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Rudin W. — Principles of Mathematical Analysis
Rudin W. — Principles of Mathematical Analysis

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Название: Principles of Mathematical Analysis

Автор: Rudin W.

Аннотация:

This book is intended lo serve as a text for the course in analysis that is usually taken by advanced undergraduates or by first-year students who study mathematics.
The present edition covers essentially the same topics as the second one, with some additions, a few minor omissions, and considerable rearrangement. I hope that these changes will make the material more accessible amd more attractive to the students who take such a course.


Язык: en

Рубрика: Математика/Анализ/Учебники по элементарному анализу/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: third edition

Год издания: 1976

Количество страниц: 351

Добавлена в каталог: 14.10.2004

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\mathscr{C}''$-equivalence      280
$\pi$      183
$\sigma$-ring      301
Abel, N.H.      75 174
Absolute convergence      71
Absolute convergence of integral      138
Absolute value      14
Addition      see “Sum”
Addition formula      178
Additivity      301
Affine chain      268
Affine mapping      266
Affine simplex      266
Algebra      161
Algebra, self-adjoint      165
Algebra, uniformly closed      161
Algebraic numbers      43
Almost everywhere      317
Alternating series      71
Analytic function      172
Anticommutative law      256
ARC      136
Area dement      283
Arithmetic means      80 199
Artin, E.      192 195
Associative law      5 28 259
Axioms      5
Baire's theorem      46 82
Ball      31
Base      45
Basic form      257
Basis      205
Bellman, R.      198
Bessel inequality      188 328
beta function      193
Binomial series      201
Bohr — Mollerup theorem      193
Borel set      309
Borel-measurable function      313
Boundary      269
Bounded convergence      322
Bounded function      89
Bounded sequence      48
Bounded set      32
Brouwer's theorem      203
Buck, R.C.      195
Cantor set      41 81 138 168 309
Cantor, G.      21 30 186
cardinal number      25
Cauchy criterion      54 59 147
Cauchy sequence      21 52 82 329
Cauchy's condensation test      61
cell      31
Chain      268
Chain, affine      268
Chain, differentiable      270
Chain, rule      105 214
Change of variables      132 252 262
Characteristic function      313
Circle of convergence      69
Closed curve      136
Closed form      275
Closed set      32
Closure      35
Closure, uniform      151 161
Collection      27
Column matrix      217
Column vector      210
Common refinement      123
Commutative law      5 28
Compact metric space      36
Compact set      36
Comparison Test      60
Complement      32
Complete metric space      54 82 151 329
Complete orthonormal set      331
Completion      82
Complex field      12 184
Complex number      12
Complex plane      17
Component of a function      87 215
composition      86 105 127 207
Condensation point      45
conjugate      14
Connected set      42
Constant function      85
Continuity      85
Continuity uniform      90
Continuous functions, space of      150
Continuous mapping      85
Continuously differentiable curve      136
Continuously differentiable mapping      219
Contraction      220
Convergence      47
Convergence of integral      138
Convergence of sequences      47
Convergence of series      59
Convergence, absolute      71
Convergence, bounded      322
Convergence, dominated      321
Convergence, pointwise      144
Convergence, radius of      69 79
Convergence, uniform      147
Convex function      101
Convex set      31
Coordinate function      88
coordinates      16 205
Countable additivity      301
Countable base      45
Countable set      25
Cover      36
Cunningham, F.      167
Curl      181
Curve      136
Curve, closed      136
Curve, continuously differentiable      136
Curve, rectifiable      136
Curve, space-filing      168
Cut      17
Davis, P.J.      191
Decimals      11
Dedekind, R.      21
Dense subset      9 32
Dependent set      205
Derivative      104
Derivative of a form      260
Derivative of a transformation      214
Derivative of a vector-valued function      112
Derivative of an integral      133 236 324
Derivative of higher order      110
Derivative of power series      173
Derivative, directional      218
Derivative, integration of      134 324
Derivative, partial      215
Derivative, total      213
Determinant      232
