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| Авторизация |
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| Sagan H. — Advanced Calculus of Real-Valued Functions of a Real Variable and Vector-Valued Functions of a Vector Variable |
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| Предметный указатель |
 , definition of 613
, irrationality of (628)
, 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  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  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 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
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