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Efimov A.V. — Mathematical analysis: advanced topics. Part 2. Application of some methods of mathematical and functional analysis
Efimov A.V. — Mathematical analysis: advanced topics. Part 2. Application of some methods of mathematical and functional analysis

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Название: Mathematical analysis: advanced topics. Part 2. Application of some methods of mathematical and functional analysis

Автор: Efimov A.V.

Язык: en

Рубрика: Математика/

Серия: Сделано в холле

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1985

Количество страниц: 382

Добавлена в каталог: 23.01.2012

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Abelian group      153
Accessory conditions      227
action      257
Affine transformation      125
Alternance, Chebyshev's      298
Alternance, Valle-Poussin's      298
Application of contraction mapping principle to solution of equations      140
Application of Galerkin's method directly to solving boundary-value problems      270
Application of Hilbert-Schmidt theorem      190—202
Application of interpolation to problems of numerical differentiation and integration      304—338
Application of Ostrogradsky — Gauss formula to a special kind of the vector field      86
Application of Schauder's theorem      163—172
Application of Tailor's formula to the difference of equations      228
Arzela's theorem      148
Axiom of the metric      122
Banach — Steinhaus theorem      307
Bernstein's theorem      298
Bolzano — Weierstrass theorem      145
Brouwer's theorem      164
Cauchy — Buniakowski inequality      117
Cauchy's sequence      133
Chebyshev polynomials of the first kind      301
Chebyshev's theorem      29
Circulation of vector field      51
Compact sets      144—152
Completely ordered set      168
Computation of curl in Cartesian coordinates      54
Computational error      285
Computing the norm of a self-adjoint operator      183
Condition(s), accessory      227
Condition(s), field potentiality      67—71
Condition(s), isoperimetric      204
Condition(s), natural boundary      247—248
Condition(s), transversality      249
Construction problems      290
Continuity equation      104
Continuous operator      131 156
contour      11
Contraction mapping principle      139
Convergence in norm      154
Coordinate, axes      15
Coordinate, basis      15
Coordinate, line      15
Coordinate, surface      15
Coordinate, system      15
Cubic spline      317
Curl      53
Curl, computation of, in an orthogonal curvilinear coordinate system      58
Curl, computation of, in Cartesian coordinates      54
Curve(s), orientation of      10
Curve(s), orientation of, negative      10
Curve(s), orientation of, positive      10
Curve(s), oriented      10
Curve(s), piecewise smooth      11
Curve(s), smooth      9
Difference scheme(s), explicit      364
Difference scheme(s), implicit      364
Difference scheme(s), stable      363
Differential operations of the second order      84
Direct methods in the calculus of variations      263
Directional derivative      21
Distance between the elements      122
Divergence      45—51
Divergence, computing of, in Cartesian coordinates      46—47
Divergence, computing of, in orthogonal curvilinear coordinates      50—51
Divergence, notion of      45
Divergence, of a field at a point      46
Divergence, properties of      47—48
Divided difference(s), first-order      311
Divided difference(s), n-order      311
Divided difference(s), second-order      311
Domain, multiply connected      59
Domain, simple      32
Domain, simply connected      59
Domain, superficially simply connected      60
Element of best approximation      289
Equation(s) of mathematical physics      104—110
Equation(s) of string vibrations      259
Equation(s), continuity      104
Equation(s), Euler's      215
Equation(s), Euler's, particular cases of      217—222
Equation(s), Fredholm symmetric integral      194
Equation(s), Fredholm's integral      174
Equation(s), heat      108
Equation(s), Laplace's      88
Equation(s), membrane motion      260
Equation(s), Poisson's      94 254
Error(s) of the method      285
Error(s), absolute      283
Error(s), computational      285
Error(s), due to approximate calculations      283—288
Error(s), due to arithmetic operations      285
Error(s), irreducible      283
Error(s), relative      283
Exact methods      339
Expanding the values of an operator into a series      190
Extremal(s)      216 252
Extremum, necessary condition for      212
Extremum, strong      212
Extremum, weak      212
Field(s)      19
Field(s) of a point source      79
Field(s) of sources and sinks      79
Field(s), central-symmetric      48
Field(s), nonstationary      20
Field(s), scalar      19
Field(s), scalar, examples of      19
Field(s), stationary      20
Field(s), vector      19
Field(s), vector lines of      79
Flux of a vector field      36—45
Flux of a velocity vector      39
Formula(s) for numerical differentiation      318
Formula(s) in vector form      48—50
Formula(s), complicated quadrature      325
Formula(s), cubature      333
Formula(s), Gaussian      330
Formula(s), Green's      32 86
Formula(s), Green's, first      86
Formula(s), Green's, second      86
Formula(s), Green's, third      87
Formula(s), interpolation quadrature      324
Formula(s), Ostrogradsky — Gauss      41—45
Formula(s), quadrature      323
Formula(s), rectangular      324
Formula(s), Simpson's      324
Formula(s), Stokes'      59
Formula(s), trapezoidal      324
Function(s) of a point source      98
Function(s), Green's, of the Dirichlet problem      97
Function(s), harmonic      87—88
Function(s), harmonic, properties of      91
Function(s), integral representation of      88
Function(s), net      362
Functional(s), dependent on higher-order derivatives      224—227
Functional(s), extremum of      208 211
Functional(s), extremum of, strong      212
Functional(s), extremum of, weak      212
Functional(s), increment of      208
