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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 |
Lower Darboux integral (156) 415
Lower semicontinuous (119)
Lower sum 152 394
Ludolph van Ceulen 613
Ludolph's number 613
Machin, John 616
Manifold, smooth 487
Map, bijective 15
Map, injective 13
Map, surjective 12. See also function
Mass of planar region (473)
Mass of rod 470
Matrix, product 298
Matrix, rank of 299
Matrix, representation of linear function 299
Maximum norm 207
Maximum of a continuous function on a compact set 117 252
Maximum, relative See extreme values
Mean-value theorem of differential calculus 130 344
Mean-value theorem of differential calculus, Cauchy's 132
Mean-value theorem of integral calculus 179 412
Mean-value theorem of integral calculus, second 180
Metric space 208
Metric space, complete 223
Minimum of a continuous function on a compact set 117 252
Minimum, relative See extreme values
Minkowski inequality (391)
Minkowski, Hermann 391
Moebius strip 508 557
Moebius, A.F. 508
Moment of arc (519)
Moment of patch (523)
Moment of planar region (473)
Moment of rod 471
Monotonic function 162
Monotonic sequence 68
Moser, Leo 210
Multiple integrals 392ff
Multiple integrals, transformation of 432 457
Multiplication, Cauchy 596
Multiplication, cross 503
Multiplication, dot 202
Multiplication, matrix 298
Multiplication, wedge 528
Multiplicative identity 21
Multiplicative inverse 21
Multiplier rule 387
n-space, Cartesian 198
n-space, Euclidean 209
nabla 533
Natural logarithm 187 609
Neighborhood 80 211
Neighborhood, deleted 80 211
Nested-interval property 75 216
Niven, Ivan 616n 661
Nonlinear equations, solution of 363 370 374 377
Norm 205
Norm of partition 161
Norm, Chebyshev 207
Norm, Euclidean 206
Norm, maximum 207
Normal vector 505
Normed vector space 205
Null sequence 66
Null space of linear function 303
Number line 73
Numbers, algebraic irrational 47
Numbers, cardinal 48ff
Numbers, complex (22)
Numbers, irrational 46
Numbers, natural 20
Numbers, rational 21
Numbers, real 30
Numbers, transcendental 47
One-form in  526
One-to-one and onto function 15 371ff
One-to-one and onto function, linear 305
One-to-one function 13 359ff
One-to-one function, linear 305
Onto function 12 366ff
Onto function, linear 301 309
Open cover 109 249
Open intervals in 216
Open intervals in R 4
Open sets 101 212
Open sets, intersection of 104 213
Open sets, representation as union of neighborhoods (107) 213
Open sets, union of 104 105 213
Open, relatively 245
Order relation 24
Ordered field 23
Ordered n-tuple 198
Ordered pair 9
Orientable curve 502
Orientable surface 507
Orientation of boundary 544 547 562
Orientation of curve 500 501
Orientation of curve with respect to containing plaster 552
Orientation of k-dimensional plaster in 524
Orientation of surface 506
Orientation-preserving diffeomorphism 501
Orientation-reversing diffeomorphism 501
Oriented volume integral 532
Outer Jordan content 405
Outward normal 508
Paraboloid 484
Parallelogram, Jordan content of 421
PARAMETER 474 481
Parameter, elimination of (492)
Parameter, representation of curve 474
Parameter, representation of plaster 486
Parameter, representation of surface 481
Parameter, transformation, bijective 478
Parametrization 474 481 486
Parametrization, injective 478
Partial derivatives 321
Partial derivatives of higher order 347
Partial derivatives, interchange of order of differentiation 349
Partial sum 70 566
Partition 151 393
Partition, norm of 161
Partition, refinement of 151 394
Patch 511
Peano curves 440
Peano, Giuseppe 440
Plane curve 474
Plaster 486
Plastered manifold 487
Pointwise convergence of sequence 265
Pointwise convergence of series 599
Polar coordinates 227 435
Position vector 199
Positive class 24
Positive side of surface 506
Potential function 536
Power series 603
Power series representation of Bessel functions (607)
Power series representation of cosh 610
Power series representation of cosine 612
Power series representation of exponential function 607
Power series representation of inverse sine (616) (627)
Power series representation of inverse tangent 615
Power series representation of natural logarithm 606
Power series representation of sine 612
Power series representation of sinh 610
Power series representation of tangent 620
Power series, absolute convergence of 603
Power series, division of 620
Power series, multiplication of 619
Power series, termwise differentiation of 604
| Power series, termwise integration of 604
Power series, uniform convergence of 603
Power set (54)
Pre-Hilbert space 210
Product of infinite series 596
Product of power series 619. See also multiplication
Proper fraction 46
quilt 513
Radius of convergence 604
Range of function 11
Range of linear function 298
Rank of linear function 298
Rank of matrix 299
Ratio Test 581
Rational numbers 21
Real numbers 30
Real numbers as complete ordered field 28ff
Real numbers as limits of irrational sequences 79
Real numbers as limits of rational sequences 79
Real numbers, representation by decimals 37
Rearrangement of series 576 579
Rectangle, area measure of 146ff
Refinement of partition 151 394
Regular curve 514
Regular surface 514
Relation 10
Relative maximum, minimum See extreme values
Relatively closed set 246
Relatively open set 245
Remainder in Taylor's theorem 623
Remainder in Taylor's theorem, Cauchy's form 623
Remainder in Taylor's theorem, Lagrange's form 623
Removable discontinuity 92 (95)
Representation of derivative by Jacobian matrix 325
Respectable set 8
Restriction of a function (14)
Riemann condition 157 396
Riemann integral See integral.
