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Bartle R.G. — The Elements of Real Analysis
Bartle R.G. — The Elements of Real Analysis

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Название: The Elements of Real Analysis

Автор: Bartle R.G.

Аннотация:

Presents the basic theory of real analysis. The algebraic and order properties of the real number system are presented in a simpler fashion than in the previous edition.


Язык: en

Рубрика: Математика/Анализ/Учебники по элементарному анализу/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1967

Количество страниц: 447

Добавлена в каталог: 20.10.2004

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Abel summability      416
Abel's lemma on partial summation      397
Abel's test for convergence      398
Abel's test for uniform convergence      407
Abel's theorem      415
Abel, N.H.      397
Absolute convergence of a series      378
Absolute convergence of an integral      351
Absolute value in an ordered field      38
Absolute value of a complex number      96
Absolute value of a function      153
Accumulation point      73
Additive function      158
Alternating series      399
Angle between two vectors      62
Appell, P.      419
Approximation theorems      177—186
Archimedean field      40
Archimedes      40
Arithmetic mean      67 272
Arzela — Ascoli theorem      191
Arzela, C.      191
Ascoli, G.      191
Axiom of Choice      26
Baire's theorem      90
Baire, R.      90
Ball in a Cartesian space      64
Bernoulli's inequality      44
Bernoulli, J.      44
Bernstein's approximation theorem      182
Bernstein's theorem      414
Bernstein, S.N.      180
Bessel, F.W.      213
beta function      371
Bilinearity of the Riemann — Stieltjes integral      280
Binary operation      28
Binominal expansion      419
Bolzano intermediate value theorem      162
Bolzano — Weierstrass theorem for sequences      115
Bolzano — Weierstrass theorem for sets      76
Bolzano, B.      75
Bonnet, O.      305
Borel, E.      85
Bound, lower      47
Bound, upper      47
Boundary point      83 324
Bounded convergence theorem      288
Bounded set in a Cartesian space      75
Bounded variation      283
Bunyakovskii, V.      61
Cantor intersection theorem      88
Cantor set      51
Cantor, G.      25
Cartesian product      9
Cartesian spaces      59—69
Category      90
Cauchy condensation test      386
Cauchy convergence criteria      117 130 140 279 321 345 352 378 407
Cauchy mean value theorem      210
Cauchy principal value      343 345
Cauchy product      384
Cauchy root test      388
Cauchy sequences      115 121
Cauchy — Bunyakovskii — Schwarz inequality      61—62 297
Cauchy — Hadamard theorem      410
Cauchy, A.L.      61
Cesaro's method of summation      137
Cesaro's theorem      387
Cesaro, E.      137
Chain rule      235
Change of variable      305
Characteristic zero      32
Chebyshev's inequality      69
Chebyshev, P.L.      69
Choice, axiom of      26
Circumscribing contour theorem      90
class      1
Class C'      250
Closed set      71—72
Cluster point      73
Collection      1
Compact set      84
Compactness, preservation of      163
Comparison tests      346—347 388
Complete Archimedean field      45 121
Complex number system      94—97
Components of a vector      59
Conditional convergence      387
Conjugate of a complex number      94
Connected set      77
Connectedness, preservation of      162
Constraint      266
Content of a set      325
Content of an interval      316
Content, zero      317
Continuity      146—175 especially
Continuity of the inverse function      166
Continuity, one-sided      278
Continuity, uniform      166
contour      90
Contraction      169—170
Convergence in a metric space      110
Convergence of a sequence      100
Convergence of a sequence of functions      122
Convergence, absolute      351 378
Convergence, interval of      409
Convergence, radius of      409
Convergence, uniform      126 352 406—407 411
Convex function      224
Convex set      66
Coordinates of a vector      59
Correspondence      24
Countable set      23
Covering      84
Critical point      262
Curve, polygonal      80
Curve, space-filling      319
Cut      50
D'Alembert, J.      390
Darboux's theorem      219
Darboux, G.      211
de Moivre, A.      300
De Morgan's laws      9 11
De Morgan, A.      8
Dedekind, R.      50
Density of the rational elements      41
Denumerable set      23
Derivative      206—249 especially 228
Derivative, directional      225
Derivative, partial      226
Descartes, R.      9
Diagonal method      25—26 193
Difference of two functions      153
Difference of two sequences      99
Differentiable functions      227
Differentiation theorem for integrals      301
Differentiation theorem for power series      411
Dini, U.      194
Direct image      19
Directional derivative      225
Dirichlet's discontinuous function      150
Dirichlet, P.G.L.      150
Diriehlet's test for convergence      347 397
Diriehlet's test for uniform convergence      353 407
