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| Авторизация |
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| Поиск по указателям |
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| Estep D.J. — Practical Analysis in One Variable |
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| Предметный указатель |
![$C^q([a, b])$](/math_tex/f1810786ce3af515712e25586aa7fdb982.gif) 570
 372
 363
 17
 18 48
 302
 19
 23 37 39 45
 143
 52
 62
1 – 1 185
Absolute area between curves 350
Absolute area underneath a curve 349
Absolute value 24 69
Acceleration 267 286
Acceleration of gravity 287
Accumulation of errors 119
Accuracy 100
Algebraic equation 12
Algorithm 12
Algorithm, BISECTION 130 166 168 186
Algorithm, Decasection 173
Algorithm, Fixed Point Iteration 198 200 573
Algorithm, Forward Euler Method 584
Algorithm, hybrid-Newton method 425
Algorithm, long division 23
Algorithm, Newton's method 418
Algorithm, polynomial long division 79
Analytic functions 538
Antiderivative 301
Antidifferentiation 301
Approximation theory 555
Archimedes 345
Area between curves 350
Area underneath a curve 348
Argument 52
Arithmetic Properties of the Real Numbers 140
Arzela 591
Arzela, Arzela's Theorem 591
Associative rule for addition 16
Associative rule for multiplication 16
Average, rate of change 241
Average, value of a function 351
Axiom of Completeness 149
Axis 56
Babylonians 7
bacteria 45 46 385
Banach 205 573
Barrows 436
Basis 544
Basis, coefficients with respect to a 544
Bernoulli, Jacob 246 436 514
Bernoulli, Johann 246 436 497 539
Bernstein 510
Bernstein, Approximation Theorem 518
Bernstein, polynomial 517 538
Big O 505
Binomial coefficient 510
Binomial expansion 511
Binomial polynomials 513
Bisection Algorithm 130 166 168 186
Blows up 564
Bolzano 169 238 437 442 455
Bolzano, Bolzano's Theorem 169 444
Bounded function 93
Bounded sequence 112
Bounded set of numbers 88 454
Brouwer 20
Cantor 20 136 149 437
Cauchy 88 106 169 238 437 442 599
Cauchy Criterion for Convergence 147
Cauchy sequence 131 136 144
Cauchy, uniform Cauchy sequence 325
Chain rule 264
Chemical equilibrium 46 166 201 205
choose 510
Closed interval 48 142
Closed set of numbers 16 21 40
Coefficients 61
Coefficients of a linear combination 65 74
Coefficients with respect to a basis 544
Common denominator 39
Commutative rule for addition 16
Commutative rule for multiplication 16
Competition 45 560
Complete set of numbers 147
Complex analysis 538
composition 80
Composition of continuous functions 443
Composition of differentiable functions 263
Composition of Lipschitz continuous functions 96
Compound interest 370 380
Computing limits 116 117 148
Computing roots 171
Constant, interpolant 317
Constant, polynomial 62
Constant, relative rate of change 370 374
Constructive solution procedure 12
Constructivists 19
Continuity on an interval 443
Continuous function 83 442
Continuous model 371
Contraction map 203 573
Contraction mapping principle 205 573
Convergence of a function 158 160
Convergence of a sequence 102 103 144
Convergence of a series 110
Convergence, factor 207 416
Convergence, global 408
Convergence, linear 207
Convergence, local 410
Convergence, order of 415
Convergence, pointwise 464
Convergence, quadratic 208 415
Convergence, second order rate of 415
Convergence, uniform 323 464
Convergent sequence 101
Coordinate plane, axis of the 56
Coordinate plane, integer 56
Coordinate plane, origin of the 56
Coordinate plane, rational 58
coordinates 57
Cost 173
D'Alembert 3
Darboux 491
Darboux integral 491
Decasection Algorithm 173
Decimal expansion, finite 41
Decimal expansion, infinite 99
Decimal expansion, infinite nonperiodic 128
Decimal expansion, infinite periodic 42
Decimal expansion, periodic 42
Decimal expansion, truncated 44
Dedekind 149 437
Dedekind cut 149
Degenerate differential equation 289
Degree 62
Degrees of freedom 544
Denominator 37
Dense set of numbers 148
Denseness of the Rational Numbers 147
Dependent variable 53
Derivative 223 237 245
Derivative, left 255
Derivative, right 254
Derivative, second 267
Difference of polynomials 65
Differentiability and strong differentiability 242
Differentiable at a point 238
| Differentiable, strongly 223
Differential 307
Differential equation 285
Differential equation, degenerate 289
Differential equation, energy argument for a 395
Differential equation, general solution of a 310
Differential equation, global existence of a solution of a 579
Differential equation, initial value problem for a 316 559
