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Spivak M. — Calculus
Spivak M. — Calculus

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Название: Calculus

Автор: Spivak M.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: Second Edition

Год издания: 1980

Количество страниц: 647

Добавлена в каталог: 03.04.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\pi$      288
$\pi$, Archimedes’s approximation of      127
$\pi$, irrationality of      309
$\pi$, relation to e      415 530
$\pi$, transcendentality of      415
$\pi$, value of      403
$\pi$, Vieta’s product for $2/\pi$,      312
$\pi$, Wallis’s product for $\pi/2$      370
AalbmcndoE      256
Abel summable      487
Abel, Niels Henrik      378 487
Abel’s formula for summation by parts      367
Abel’s lemma      368
Abel’s Test      462
Abel’s theorem      487
Absolute value      11
Absolute value of a complex number      499
Absolutely convergent      447 521
Absolutely summable      447
Acceleration      147
Acta Eruditorum      134
Addition      3
Addition formula for arcsin      300
Addition formula for arctan      300
Addition formula for cos      296
Addition formula for sin      295 296
Addition formula for tan      299
Addition, associative law for      9
Addition, commutative law of      9
Addition, of complex numbers      496
Addition, of complex numbers, geometric interpretation of      500
Additive identity, existence of      9
Additive inverses, existence of      9
Algebra, fundamental theorem of      351 503 513 533
Algebraic functions      336
Algebraic number      409
Algebraist’s real numbers      565
Almost lower bound      128
Almost upper bound      128
Analyst’s real numbers      565
angle      286
Angle, directed      286
Antidiagonal      228
Arabic numerals, multiplication of      8
Arc length      258 264
ArcCos      294
Archimedes      124 127 243
Archimedian property for the rational numbers      550
Archimedian property for the real numbers      124
Archimedian spiral      76
arcsec      302 356
arcsin      293
Arcsin, addition formula for      300
Arcsin, derivative of      294
Arcsin, Taylor series for      483
arctan      294
Arctan, addition formula for      300
Arctan, derivative of      294
Arctan, Taylor polynomials for      381 388
Arctan, Taylor polynomials for, remainder term for      397
Area      233 238
Arg cosh      327
arg sinh      327
Arg tanh      327
Argument      501
Argument function      507
Argument function, discontinuities of      511
Argument of the hyperbolic functions      327
Arithmetic mean      33
Arrow, “x arrow $\sin(x^2)$”,      45
Ars Conjectandi      540
Associative law for addition      9
Associative law for multiplication      9
Average velocity      138
Axis, horizontal      57
Axis, imaginary      499
Axis, real      499
Axis, vertical      57
Bacon, Francis      vi
Bandes, D., handiwork of      637—647
Basic properties of numbers      3
bernoulli      134 540
Bernoulli numbers      538
Bernoulli polynomials      541
Bernoulli’s inequality      32
Big game hunting, mathematical theory of      517
Binary operation      547
Binomial coefficient      27 403
Binomial series      461 484
Binomial theorem      28
Bisection argument      128 517
Bohr, Harald      370
Bolzano — Weierstrass theorem      425 436 517
Bound, almost lower      128
Bound, almost upper      128
Bound, greatest lower      120
Bound, least upper      119 550
Bound, lower      120
Bound, upper      119 550
Bounded above      108 119 424 550
Bounded below      120 424
Bourbaki, Nicholas      134
Cardoid      76 231
Cartesian coordinates      75
Cauchy      261
Cauchy Condensation Theorem      462
Cauchy criterion      440
Cauchy form of the remainder      391 393
Cauchy mean value theorem      188
Cauchy product      460 479
Cauchy sequence      426 537
Cauchy sequences, equivalence of      565
Cauchy — Hadamard formula      534
Cauchy — Schwarz inequality      261
Cavalieri      255
Cesaro summable      460
Chain rule      160 ff.
Chain Rule, proof of      164
Change, rate of      138
Characteristic (of a field)      552
circle      65
Circle of convergence      524
Circle, unit      66
Circle, “f circle g”,      44
Classical notation for derivatives      140—141 148 152—153 172 227
Classical notation for integrals      244
Cleio      171
Closed interval      57
Closed rectangle      512
Closure under addition      9
Closure under multiplication      9
Commutative law for addition      9
Commutative law for multiplication      9
Comparison Test      441 442
Comparison theorem, Sturm      305
Complete induction      23
Complete ordered field      550 569
Completing the square      17 352
Complex analysis      531
Complex function, continuous      511
Complex function, differentiable      515
Complex function, graph of      507
Complex function, limit of      507
Complex function, nondifferentiable      516
Complex function, Taylor series for      528
Complex nth root      501
complex numbers      491 496