Functional(s), linear      207
Functional(s), maximum of      211
Functional(s), minimum of      211
Functional(s), natural boundary conditions for      247
Functional(s), variation of      208
Fundamentals of the theory of function approximation      288—293
Geodesies      231
Gradient in a scalar field      22
Gradient in orthogonal curvilinear coordinate system      23
Hamiltonian operator      55
Harmonic      88
Hausdorff's criterion      146
Hausdorff's theorem      147
Heat equation      108
Hilbert — Schmidt theorem      191
Hodograph      9
Hoelder's inequality      116
Inequality(ies), auxiliary      114
Inequality(ies), Cauchy — Buniakowski      117
Inequality(ies), Cauchy's      118
Inequality(ies), Hoelder's      116
Inequality(ies), Minkowski's      118
Inequality(ies), Schwarz's      117
Jackson's theorem      298
Jordan measure      128
Kernel(s), Fredholm's iterated      172
Lagrangian multipliers      228
Lame's coefficients      17
Laplace's equation      88
Laplace's equation, vector field      84
Laplacian (operator)      85
Level lines (surfaces)      20
Limit of a sequence      122
Line integral(s) of the first kind      28
Line integral(s) of the second kind      28
Line(s) level      21
Line(s) of force      25
Line(s) vector      25
Linear manifold      155
Local bases      15
Matrix(ces), banded      342
Matrix(ces), characteristic equation of      346
Matrix(ces), poorly conditioned      340
Matrix(ces), stable      340
Matrix(ces), symmetric      345
Matrix(ces), unstable      340
Measure, Jordan      128
Measure, Lebesgue      128
Method(s) of simple iteration      344
Method(s) of successive substitution      344
Method(s), Adams'      359
Method(s), direct, in the calculus of variations      263
Method(s), exact      339
Method(s), Galerkin's      270
Method(s), Gauss elimination      340
Method(s), Gauss elimination, backward procedure of      341
Method(s), Gauss elimination, forward procedure of      341
Method(s), general orthogonalization      124
Method(s), iteration, for solving Fredholm's equation      172
Method(s), iterative      339 344
Method(s), Kantorovich's      275
Method(s), Monte Carlo      336
Method(s), net-point      362
Method(s), Newton's, for solving systems of equations      352
Method(s), Nikolsky      326
Method(s), of finding the potential      72
Method(s), optimization      330
Method(s), Ritz'      264—270
Method(s), Runge — Kutta      356
Method(s), Seidel's      345
Method(s), sweep      344
Metric spaces      121—138
Metric spaces, complete      133
Metric spaces, isometric      138
Moebius strip      13
n-dimensional Euclidean space      124
nabla      55
Neumann's series      174
Newton's interpolation polynomial      312
Norm      153
Numerical differentiation      318—322
Numerical integration      322—325
Operator(s), characteristic value of      185
Operator(s), completely continuous      157
Operator(s), continuous      131 156
Operator(s), eigenfunction of      185
Operator(s), eigenvalue of      185
Operator(s), Fredholm's      159 172
Operator(s), monotonically increasing (decreasing)      168
Operator(s), norm of      180
Operator(s), self-adjoint      181
Orientation(s) of a curve      10
Orientation(s) of a surface      13
Orientation(s), negative      10
Orientation(s), opposite      10
Orientation(s), positive      10
Polynomial(s) of best approximation      293
Polynomial(s), construction of      299
Polynomial(s), generalized      304
Polynomial(s), Hermite interpolation      304
Polynomial(s), interpolation      304
Polynomial(s), Lagrange's interpolation      309
Polynomial(s), Newton's interpolation      312
Polynomial(s), Newton's interpolation for equal intervals      313
Potential of an electrostatic field      75
Potential, methods of finding      72
Potential, vector      82—84
Principal error term      328
Problem(s) of error estimate in an approximate solution      112
Problem(s) of the choice of a method for an exact or approximate solution      112
Problem(s) of the existence of the best approximation element      289
Problem(s) of the line of quickest descent      203
Problem(s) with differential constraints      233
Problem(s), boundary-value      94
Problem(s), construction      290
Problem(s), Dirichlet      94
Problem(s), interpolation      304 314
Problem(s), isoperimetric      234—239
Problem(s), Neumann      95
Problem(s), solution existence      112
Problem(s), solution stability      112
Problem(s), solution uniqueness      112
Problem(s), Sturm — Liouville      197
Problem(s), third boundary-value      262
Problem(s), uniqueness      289
Problem(s), variation      203
Procedure, backward sweep      344
Procedure, forward sweep      344
Reciprocity principle      240
Rectangular formula      324
Ritz' method      264—270
Runge — Kutta method      356
Schauder's theorem      163
Sequence (s) of coordinate functions      265
Sequence (s) of nested closed balls      133
Sequence (s), Cauchy's      133
Sequence (s), minimizing      264
Solving nonlinear equations      350—354
Solving the Dirichlet problem with the aid of Green's function      96
Space(s) of continuous functions      127
Space(s) of continuously differentiable functions      204
Space(s) of convergent sequences      129—130
Space(s) of pth power integrable functions      128
Space(s) of sequences with convergent series      130
Space(s) of type B      154
Space(s), Banach      154
Space(s), Hilbert      178
Space(s), Hilbert, coordinate      131
Space(s), Hilbert, functional      129
Space(s), infinite dimensional      155
Space(s), Metric      121—138
Space(s), n-dimensional Euclidean      124
Space(s), n-dimensional vector      124
Space(s), normed linear      153
Space(s), separable      151
Stokes' theorem      61
Surface integral of the second type      37
Surface(s), orientation of      13
Surface(s), orientation of, negative      13
Surface(s), orientation of, positive      13
Surface(s), oriented      13
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