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Cohen G.L. — A Course in Modern Analysis and Its Applications
Cohen G.L. — A Course in Modern Analysis  and Its Applications

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Название: A Course in Modern Analysis and Its Applications

Автор: Cohen G.L.

Аннотация:

Designed for one-semester courses at the senior undergraduate level, this book is written for mathematics students and teachers, as well as others needing to learn mathematical analysis for engineering, physics, biology or finance. Nominal divisions between pure and applied mathematics have been merged to provide easier access. Applications are included from differential and integral equations, systems of linear algebraic equations, approximation theory, numerical analysis and quantum mechanics.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2003

Количество страниц: 333

Добавлена в каталог: 05.12.2009

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$C^{'}[a, b]$      246
$C^{(1)}[a, b]$      74
$C^{w}[a, b]$      265
$C_{1}[a, b]$      94 178
$C_{2}[a, b]$      94 178 255
$L_{1}$      92
$L_{2}$      90 175 177 255
$l_{P}$      92
$T_{1}$-space      173
$\aleph_{0}$      19
$\delta$-neighbourhood      20
$\epsilon$-net      152
$\mathbf{c}$      19
$\mathbf{C}^{n}$      8 72 80 90 177 254
$\mathbf{M}$      5
$\mathbf{Q}$      5 17
$\mathbf{R}$, $\mathbf{R}_{+}$      5 17
$\mathbf{R}^{n}$      8 72 80 87 177 254
$\mathbf{Z}$      5
Absolute value      4 54
Adjoint      285
Annihilator      279
Approximation theory      149 192 280 283
Arzela      148
Ascoli's theorem      146
B(x, y)      215
Banach space      178
Basis      75 294
Basis, orthonormal      295
Bernstein polynomials      202
Bessel's inequality      270 299
Best approximation      150 194 268
Bijection      11
Binomial coefficient      51
Binomial theorem      51 201
Bolzano — Weierstrass property      162
Bolzano — Weierstrass theorem      23
Bolzano — Weierstrass theorem for sequences      40
Bounds, lower and upper      21 35
C      73
cardinal number      19
Cartesian product      7
Cauchy convergence criterion      41 45
Cauchy sequence      101 178
Cauchy — Schwarz inequality      88 96 256 257
Chebyshev norm      195
Chebyshev polynomials      198 266
Chebyshev polynomials of the second kind      267
Chebyshev theory      195
Closed disc      108
Closed set      28 107 156
Closure      157
Cluster point      22 35 159
Cluster point, greatest, least      25 36
Collection      29
Compactness      29 141
Compactness, countable      162
Compactness, relative      141
Comparison Test      48
Complement      7
Complete orthonormal set      295
Completeness      4 25 42 47 57 102 179
Complex number      5
Condition number      239
conjugate      5 80
Connectedness      169
Continuum Hypothesis      19
Contraction constant      116
Contraction mapping      116
Convergence in mean square      303
Convergence of a sequence      36 43 98 164 178
Convergence of a series      45 179
Convergence, absolute      46 179
Convergence, pointwise      60
Convergence, strong      308
Convergence, uniform      59
Convergence, weak      308
Countability      14
C[a, b]      59 73 93 177
De Morgan's laws      9
Definite integral      58 65
Derivative      57
Derived set      159
Determinant      82
Diameter      110
Differential equations      58 123 129
DIMENSION      75
Distance function      85
Distributive laws      235
Domain      10
Double integral      58
Dual space      219 282
Economisation of power series      206
Eigenvalue, eigenvector      225 286
Empty set      6 8
Equal-ripple property      197
Equicontinuity      145
Equivalent norms      189
Error      237
Euclidean space      87 252
Finite differences      153
Fixed point      116
Fixed point theorem      116 152
Fourier coefficients      299
Fourier series      58 298 299
Fourier series theorem      297 299
Fredholm integral equation      126 243
Functional      13 218
Functional analysis      3
Functions      10 52 see
Functions, bounded      55
Functions, complex-valued      58
Functions, composition of      13
Functions, constant      54
Functions, continuous      52 53
Functions, identity      14
Functions, inverse      13
Functions, one-to-one      11
Functions, onto      11
Functions, uniformly bounded      145
Functions, WEIGHT      265
Gram matrix      280
Gram — Schmidt orthonormalisation process      261
Graph      52 222
Greatest lower bound      21 35
Greatest-integer function      53
Hamel base      295
Harmonic series      46
Hausdorff space      160
