|
|
 |
| Авторизация |
|
|
|
| Поиск по указателям |
|
|
|
|
|
|
|
 |
|
|
|
| Spivak M. — Calculus |
|
|
|
| Предметный указатель |
 288
, Archimedes’s approximation of 127
, irrationality of 309
, relation to e 415 530
, transcendentality of 415
, value of 403
, Vieta’s product for  , 312
, Wallis’s product for  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  ”, 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 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
|
|
|
| Реклама |
|
|
|
|
|
О проекте