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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
Euclidean norm      206
Euler's constant      47 (574)
Euler, Leonhard      609 613n
Everywhere dense set      81
Exponential function      607ff
Extreme values, relative, constrained      386 387
Extreme values, relative, of real-valued function of real variable      129 (135)
Extreme values, relative, of real-valued function of vector variable      384 (390)
FIE      See fundamental inequality
Field      21
Field, Archimedean      (28) 34
Field, complete ordered      30
Field, ordered      24
Finite intersection property      (251)
Finite set      49
Finite subcover      110 249
First fundamental form      (502)
Fixed point of contraction mapping      263
Fixed point theorem, Brouwer's      259
Flow, steady, of incompressible fluid      472
Force field      534
Friedman, M.D.      518n
Fubini's theorem      417
Fubini's theorem, applications of      420ff
Fubini, Guido      415
Function      10
Function, additive      138
Function, composite      124 241
Function, continuous      91 231
Function, continuous, almost everywhere      168 398
Function, continuous, nowhere differentiable      284
Function, decreasing      162
Function, decreasing, strictly      18
Function, derivative of      120 312
Function, domain of      11
Function, homogeneous      138
Function, increasing      162
Function, increasing, strictly      18
Function, inverse      14 371ff
Function, limit of      85 229
Function, linear      138 296
Function, machine      11
Function, monotonic      162
Function, one-to-one      13 359ff
Function, one-to-one and onto      15 371ff
Function, onto      12 366ff
Function, range of      11
Function, real-valued, of a real variable      11
Function, real-valued, of a vector variable      226
Function, restriction of      (14)
Function, uniformly continuous      113 261
Function, value of      11
Function, vector-valued, of a real variable      226
Function, vector-valued, of a vector variable      226
Fundamental form, first      (502)
Fundamental inequality      219
Fundamental theorem of integral calculus      184
Fundamental vectors      201
Galois' Theorem      132
Galois, Evariste      132
Gamma function      193
Gamma function, value at $\frak{1}{2}$      462
Gauss' theorem      538 540 560ff 562
Gauss, Carl Friedrich      538
Gelfond, A.      47
Geometric mean      389
Geometric series      71
Global characterization of continuous functions      246
Global Lipschitz condition      263
Godement, R.      616n
Golden ratio      (70)
Gradient      533
Graph of a function      9
Greatest lower bound      30
Green's theorem      539 544ff 547
Green, George      539
Gregory, James      615
Hadamard, Jacques      605
Hardy, C.H.      290n
Harmonic function      (564)
Harmonic series      572
Heine — Borel property      110 249
Heine — Borel theorem      111 250
Heine, Edward      109
Helix      477
Hermite, Charles      47
Hilbert number      47
Hilbert space      589
Hilbert, David      210
Hoelder inequality      (391)
Hoelder, Otto      391
Homogeneous function      138
Hyperbolic functions      610
Hyperbolic functions, inverses of      611
Image, direct      234
Image, inverse      234
Implicit differentiation      382
Implicit function theorem      356 377
Improper integral of first kind      190
Improper integral of second kind      192
Improper limit of a function      90
Increasing function      162
Increasing function, strictly      18
Increasing sequence      68
Increasing sequence of functions      (277)
Indefinite integral      See integral with variable upper limit.
Independence, linear, of vectors      297
Indeterminate forms      133 134
Inequality, CBS      202
Inequality, fundamental      219
Inequality, Hoelder      (391)
Inequality, Minkowski      (391)
Inequality, triangle      25 179 205 208 412 590
inf      30
Inferior limit      583
Infinite discontinuity      92 (95)
Infinite series      See series
Injective map      13
Injective mapping theorem      362
Injective parametrizations of curves      478
Injective parametrizations of surfaces      485
Injective parametrizations, equivalence of      478 485
Inner product      202
Integers      20
Integrability condition      549
Integrability of bounded a.e. continuous functions      170 402 411
Integrability of bounded continuous functions      161 397
Integrability of derivative      184
Integrability of limit of sequence      287
Integrability of monotonic functions      162
Integrability of sum of series      600
Integral as additive set function      180 412
Integral on interval in R      155
Integral on Jordan-measurable set      411
Integral test      571
Integral with variable upper limit      182
Integral, Cauchy principal value of      (194) (195)
Integral, differentiation of      425 426
Integral, improper      190 192
Integral, iterated      419
Integral, line      526
Integral, linearity of      177 398 414
Integral, lower Darboux      (156) 415
Integral, multiple      392ff
Integral, on interval in $E^n$      395
Integral, transformation of      186 432 457
Integral, triangle inequality for      179 412
Integral, upper Darboux      (156) 415
Integration by iteration      417
Integration by parts      186
Integration by substitution      186
Integration variable, change of      186 430 457
Interchange of limit and differentiation      291 292
Interchange of limit and integration      288