Riemann — Stieltjes integral See Stieltjes integral.
Riemann's zeta function (574)
Riemann, Bernhard 154
Right inverse of linear function 302
Right-sided derivative (123)
Right-sided limit (87)
Ritt, J.F. 44n
Robbins, H. 549n
Rolle's theorem 130
Rolle, Michael 130
Root test 581
Russell paradox 7
Russell, Bertrand 7
Scalar multiplication in  199
Schneider, Th. 47
Schoenberg's space filling curve 438
Schoenberg, Isaac J. 438
Schwarz, Hermann Amandus 202
Second (iterated) derivative (135)
Semiclosed interval 4
Semicontinuous function (119)
Semiopen interval 4
Sequence in 218
Sequence in R 58
Sequence of functions 265ff
Sequence of functions, pointwise convergence of 265
Sequence of functions, termwise differentiation of 291
Sequence of functions, termwise integration of 288
Sequence of functions, uniform convergence of 271
Sequence, Cauchy 221
Sequence, constant 59
Sequence, decreasing 68
Sequence, increasing 68
Sequence, limit of 58
Sequence, monotonic 68
Series of functions 598ff
Series of functions, absolute convergence of 598
Series of functions, pointwise convergence of 598
Series of functions, termwise differentiation of 600
Series of functions, termwise integration of 600
Series of functions, uniform convergence of 598
Series, absolutely convergent 574
Series, alternating 572
Series, conditionally convergent 574
Series, double 591
Series, geometric 71
Series, harmonic 572
Series, multiples of 570
Series, power 603
Series, product of 570
Series, sums of 570
Series, Taylor 624
Set 1ff
Set of all cardinal numbers (55)
Set of excluded middle third 56
Set of Lebesgue measure zero 165 397
Set, bounded 30 217
Set, Cantor 56
Set, closed 102 212
Set, connected 255
Set, convex (257)
Set, derived 81
Set, disconnected 255
Set, empty 1
Set, equivalence 19
Set, intersection 4 6
Set, Jordan-measurable 405
Set, open 101 212
Set, power (54)
Set, respectable 8
Set, union 4 6
Set, universal 1
Simple closed curve 479
Simple curve 478
Simple surface 484
Simply connected set 549
Sink 564
Smooth curve 488
Smooth manifold 487
Smooth plaster See plaster
Smooth surface 488
Source 564
Source density 563
Space curve 474
Space filling curve 438
Space, Banach (278)
Space, complete 223
Space, Euclidean 209
Space, linear 200
Space, metric 208
Space, normed vector 205
Space, pre-Hilbert 210
Space, vector 200
Sphere 482
Spherical coordinates 227 436
Spivak, Michael 543n
Square summable sequences 588
Standard oriented solid 562
Standard patch 554
Standard position 524
Standard region 546
Standard surface 554
Steady flow 472 536 539
Stieltjes integral (160) (164) (177) (178) (181)
Stieltjes, Thomas Johannes 160
Stokes, G.G. 552
Stokes1 theorem 552ff 555
Strictly decreasing function 18
Strictly increasing function 18
Subcover, denumerable (110)
Subcover, finite 110 249
Subfield 26
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