|
|
 |
| Авторизация |
|
|
|
| Поиск по указателям |
|
|
|
|
|
|
|
 |
|
|
|
| Spivak M. — Calculus |
|
|
|
| Предметный указатель |
nth root, existence of 111 501 518
nth root, primitive 505
Null set 23
Number, algebraic 402
Number, complex 491 496
Number, counting 21
Number, even 25
Number, imaginary 491
Number, irrational 25
Number, natural 21 34
Number, odd 25
Number, prime 31
Number, rational 25
Number, real 25 499 555
Number, transcendental 409
Numbers, basic properties of 3
Odd function 51 184
odd number 25
One-one function 215
Open interval 56
Order of equality 386
Ordered field 549
Ordered field, complete 550
Ordered pair 47 54
Origin (of a coordinate system) 57
pair 46
Pair, ordered 47 54
parabola 60
Parabola, area under 243
Parametric representation of a curve 229
Partial fraction decomposition 351
Partial sums 438
Partition 234
Parts, Abel’s formula for summation by 367
Parts, integration by 339 ff.
Pascal’s triangle 27
Peak point 425
Period of a function 71 150 282
Periodic function 71 150 282
Perpendicularity of lines 70
Petard, H. 517
Pig, yellow v 348
Pigheaded 171
Plane 58
Plane, complex 498
Point 56
Point of contact 205
Point-slope form of equation of a line 59 70
Polar coordinates 75 ff.
Polynomial function 42
Polynomial function, graph of 61 183
Polynomial function, multiplicity of roots 116 171
Polynomials, Bernoulli 541
Polynomials, Taylor 380 ff. (see also “Specific functions”)
Position, rate of change of 138
Positive element of  560
Positive elements of an ordered field 549
Positive number 9
Positive part of a function 51
Power functions 60
Power series centered at a 476 530
Power series representation, uniqueness of 486
Power series, complex 522
Powers of 2, table of 402
Prime number 31
Prime number, characteristic of a field 552
Prime number, infinitely many of 32
Prime number, unique factorization into 31—32
primitive 336
Primitive nth root 505
Principia 256
PRODUCT 5
Product, Cauchy 460 479
Product, infinite 312 370 463
Product, of functions 43
Product, of two negative numbers 7
Pyramid, surface area of 266
Pyramid, volume of 366
Pythagorean Theorem 25 58
Quaternions 553
Quotient of functions 43
Rabbits, growth of population 32
Radian measure 63 287—288
Radioactive decay 329
Radius of convergence of complex, power series 524
Rate of change of mass 138
Rate of change of position 138
Ratio Test 443
Ratio test, delicate 460
Rational functions 42
Rational functions, integration of 350 ff.
Rational numbers 25
Real axis 499
Real line 56
Real number (formal definition) 555
Real numbers 25
Real numbers, algebraist’s 565
Real numbers, analysist’s 565
Real numbers, Archimedian property of 124
Real numbers, construction of 554 ff.
Real numbers, high-school student’s 565
Real numbers, inductive set of 34
Real part function 506
Real part of a complex number 496
Real-valued function 506
Rearrangement of a sequence 450
Rectangle, closed 512
Recursive definition 23
Reduction formulas 350
Regulated function 489
Remainder term for Taylor polynomials 389
Removable discontinuity 107
Revolution, ellipsoid of 364
Revolution, solid of 265
Riemann sum 262
Riemann — Lebesgue lemma 303 366
Right-hand derivative 142
Rising Sun Lemma 129
Rolle 171
Rolle’s Theorem 178
Root of a polynomial function 50
Root of a polynomial function, double 171
Root of a polynomial function, multiplicity of 116 (see also “nth roots”)
Root test 459
Root test, delicate 460
Same sign 12
Schwarz inequality 18 33 261
Schwarz second derivative 405
Schwarz, H.A. 18 202
Schwarzian derivative 170
sec 293
Sec, inverse of see “Arcsec”
Secant line 136
Second coordinate 57
Second derivative 147
Second derivative test for maxima and minima 186
Second derivative, Schwarz 405
Second fundamental theorem of calculus 272
Second Mean Value Theorem for integrals 367
Sequence, absolutely summable 447
Sequence, Cauchy 426 565
Sequence, Cauchy, complex 537