Heine — Borel theorem      31
Heisenberg      282
Heisenberg's uncertainty principle      249
Hermite polynomials      267
hilbert      282
Hilbert space      281
Hoelder inequality      89
Homeomorphism      167
Image      11 164
Image, inverse      164
Imaginary part      5
Infimum      22
Injection      11
Inner product      252
Inner product space      252
INTEGER      4
Integral equations      2 137
Integral equations, Fredholm      126 243
Integral equations, nonlinear      133
Integral equations, Volterra      127 229
Interior      157
Intersection      7
Intervals      20
Irrational number      4
Isomorphism      74 305
Jacobi polynomials      267
Kernel      220
Laguerre polynomials      267
Least squares approximation      195 267
Least upper bound      21 35
Least Upper Bound Axiom      26
Lebesgue integral      281
Legendre polynomials      264
LIMIT      36 98
Limit Comparison Test      51
Limit, greatest, least      26 36
Limit, inferior, superior      36
Limit, point      26 159
Lindeloef's theorem      171
linear combination      75
Linear dependence      75 260
Linear mapping      210
Linear space      70
Lipschitz condition      118
M      111
MAP      13
Mappings      13 113 see
Mappings, additive      236
Mappings, affine      228
Mappings, bounded      210
Mappings, closed      222
Mappings, continuous      115 164 165
Mappings, contraction      116
Mappings, homogeneous      236
Mappings, identity      114 213
Mappings, ill-conditioned      239
Mappings, inverse      225
Mappings, linear      210
Mappings, momentum      249
Mappings, perfectly conditioned      239
Mappings, perturbation      130
Mappings, position      249
Mappings, product of      113 231
Mappings, unitary      308
Matrix      79
Matrix, hermitian      287
Matrix, inverse      82 241
Matrix, symmetric      288
Maximum, minimum      21 35
Metric      85 176
Metric space      44 85
Metric space, closed      107
Metric space, complete      102
Metric topology      157
Metric, associated      177
Metric, chordal      92
Metric, discrete      94
Metric, Euclidean      87
Metric, homogeneous      185
Metric, induced      177
Metric, natural      86
Metric, sup      92
Metric, translation invariant      185
Metric, trivial      94
Metric, uniform      92
Minimax approximation      151 195
Minkowski inequality      89
Modulus      5
Moments      204
Neighbourhood      20 159
Nested intervals axiom      25 42 47
Newton's method      115
Norm      175 256
Norm of a functional      219
Norm of an operator      216
Norm, Chebyshev      195
Norm, cubic      185
Norm, matrix      242
Norm, octahedral      185
Normal equations      271
Normed space      176
Normed space, strictly convex      193 268
Null set      6
Null space      220
Numerical analysis      131 153 235
Observables      249
One-to-one correspondence      14
Open ball      158
Open base      170
Open covering      30 161
Open covering, countable      162
Open set      28 156
Operator      13 211
Operator, adjoint      285
Ordered pair      6
Orthonormal set      259
Orthonormal set, complete      295
Orthonormal set, total      299
Parallelogram law      257
Parseval's identities      299
Perturbation      130 237
Picard's theorem      123
Point set      20
Polarisation identity      278
Pre-Hilbert space      252
Preimage      164
Probability density function      204
Pythagorean identities      278
quantum mechanics      248 282
RANGE      11
Ratio Test      50
Rational number      4
Real number      4
Real part      5
Restriction      107
Riemann integral      58
Riemann — Lebesgue lemma      303
Riesz representation theorem      273 282
Riesz — Fischer theorem      305
Riesz — Frechet theorem      275
Root test      51
Rubber sheet geometry      168
S      97
scalar      69
Scalar, multiple      70
Scalar, product      251 252
Schroedinger      282
Second axiom of countability      170
Self-adjoint operator      285
Semimetric space      97
Seminorm      187
Separability      288
Separation      161 169
SEQUENCE      33
Sequence, Cauchy      101 178
Sequence, complex-valued      42
Sequence, convergent      36 43 98 164 178
Sequence, decreasing, increasing      38
Sequence, monotone      38
Sequence, uniformly convergent      60
Series      45
Series, absolutely convergent      46 179
Series, conditionally convergent      46
Series, geometric      49 229
Series, harmonic      46
Series, uniformly convergent      67
Sets      3
Sets, bounded      21 110
Sets, closed      28 107 156
Sets, compact      29 143 161 178
Sets, countable      15
1 2
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