.2010

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Предметный указатель

Approximation, with continuous functions in $L_{p}$       159
Approximation, with continuous functions in L      372
Area of a sphere      77
Area of a surface      73—75
Area of a torus      78
Banach space      147
Banach, S.      147
Bernoulli's polynomials      216
Bernoulli, Daniel      216
Bessel, F.W.      173
beta function      133
Boundedness of a Riemann integrable function      26
Brouwer's theorem      67
Brouwer, L.E.J.      67
Bunyakovsky's inequality      153
Bunyakovsky, V.Ya.      153
Carleson, L.      209
Carrier (or support) of a function      140
Cauchy's inequality      153
Cauchy, A.L.      153
Change of variables in improper integral      71
Change of variables in Lebesgue's integral      384
Change of variables in multiple integral      54 56
Characteristic function      376
Chebyshev's polynomials      235
Chebyshev, P.L.      235
Coherent orientation      306
Compact      291
Complete normed linear space      147
Completeness of $L_{p}$       382
Complex form of Fourier series      211
Continuity of multiple integral with respect to parameter      48
Continuity of uniformly convergent improper integral      128 135
Convergence in measure      353
Convergence in the mean square      156
Convergence of Fourier's single integral      245
Convergence uniform, of an improper integral      128
Convolution (faltung)      254 333
Cosine transformation, Fourier's      247
Curl (or rotation) of a vector      86 114
Derivative of Fourier's transform      249
Derivative, generalized (Sobolev)      392
Diameter of a set      9
Difference of differential forms      311
Difference of elementary figures      11
Differentiable manifold      289
Differential form      310
Differential of a form (exterior differential)      312
Differentiation of Fourier's series      213 287
Differentiation of gamma function      136
Differentiation of integral with respect to parameter      118
Dirac, P.A.      257
Dirichlet's integral      195
Dirichlet's kernel      196
Dirichlet's sum      195
Dirichlet, P.G.L.      195 196
Divergence of a vector field      108
Du Bois-Reymond, R.      209
Essential supremum      333
Estimation for the remainder of Fourier's series      216 232
Example of a Jordan nonmeasurable set      17
Extension of function with respect to metric of C      433
Fejer's sum      221
Fejer, L.      221
Finitely-valued function      156
Flux of vector through an oriented surface      104
Formula for remainder of Fourier's series      197
Formula, Green's      92
Formula, Stokes'      114 320
Fourier's coefficients      171 211 284
Fourier's cosine transform      249
Fourier's integral      240
Fourier's inverse transform      247
Fourier's series      171
Fourier's sine transform      249
Fourier's single integral formula      242
Fourier's transform      247
Fourier's transformation      247 248
Fourier's transformation, inverse      248
Fourier, J.B.J.      171 211 216 226 240 247 249
Fubini's theorem      375
Fubini, G.      375
Function, $\delta(x)$       257
Function, absolutely continuous      397
Function, Beta      133
Function, essentially bounded      333
Function, finite      156
Function, finitely-valued      156
Function, Gamma      136
Function, Heaviside      258
Function, Lebesgue integrable      356
Function, locally absolutely continuous      398
Function, locally integrable      247
Function, locally measurable      149
Function, locally piecewise smooth      246
Function, measurable      348
Function, polygonal      165
Function, Riemann integrable      26
Function, satisfying a Lipschitz condition      204
Function, simple      356
Function, step      273
Function, summable      357
Gamma function      136
Gauss — Ostrogradsky theorem      107
Gauss, K.F.      107
Generalized function (continuous linear functional)      255
Generalized function (continuous linear functional) on D'      404
Generalized function (continuous linear functional) on S      255
Generalized function (continuous linear functional) on S*      283
Generalized function (continuous linear functional), $P\cdot\frac{1}{x}$       259
Generalized function (continuous linear functional), periodic      326
Generalized function (continuous linear functional), regular      257
Generalized function (continuous linear functional), singular      257
Generalized, (Sobolev) derivative      392
Generalized, Minkowski's inequality      326
Geometrical interpretation of sign of determinant      51
Gibbs' phenomenon      219
Gibbs, J.W.      194 219
Green's formula      92
Green, G.      92
Harmonics of a trigonometric series      193
Heaviside O.      258
Hilbert, D.      156
Hoelder's condition      203
Hoelder's inequality      153
Hoelder, O.      153 203
Hunt, R.A.      209
Hurewicz, W.      67
Incompleteness of the space $L^{'}_{p}$       407
Inequality, Bessel's      173
Inequality, Bunyakovsky's      153
Inequality, Cauchy's      153
Inequality, Hoelder's      153
Infinite-dimensional linear space      164
Integrability of product      39
Integrability of quotient      39
Integrability of sum      39
Integral of a differential form      316
Integral, Dirichlet's      195
Integral, Fourier's      240
Integral, improper      71 121
Integral, improper, nonuniformly convergent      131
Integral, improper, uniformly convergent      128
Integral, Lebesgue's      338 355
Integral, Lebesgue's, generalized      424
Integral, Lebesgue's, over an unbounded set      388
Integral, line of the first type      80
Integral, line of the second type      81
Integral, Poisson's      140
Integral, Riemann      25

