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Sagan H. — Advanced Calculus of Real-Valued Functions of a Real Variable and Vector-Valued Functions of a Vector Variable
Sagan H. — Advanced Calculus of Real-Valued Functions of a Real Variable and Vector-Valued Functions of a Vector Variable

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Название: Advanced Calculus of Real-Valued Functions of a Real Variable and Vector-Valued Functions of a Vector Variable

Автор: Sagan H.

Язык: en

Рубрика: Математика/Анализ/Тензорный анализ, формы/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1974

Количество страниц: 671

Добавлена в каталог: 15.04.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\pi$, definition of      613
$\pi$, irrationality of      (628)
$\pi$, series representation of      615 (616) (627)
a.e      See almost everywhere
Absolute convergence of double series      591
Absolute convergence of power series      603
Absolute convergence of series      574
Absolute convergence of series of functions      599
Absolute convergence, tests for      580 581 584 592
Absolute value      25
Accumulation point      80 211
Additive function      138
Additive identity      21
Additive inverse      21
Aleph      49
Algebraic irrational numbers      47
Almost everywhere      168
Almost nowhere      168
Alternating series      572
Analytic function      624
Antiderivative      185
Apostol, T.      597n
Approximation of continuous functions by piecewise linear functions      (281)
Approximation of continuous functions by polynomials      279
ARC      514
Arc length      515
Archimedean field      (28) 34
Archimedes of Syracuse      149
Archimedes' number      613
Area measure      144
Area measure of patch      521
Area measure of rectangle      146ff
Area measure of regular surface      521
Area measure of triangle      147
Area measure of triangulated point sets      147
Area measure, monotonicity of      144
Area measure, properties of      144 465
Area under a curve      156
Arithmetic mean      389
Ascoli, Giulio      (278)
Ascoli, Giulio, lemma of      (278)
Ball, n-dimensional, Jordan content of      465
Banach, Stephen      (278)
Banach, Stephen, space      (278)
Basis for $R^n$      201
Bernoulli numbers      620
Bernoulli, Jakob      620
Bernstein polynomials      278
Bernstein, Serge N.      278
Bessel, Friedrich Wilhelm      (429)
Bessel, Friedrich Wilhelm, equation      (429) (607)
Bessel, Friedrich Wilhelm, functions      (429) (607)
beta function      (429)
Bijection      See bijective parameter transformation
Bijective map      15
Bijective parameter transformation      478 485
Binary representation      (32)
Binomial series      624
Bolzano, Bernard      107
Bolzano-compact set      108
Bolzano-Weierstrass Theorem      107 217
Borel, Emile      109
Bound, greatest lower      30
Bound, least upper      30
Bound, lower      29
Bound, upper      29
Boundary of patch      511
Boundary of point set      401
Boundary point      401
Boundary, oriented      544 552 562
Bounded function      152
Bounded sequence      61 220
Bounded set      29 143 217
Brouwer, L.E.J.      259
Brouwer, L.E.J., fixed-point theorem of      259
Buniakovskii, Victor      202
Byrd, P.F.      518n
Cantor set      56
Cantor, Georg      1 48
cardinal number      48ff
Cardinal number, transfinite      49
Cardinality of      57
Cardinality of set of algebraic irrational numbers      52
Cardinality of set of integers      49
Cardinality of set of positive integers      49
Cardinality of set of rational numbers      51
Cardinality of set of real numbers      53
Cardinality of set of transcendental numbers      (54)
Cardioid      435
Cartesian n-space      198
Cartesian n-space, addition in      199
Cartesian n-space, scalar multiplication in      199
Cartesian product      9 198
Cartesian product of Euclidean n-spaces      209 214
Cartesius      See Descartes
Cat's tail      512
Cauchy Criterion for Convergence      223
Cauchy principal value      (194) (195)
Cauchy product      596
Cauchy product of power series      619
Cauchy sequence      221
Cauchy sequence of functions      270
Cauchy sequence of functions, uniformly convergent      273
Cauchy — Buniakovskii — Schwarz inequality      202
Cauchy — Hadamard rule      605
Cauchy, Augustin-Louis      132
CBS inequality      202
CBS inequality for integrable functions      204
CBS inequality for square summable sequences      590
Centroid of arc      (519)
Centroid of patch      (523)
Centroid of planar region      (473)
Centroid of rod      471
Chain rule      125 339
Change of integration variable      186 457
Characteristic function      404
Chebyshev, Pafnuti L.      207
Chebyshev, Pafnuti L., norm      207
circle      474
Circle, length of      517
Circulation      539
Circulation, density      550 559
Closed curve      479
Closed intervals in $E^n$      216
Closed intervals in R      4
Closed sets      102 212
Closed sets, intersection of      104 105 213
Closed sets, relatively      246
Closed sets, union of      104 105 213
Compact sets      110 250
Compact sets with Jordan content zero      408
Compact sets, continuous image of      116 252
Compact-in-itself set      108
Comparison test for convergence of series      580
Comparison test for improper integrals      192
Complement of set      3
Complement of set intersection      6
Complement of set union      6
Complete metric space      223
Complete ordered field      30
Complete ordered field, existence and uniqueness      41ff
Complete ordered field, representation by decimals      37
complex numbers      (22)