Determinant of an operator      234
Determinant, product of      233
Diagonal process      30 157
Diameter      52
Differentiable function      104 212
Differential      213
Differential equation      119 170
Differential form      see “Form”
Differentiation      see “Derivative”
DIMENSION      205
Directional derivative      218
Dirichlet's kernel      189
Discontinuities      94
Disjoint sets      27
Distance      30
Distributive law      6 20 28
Divergence      281
Divergence theorem      253 272 288
Divergent sequence      47
Divergent series      59
Domain      24
Dominated Convergence Theorem      155 167 321
Double sequence      144
e      63
Eberlein, W.F.      184
Elementary set      303
Empty set      3
Equicontinuity      156
Equivalence relation      25
Euclidean space      16 30
Euler's constant      197
Exact form      273
Existence theorem      170
Exponential function      178
Extended real number system      11
Extension      99
Family      27
Fatou's theorem      320
Fejer's kernel      199
Fejer's theorem      199
Field axioms      5
Fine, N.J.      100
Finite set      23
Fixed point      117
Fixed point theorems      117 203 220
Fleming, W.H.      280
Flip      249
FORM      234
Form of class $\mathscr{C}'$, $\mathscr{C}''$      254
Form, basic      237
Form, closed      275
Form, derivative of      260
Form, exact      275
Form, product of      258 260
Form, sum of      256
Fourier coefficients      186 187
Fourier scries      186 187 328
Fourier, J.B.      186
Function      24
Function, absolute value      88
Function, analytic      172
Function, Borel-measurable      313
Function, bounded      89
Function, characteristic      313
Function, component of      87
Function, constant      85
Function, continuous      85
Function, continuous from left      97
Function, continuous from right      97
Function, continuously differentiable      104 212
Function, convex      101
Function, decreasing      95
Function, differentiable      104 212
Function, exponential      178
Function, harmonic      297
Function, increasing      95
Function, inverse      90
Function, Lebesgue-integrable      315
Function, limit      144
Function, linear      206
Function, logarithmic      180
Function, measurable      310
Function, monotonic      93
Function, nowhere differentiable continuous      154
Function, one-to-one      25
Function, orthogonal      187
Function, periodic      183
Function, product of      85
Function, rational      88
Function, Riemann-integrable      121
Function, simple      313
Function, sum of      85
Function, summable      315
Function, trigonometric      182
Function, uniformly continuous      90
Function, uniformly differentiable      115
Function, vector-valued      85
Fundamental theorem of calculus      134 324
Gamma function      192
Geometric series      61
Gradient      217 281
Graph      99
Greatest lower bound      4
Green's identities      297
Green's theorem      253 255 272 282
Half-open interval      31
Harmonic function      297
Havin, V.P.      113
Heine — Borel theorem      39
Helly's selection theorem      167
Herstein, I.N.      65
Hewitt, E.      21
Higher-order derivative      110
Hilbert space      332
Holder's inequality      139
i      13
Identity operator      232
Image      24
Imaginary part      14
Implicit function theorem      224
Improper integral      139
Increasing index      357
Increasing sequence      55
Independent set      205
Index of a curve      201
Infimum      4
Infinite series      59
Infinite set      25
infinity      11
Initial-value problem      119 170
Inner product      16
Integrable functions, spaces of      315 326
Integral test      139
Integral, countable additivity of      316
Integral, differentiation of      133 236 324
Integral, Lebesgue      314
Integral, lower      121 122
Integral, Riemann      121
Integral, Stiertjes      122
Integral, upper      121 122
Integration of derivative      134 324
Integration, by parts      134 139 141
Interior      43
Interior point      32
Intermediate value      93 100 108
Intersection      27
interval      31 302
INTO      24
Inverse function      90
Inverse function theorem      221
Inverse image      24
Inverse mapping      90
Inverse of linear operator      207
Invertible transformation      207
Irrational number      1 10 65
Isolated point      32
Isometry      82 170
Isomorphism      21
Jacobian      234
Kellogg, O.D.      281
Kestelman, H.      167
Knopp, K.      21 63
l'Hospital's rule      109 113
Landau, E.G.H.      21
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