Interchange of order of iterated integration      419
Interchange of summation and differentiation      349 600
Interchange of summation and integration      600
Interior      142 402
Interior mapping theorem      367
Interior of patch      511
Interior of point set      142 402
Interior point      100 142 211
Intermediate sum      (157) 159
Intermediate-value property of continuous function      97
Intermediate-value property of derivative      136
Intermediate-value theorem      97
Intersection of closed sets      105
Intersection of open sets      104
Intersection of sets      4 6
Intervals, closed, in $E^n$      216 392
Intervals, closed, in R      4
Intervals, content of      393
Intervals, continuous image of      258
Intervals, open in $E^n$      216 392
Intervals, open In R      4
Intervals, representation of      4 5
Inverse function      14
Inverse function of cosine      (617)
Inverse function of hyperbolic functions      611
Inverse function of linear function      305
Inverse function of sine      (616)
Inverse function of strictly increasing function      98
Inverse function of tangent      615
Inverse function theorem      353 371
Inverse function, derivative of      126 132 342
Inverse function, left      304
Inverse function, power series of      (617)
Inverse function, right      302
Inverse function, uniqueness of      17
Inverse image      234
Inverse image of complement      238
Inverse image of direct image      235
Inverse image of intersection      237
Inverse image of union      236
Inverse image under composite function      241
Invertible function      14
Irrational numbers      46
Isolated point      82 211
Isomorphism, order-      45
Iterated integral      419 421 422
Iterated limit      (230)
Iterated series      592
Jacobi's theorem      457
Jacobi, Carl Gustav Jacob      324
Jacobian      371
Jacobian matrix      324
Jordan content      405
Jordan content as length, area, volume measure      465
Jordan content of ball      465
Jordan content of congruent sets      465
Jordan content of images of intervals      450ff
Jordan content of images of Jordan-measurable sets      457
Jordan content of intervals      407
Jordan content of parallelograms      421
Jordan content, inner      404
Jordan content, invariance under orthogonal transformations      449
Jordan content, invariance under translations      465
Jordan content, outer      405
Jordan content, zero      406
Jordan's curve theorem      549n
Jordan, Camille      404
Jordan-measurable sets      405
Jordan-measurable sets, complement of      410
Jordan-measurable sets, image of      443
Jordan-measurable sets, intersection of      409
Jordan-measurable sets, linear image of      446
Jordan-measurable sets, union of      409
Jump discontinuity      92 (95)
Kronecker, Leopold      20
L'Hopital's rules for indeterminate forms, $\infty / \infty$      134
L'Hopital's rules for indeterminate forms, 0/0      133
L'Hopital, Guillaume Francois Marquis de      133
Lagrange multiplier rule      387
Lagrange, Joseph Louis de      386
Laplace operator      (564)
Laplace transform      (196)
Laplace, Pierre Simon      196
Least square method      (390)
Least upper bound      30
Least upper bound, properties of      33ff
Lebesgue measure zero      165 397
Lebesgue's criterion for integrability      175
Lebesgue, Henri      165
Left-sided derivative      (123)
Left-sided limit      (87)
Leibniz, Gottfried Wilhelm      615
Lemniscate      (437)
Length of arc      515
Length of arc in terms of first fundamental form      (519)
Length of regular curve      516
Length of vector      204
lim inf      583
lim sup      583
Limit function of a sequence, boundedness of      276
Limit function of a sequence, continuity of      275
Limit function of a sequence, differentiability of      291
Limit function of a sequence, integrability of      287
Limit of composite function      (243)
Limit of functions      85 88 229
Limit of functions at infinity      190
Limit of functions, product, quotient, sum      89
Limit of sequences      58 218
Limit of sequences, product, quotient, sum      63
Limit of sequences, uniqueness of      61
Limit tests      584
Limit, improper      90
Limit, inferior      583
Limit, iterated      (230)
Limit, left-sided      (87)
Limit, right-sided      (87)
Limit, superior      583
Lindemann, C.L.F.      47 616
Line integral      526
Line integral, independence of path      527 549
Linear approximation      139
Linear dependence of vectors      297
Linear function      138 296
Linear function, elementary      446
Linear function, inverse of      305
Linear function, left inverse of      304
Linear function, one-to-one      303 307
Linear function, one-to-one and onto      305
Linear function, onto      301 309
Linear function, range of      298
Linear function, rank of      298
Linear function, representation by matrix      299
Linear function, right inverse of      302
Linear function, uniform continuity of      307
Linear image of intervals      445ff
Linear image of intervals, Jordan content of      446
Linear image of Jordan-measurable sets      44511
Linear image of Jordan-measurable sets, Jordan content of      447
Linear independence of vectors      297
Linear space      200
Linear subspace      297
Lipschitz condition, global      263
Lipschitz condition, uniform      441
Lipschitz, Rudolph      263
Logarithm, natural      187 609
Lower bound      29
1 2 3 4
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