Discrete metric      67
Disjoint sets      5
Divergence of a sequence      100
Domain of a function      13
Dominated Convergence Theorem      359
Dot product      61
Double limit      139
Double sequences      139 ff.
Double series      381 ff.
Element of a set      1
Equicontinuity      190
Euler, L.      248
Exponential function      56 174 220 420
Extension of a continuous function      187
Extreme point      66
Fejer, L.      138
Field      28—34 especially
Field, Archimedean      40
Field, ordered      34—45 especially
figure      337
Finite set      23
First mean value theorem      301 303
Fixed points      170—172
Flyswatter principle      109
Fresnel integral      349
Fresnel, A.      349
Frobenius, G.      420
Function      11—22 especially
Function, absolute value of      38
Function, additive      158
Function, Beta      371
Function, bounded variation      283
Function, Class C'      250
Function, composition of      16
Function, continuous      146
Function, convex      224
Function, derivative of      207 228
Function, differentiable      227
Function, direct image of      19
Function, domain of      13
Function, exponential      56 174 220 420
Function, Gamma      350 371
Function, harmonic      271
Function, homogeneous      248
Function, hyperbolic      223
Function, inverse      17—18
Function, inverse image of      20
Function, Laplace transform of      372
Function, linear      154
Function, logarithm      56 221 314
Function, non-differentiable      208
Function, piecewise linear      178
Function, polynomial      186
Function, positively homogeneous      248
Function, range of      13
Function, semi-continuous      202
Function, step      177
Function, trigonometric      222 315 420
Fundamental theorem of algebra      96
Fundamental theorem of integral calculus      302
Gamma function      350 371
Gauss, C.F.      96
Geometric mean      67 272
Geometric series      378
Global continuity theorem      160
Gradient      247
Hadamard, J.      410
Half-closed interval      39
Half-open interval      39
Hardy, G.H.      344
Harmonic function      271
Harmonic series      119 379
Heine — Borel theorem      84—94
Heine, E.      85
Hoelder's inequality      68—69 215 272
Hoelder, O.      68
Homogeneous function      248
Hyperbolic function      223
Hypergeometric series      403
Identity element of a field      28
Imaginary part of a complex number      94
Implicit function theorem      260 273
Improper integrals      341 ff.
Inequalities, basic properties of      34—37
Inequality, arithmetic-geometric      67 272
Inequality, Bernoulli      44
Inequality, C.—B.—S. (Cauchy — Bunyakovskii — Schwarz)      61—62 297
Inequality, Chebyshev      69
Inequality, Hoelder      68—69 215 272
Inequality, Minkowski      69 273
Inequality, triangle      38 64
Infimum      47
Infinite integral      344 ff.
Infinite product      403—405.
Infinite series      375—421
Infinite sets      23
Inner product      61 297
Integrability theorems      283 323—324
integral      274—374
Integral test, for series      393
Integral, infinite      344 ff.
Integral, iterated      328 ff.
Integral, lower      298—299
Integral, partial      343
Integral, transformation of      331 ff.
Integral, upper      298—299
integrand      277
Integration, by parts      282 304
Integrator      277
Interchange theorems, relating to continuity      175—176 306 355 406
Interchange theorems, relating to differentiation      217 243 307 356 406 411
Interchange theorems, relating to infinite integrals      355—356 358—367
Interchange theorems, relating to integration      285—289 306—308 355 406
Interchange theorems, relating to sequences      175—176 217 285—289 358—360
Interchange theorems, relating to series      406 411
Interior maximum      209
Interior point      73
Intermediate Value Theorem      162
Intersection of sets      4 7
Interval of convergence of a series      409
Interval, in a Cartesian space      74
Interval, in an ordered field      39
Interval, unit      4
Inverse function      17—19 166
Inverse image      20
Inversion mapping      97
Inversion theorems      252 256
Irrational elements of a field      33
Irrational powers of a real number      56
Isomorphism      46
Iterated integrals      328 ff.
Iterated limits      140 143
Iterated suprema      54
Jacobi, C.G.J.      232
Jacobian determinant      232
Jacobian theorem      334
Jerrard's series      378
Kronecker, L.      46
l'Hospital, G.F.      215
Lagrange identity      68
Lagrange method      267
Lagrange multiplier      266
Lagrange, J.-L.      68
Landau, E.      135
Laplace transform      372
Laplace, P.-S.      372
Least squares      271
Lebesgue covering theorem      89
Lebesgue integral      274
Lebesgue number      89
Lebesgue, H.      89
Leibniz's alternating series test      399
Leibniz's formula      230
Leibniz, G.W.      230
Length of a vector      61
Limit of a double sequence      139
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