Sequence, Cauchy, equivalence of 565
Sequence, convergent 420
Sequence, convergent, pointwise 468
Sequence, decreasing 424
| Sequence, divergent 420
Sequence, Fibonacci 32 486 537—538
Sequence, increasing 424
Sequence, infinite 419
Sequence, limit of 420
Sequence, nondecreasing 424
Sequence, nonincreasing 424
Sequence, of complex numbers 520
Sequence, rearrangement of 450
Sequence, summable 439
Series, absolutely convergent 447
Series, conditionally convergent 448
Series, convergent 439
Series, Fourier 300 303
Series, geometric 440
Series, power 476 530
Series, Taylor 477
Set 22
Set, empty 23
Sets, intersection of 43
Sets, notation for 43—44
Shadow point 129
Shell method 266
sigma 24
SIGN 12
Simpson’s rule 376
sin 43 286 289 303—304 529
Sin, addition formula for 296
Sin, derivative of 158 290 303—304
Sin, inverse of see “Arcsin”
Sin, Taylor polynomials for 380
Sin, Taylor polynomials for, remainder term for 394
Sine function 43
Sine, hyperbolic 326
sinh 326
Sketching graphs 181—186
Skew-field 553
Slope of a straight line 58
Solid of revolution 265
Speed, instantaneous 138
Spiral, Archimedian 76
Spiral, hyperbolic 299
Square root 12 492
Square root function 511—512
Square root in a field 552
Square root, existence of 110—111
Squaring the circle 414
Step function 258
Stirling’s formula 543
Straight line (analytic definition) 58
Straight line (analytic definition), shortest distance between two points 258
Straight line (analytic definition), slope of 58
Strict maximum point 203
Strictly convex 214
Sturm comparison theorem 305
Subsequence 425
Substitution formula 342
Substitution, world’s sneakiest 360
Subtraction 5
Sum of squares 517
Sum, finite 3—4
Sum, infinite 400 438
Sum, lower 234
Sum, of an infinite sequence 439
Sum, of an infinite sequence of complex numbers 520
Sum, of functions 43
Sum, partial 438
Sum, sigma notation for 24
Sum, upper 234
Summable 439 521
Summable, Abel 487
Summable, absolutely 447
Summable, Cesaro 460
Summable, uniformly 472
Summation by parts, Abel’s formula for 367
Supremum 120
Surface area of cone 267
Surface area of pyramid 266
Surface area of solid of revolution 267
Swift, Jonathan 546
Symmetry in graphs 184
tan 293
Tan, inverse of see “Arctan”
Tan, Taylor series for 539
Tangent line 135 137
Tangent line, point of contact of 205
Tangent, hyperbolic 326
tanh 326
Taylor polynomial 380
Taylor polynomial, remainder term of 389 391 392
Taylor series 477 528
Taylor’s Theorem 391
Torus 365
Transcendental number 409
Trapezoid Rule 374
Triangle inequality 71
Trichotomy Law 9
Trigonometric functions 286 (see also “Cos” “Cot” “Csc” “Sec” “Sin” “Tan”)
Trigonometric functions, integration of 349—350
Trigonometric functions, inverses of 293 (see also “Arccos” “Arcsec” “Arcsin” “Arctan”)
Trumpet, infinite 366
Two-times differentiable 147
Uniform limit 468
uniformly 486
Uniformly continuous function 130
Uniformly convergent sequence 468
Uniformly convergent series 472
Uniformly distributed sequence 437
Uniformly summable 472
Uniqueness of factorization into primes 31
Uniqueness of limits 86
Uniqueness of power series representations 486
Unit circle 66
Upper bound 119 550
Upper bound, almost 128
Upper bound, least 119 550
Upper integral 277
Upper limit of integration 238
Upper sum 234
Value of f at x 40
Value, absolute see “Absolute value”
Vanishing condition 440
Velocity, average 138
Velocity, instantaneous 138
Vertical axis 57
Viete, Francois 312
Volume 265—266
Wallis’ product 370
Weakly convex 214
Weierstrass see “Bolzano — Weierstrass Theorem”
Weierstrass M-test 473
Well-ordering principle 23
Wright 361
Young’s inequality 257
Zahl 25
Zero, division by 6
“Bent” graphs 135
“Corner” 60
“Infinitely small” 141 244
“Infinite” derivative 144
“Negative infinity”, derivative 144
“Or” 6
“Peak” 61
“Reasonable” function 68 104 135 166
“Tangent line”, vertical 144
“Valley” 61
|
|
|
| Реклама |
|
|
|
|
|
О проекте