Complex numbers, absolute value of      499
Complex numbers, addition of      496
Complex numbers, addition of, geometric interpretation of      500
Complex numbers, geometric interpretation of      498
Complex numbers, imaginary part of      496
Complex numbers, logarithm of      536
Complex numbers, modulus of      499
Complex numbers, multiplication of      496
Complex numbers, multiplication of, geometric interpretation of      500—501
Complex numbers, real part of      496
Complex numbers, sequence of      520
Complex plane      498
Complex power series      522
Complex power series, circle of convergence of      524
Complex power series, radius of convergence of      524
Complex sequences      520—521
Complex series      521
Complex-valued functions      506
Composition of functions      44
Concave function      205
Conditionally convergent series      448
Cone, surface area of      267
conjugate      499 504
Constant function      43
Construction of the real numbers      554
Continued fraction      429
Continuous at a      101 510
Continuous function      101 104 511
Continuous function, nowhere differentiable      145 475
Continuous on (a, b)      104
Continuous on [a, b]      104
Continuous, uniformly      130
Contraction      433
Contraction Lemma      433
Converge, pointwise      468
Converge, uniformly      468 472
Convergent sequence      420 520
Convergent Series      439 521
Convergent series, absolutely      447 521
Convergent series, conditionally      448
Convex function      204
Convex function, strictly      214
Convex function, weakly      214
Convex subset of the plane      214 518
Cooling, Newton’s law of      329
Coordinate system      57
Coordinate system, cartesian      75
Coordinate system, Origin of      57
Coordinate system, polar      75
Coordinate, first      57
Coordinate, second      57
cos      286 289 303—304 529
Cos, addition formula for      296
Cos, derivative of      158 290
Cos, inverse of      see “Arccos”
Cos, Taylor polynomials for      380
Cos, Taylor polynomials for, remainder term for      394
cosh      326
Cosine, hyperbolic      326
cot      293
Countable      416
Counting numbers      21
Critical point      175
Critical value      175
Csc      293
Cubic equation, general solution      493—494
Curve, parametric representation of      229
Cycloid      229
Darboux’s theorem      199
De Moivre’s Theorem      501
Decimal expansion      73 459
Decreasing function      180
Dedekind, Richard      38
Defined implicitly      226
Definite integral      338
Definition      47
Definition, recursive      23
Degree (of a polynomial)      42
Degree measurements      63 287—288
Delicate ratio test      460
Delicate root test      460
Dense      126
Derivative      135 ff. 137
Derivative of quotient, incantation for      157
Derivative, classical notation for      140—141 148 152—153 172 227
Derivative, higher-order      147
Derivative, left-hand      142
Derivative, Leibnizian notation for      see “Derivative classical
Derivative, logarithmic      325
Derivative, of f      137
Derivative, of f at a      137
Derivative, right-hand      142
Derivative, Schwarzian      170
Derivative, second      147
Derivative, second, Schwarz      405
Derivative, “infinite”      144
Derivative, “negative infinity”      144
Descartes, Rene      75
Diagonal      218
Difference operator      539
Differentiable      137 515
Differential equation      275 283 304 305 334 406
Differential equation, initial conditions for      407
Differentiation      154 ff.
Differentiation operator      539
Differentiation, implicit      226
Differentiation, logarithmic      325
Dini’s theorem      489
Directed angle      286
Dirichlet’s test      462
Disc method      265
Discontinuities of a nondecreasing function      417
Discontinuity, removable      107
Disraeli, Benjamin      2
Distance      58 499
Distance, shortest between two points      258
Distributive law      9
diverge      420 521
Division      6
Division by zero      6
Domain      40 41 47 567
Double intersection      151
Double root      171
Durege      38
e      317
e, irrationality of      399
e, relation with $\pi$      415 530
e, transcendentality of      411
e, value of      318 396
Elementary function      336
ellipse      66
Ellipsoid of revolution      364
Empty collection      23
Entire function      533
EPSILON      18
Equal up to order n      386
Equality, order of      386
Equations, differential      see “Differential equations”
Equivalent Cauchy sequences      565
Euler      541
Euler — Maclaurin summation formula      542
Euler’s number      430
Even function      51 184
Even number      25
Eventually inside      520
Exhaustion, method of      127
EXP      317 ff. 529
Exp, classical approach to      331
Exp, elementary definition of      436
Exp, Taylor polynomials for      381
Exp, Taylor polynomials for, remainder term for      395—396
Expansion, decimal      73 459
Extension of a function      101—102
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