Differential equation, integral form of a 572
Differential equation, linear 289
Differential equation, local solution of a 586
Differential equation, nonlinear 289
Differential equation, nonseparable 290
Differential equation, order of a 288
Differential equation, particular solution of a 310
Differential equation, separable 290
Differential equation, short time existence of a solution of a 564
Differential equation, solution of a 290—292
Differential equation, uniqueness of a solution of a 292 598
Differential equation, weak form of a 572
Differential operator 570
digit 23 41
Dinner Soup model 8—10 54
Dirichlet 51 436 451
Discontinuous 84
Discontinuous function 159
Discrete model 370
Distance 24
Distributive rule 16
Divergence of a sequence 107 324
Divergence to infinity 107
Division of functions 76
Domain 52
DOUBLE PRECISION 119
Dummy variable 62 101 303 308
Einstein 288
Einstein, Law of Motion 288
Einstein, Theory of Special Relativity 288
Electric current 69
Element 100
Endpoint 48 142
Energy argument 395
Equality of polynomials 67
equation 8
Equation, differential 285
Equicontinuous family of functions 588
Equilibrium point 233
Equilibrium point, stable 233
Equilibrium point, unstable 233
Error Bound for Interpolation 550
Error Formula for Interpolation 549
Error Formulas for Taylor Polynomials 533
Error of a Bernstein polynomial 518
Error of a quadratic approximation 525
Error of a Taylor polynomial 528
Error of a truncated decimal expansion 100
Error of an interpolating polynomial 548
Error of integration 333 334 481 482 487
Error of Newton's method 422
Error of the Bisection Algorithm 170
Error of the Decasection Algorithm 173
Error of the Fixed Point Iteration 206 409—412 414—417
Error of the linear approximation 222
Error, bound for polynomial interpolation 550
Error, round-off 119
Error, tolerance 424
Estimate 100
Euler 52 62 436 599
Existence of the Polynomial Interpolant 548
Existence Result of Cauchy, Lipschitz, and Peano 599
EXP 372
EXPONENT 118
Exponential function 372
Extension of a function 154
Extension of a set of numbers 22 23
Extremum Principle for a Continuous Function 456
Factor 127
Factorial 379
Factorization 23
Family of functions 586
Field axioms 149
Finite decimal expansion 41
Fixed Point Iteration 198 200 573
Fixed Point Iteration, Newton's method as a 418
Fixed point problem 191
Fixed point problem for a differential equation 572
Fixed point problem for an operator 573
Floating point number 118
Floating point number, round-off error 119
force 286
Forward Euler Method 584
FOURIER 311 422
FRACTION 37
Free Time model 194 200 205
Function 51
Function, antiderivative of a 301
Function, average rate of change of a 241
Function, average value of a 351
Function, bounded 93
Function, bounded below 95
Function, constant interpolant of a 317
Function, continuity on an interval 443
Function, continuous 83 442
Function, contraction map 203
Function, converges at  494
Function, converges at 493
Function, converges to 495
Function, converges to 495
Function, derivative of a 223 237 245
Function, differentiable at a point 238
Function, discontinuous 84 159
Function, domain of a 52
Function, exponential 372
Function, extension of a 154
Function, fixed point problem 191
Function, global behavior of a 269
Function, graph of a 55 83 156
Function, Hoelder continuous 446
Function, Hoelder exponent of a 447
Function, instantaneous rate of change of a 241
Function, integrable 302
Function, integral of a 302
Function, inverse of a 183
Function, invertible 183
Function, left derivative of a 255
Function, left linearization of a 255
Function, limit of a 158 160
Function, linear approximation of a 223 420
Function, linear model for a 420
Function, linearization of a 223
Function, Lipschitz continuous 85 217
Function, Lipschitz continuous inverse of a 281
Function, local behavior of a 269
Function, locally uniformly Lipschitz continuous 564
Function, maximum value of a 456
Function, minimum value of a 456
Function, modulus of continuity of a 516
Function, monotone 182 276
Function, nth derivative of a 267
Function, one-sided limit of a 253
Function, piecewise constant interpolant of a 320 321
Function, piecewise linear interpolant of a 553
Function, plot of a 55
Function, polynomial 61
Function, polynomial interpolation problem for a 543
Function, power 171 187 362—363
Function, quadratic approximation of a 525
Function, range of a 52
Function, rational 78
Function, restriction of a 183
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