components of vector      199
Composite function      124 241
Condensation test      (574)
Condensation test of      (574)
Condensation test of, mean-value theorem of      132
Condensation test of, remainder of      623
Conditional convergence      574
Cone      483
Congruent point sets      143 465
Connected set      255
Connected set, continuous image of      257
Conservative force field      536
Constant sequence      58
Constraint      386
Content of interval      393. See also Jordan content
Continuity of      241
Continuity of a function at accumulation point      91 231
Continuity of a function at isolated point      92 231
Continuity of a function at point      91 231
Continuity of a function on set      93 246
Continuity of a function, almost everywhere      168 398
Continuity of a function, global characterization of      246
Continuity of composite function      241
Continuity of, derivative of      125 339
Continuity of, domain of      241
Continuity of, limit of      (243)
Continuous function, approximation by piecewise linear functions      (281)
Continuous function, approximation by polynomials      279
Continuous function, global characterization of      246
Continuous function, product of      99
Continuous function, quotient of      100
Continuous function, sum of      99
Continuous functions      91 231
Continuous image of compact set      116 252
Continuous image of connected set      257
Continuous image of interval      258
Continuum      53
Contraction mapping theorem      263
Convergence of double series      591
Convergence of power series      603
Convergence of sequence      58 218
Convergence of sequence of functions      265
Convergence of series      70 566
Convergence of series of functions      598
Convergence of Taylor series      624 (628)
Convex set      (257)
Countable set      See denumerable set.
Courant, R.      549n
Covering      See open covering
Cross product      503
Curl      533
Curve      474ff
Curve space      474
Curve space filling      438
Curve, parametrization of      474
Curve, plane      474
Curve, simple      478
Curve, simple, closed      479
Cusp      479
Cut      See Dedekind cut.
Cycloid      476
Cylindrical coordinates      (437)
Darboux integral, lower      (156) 415
Darboux integral, upper      (156) 415
Darboux, Gaston      136
Decimals      36ff
Decreasing function      162
Decreasing function, strictly      18
Decreasing sequence      68
Dedekind cut      C6)
Dedekind, Richard      36
Definite integral      See integral.
Deleted neighborhood in $E^n$      211
Deleted neighborhood in R      80
DeMorgan's law      6
DeMorgan, Augustus      6
Dense set, everywhere      81
Denumerable set      50
Dependence, linear      297
Derivative of composite function      125 339
Derived set      81 211
Descartes, Rene      9
Devinatz, A.      332n 597n
Diagonal series      593
Diffeomorphism      492
Diffeomorphism, orientation-preserving      501
Diffeomorphism, orientation-reversing      501
Differentiability of limit of sequence      291 292
Differentiability of sum of series      600
Differentiable function      120 312
Differential      139 315 326
Differential form      526ff
Differential of k-form      542
Differentiation, implicit      382. See also derivative
Dimension of vector space      297
Direct image      234
Direct image of complement      237
Direct image of intersection      237
Direct image of inverse image      235
Direct image of union      236
Direct image under composite function      241
Directional      318
Directional derivative      318
Directional of dot product of functions      334
Directional of higher order      (135)
Directional of integral with respect to parameter      425 426
Directional of inverse function      126 132 342
Directional of product of functions      123 334
Directional of quotient of functions      123 334
Directional of real-valued function of real variable      120
Directional of vector-valued function of vector variable      312
Directional, existence of      239
Directional, intermediate-value property of      136
Directional, left-sided      (123)
Directional, partial      321 347
Directional, representation of      325
Directional, right-sided      (123)
Directional, second      (135)
Directional, uniqueness of      313
Dirichlet function      156 158
Dirichlet test      (587)
Dirichlet, Peter Gustav Lejeune      156
disconnected set      255
disconnection      255
Discontinuity, infinite      92 (95)
Discontinuity, jump      92 (95)
Discontinuity, removable      92 (95)
Discrete metric      See distance between apples
Disjoint sets      4
Distance      208
Distance between apples      209
Distance between people      210
Divergence of sequence      60
Divergence of vector field      533
Domain of a function      11
Dot product      202
Double integral, transformation of      432 457
Double integration, by iteration      421
Double sequence      590
Double series      591
Double series, absolute convergence of      591
e as limit of a sequence      (611)
e as sum of a series      609
e, irrationality of      (628)
Edge of patch      552
Elementary linear functions (transformations)      446
Elementary transcendental functions      616
Elimination of parameter      (492)
Empty set      1
Equicontinuity      (277)
Equivalent parametrization of curves      478
Equivalent parametrization of plasters      494
Equivalent parametrization of surfaces      484
Equivalent sets      19
Euclid      206
Euclidean distance      209
Euclidean n-space      209
1 2 3 4
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