Integral, Riemann — Stieltjes      414
Integral, Stieltjes      415
Integral, surface, of the first type      96
Integration of an improper integral with respect to parameter      129 240
Integration of Fourier's series      213
Iterated Fourier integral      247
Jordan content (measure) of a set      11 20
Jordan content (measure) of a set, generalized      408
Jordan measurable three-dimensional sets      20
Jordan squarable set      11
Jordan, C.      11 13 15 17
Kernel, Dirichlet's      195
Kernel, Fejer's      223
Kolmogorov's example      209
Kolmogorov, A.N.      209
Lebesgue measurability of intersection of measurable sets      345
Lebesgue measurability of sum of measurable sets      344
Lebesgue measurable set      338
Lebesgue's inner measure      343
Lebesgue's integral      355
Lebesgue's measure      338
Lebesgue's measure of a bounded closed set      339
Lebesgue's measure of a bounded open set      339
Lebesgue, H.L.      33 338 344 355 371
Legendre's polynomials      237
Legendre, A.M.      237
Line integral of the first type      80
Line integral of the second type      81
Linear property of Lebesgue's integral      362
Linearly dependent system of elements      163
Linearly independent system of elements      164
Lipschitz condition      204
Lipschitz, R.O.S.      204
Localization principle      199
Locally integrable function      247
Locally piecewise smooth function      246
Logarithmic potential      140
Lower integral sum, Lebesgue's      355
Lower integral sum, Riemann's      28
Lower step function      356
Manifold, differentiable      290
Manifold, orientable      296
Manifold, oriented      296
Many-dimensional Fejer's sum      221
Many-dimensional Fourier's series      221
Measurable function      348
Measure of a bounded closed set      339
Measure of a bounded open set      339
Measure, Jordan's      13
Measure, Jordan's, generalized      408
Measure, Lebesgue's      343
Minkowski's inequality      326
Minkowski, H.      153 326
Moebius strip      296
Moebius, A.F.      296
Nonuniformly convergent improper integral      131
Norm in $L^{'}_{p}$       149
Norm in $L_{p}$       149
Norm in L      149
Norm in L'      149
Normalized element of anormed space      170
Normed linear space      147
Orientable manifold      296
Orientation of a domain in the plane      91
Orientation of a surface      98
Oriented manifold      296
Orthogonal system of elements      170
Orthogonalization process      183
Orthonormal system of elements      153 170
Orthonormal system of elements, closed      176
Orthonormal system of elements, complete      174
Oscillation lemmas      199
Ostrogradsky, M.V.      107
Parseval's relation      173
Parseval, M.A.      173
Partition of the real line      355
Partition of unity      335
Plancherel's Theorem      278
Plancherel, M.      278
Poisson's integral      140
Poisson, S.D.      140
Polar coordinates in the plane      63
Polar coordinates, (spherical) in $R_{n}$       125
Polar coordinates, (spherical) in three-dimensional space      65
Polygonal function      165
Polynomials, Bernoulli's      216
Polynomials, Chebyshev's      235
Polynomials, Legendre's      237
Potential of a vector field      83
Potential of single layer      141
Potential, logarithmic      140
Potential, volume      140
Product of differential forms      311
Regularization of a function      329
Representation of surface      290
Riemann's definite integral      25
Riemann's double integral      10
Riemann's integral sum      24
Riemann's lower integral      27
Riemann's triple      10
Riemann's upper integral      27
Riemann, G.F.B.      10 24 28
Rotation (or curl) of a vector field      86 114
Scalar product in $L^{'}_{2}$       154
Scalar product in $L_{2}$       154
Schwartz, L.      250
Schwarz, H.A.      79
Separable space      165
Series of generalized functions      261
Series, Fourier's      171 188 225
Series, Fourier's, in complex form      261
Set of Lebesgue measure zero      34
Set, complete      165
Set, dense      165
Set, Jordan measurable      13 17
Set, Lebesgue measurable      343
Sine transformation, Fourier's      247
Sobolev's generalized derivative      392
Sobolev's regularization of function      393
Sobolev, S.L.      329 392
Space, $L^{'}_{2}$       154
Space, $L^{'}_{p}$       149
Space, $L_{2}$       154
Space, $l_{p}$       150
Space, Banach      147
Space, C      148
Space, D'      404
Space, L      149 341
Space, L'      149
Space, linear      147
Space, normed linear      147
Space, S      250
Space, S'      255
Space, separable      165
Spherical (polar) coordinates in $R_{n}$       125
Spherical (polar) coordinates in the three-dimensional space      65
Step function      273
Stieltjes integral      258
Stieltjes, T.J.      258
Stokes' theorem      114 320
Stokes, G.G.      114
Sum of differential forms      311
Sum of elementary figures      11
Sum, Dirichlet's      195
Sum, Fejer's      221
Sum, Fourier's, arithmetic mean      221
Support (or carrier) of a function      156
Support (or carrier) of a function, compact      156
Surface integral of the first type      96
Theorem on completeness      382

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