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| Estep D.J. — Practical Analysis in One Variable |
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| Предметный указатель |
Ordered field 149
Ordered pair of numbers 38 57
Ordering numbers 17
Origin 22 56
Output 52
Partial sums 110
Particular solution of a differential equation 310
Peano 40 599
Periodic decimal expansion 42
Picard 575
Picard, Picard Existence Theorem 577
Picard, Picard's iteration 575
Piecewise, constant interpolant 320 321
Piecewise, linear interpolant 553
Piecewise, polynomial 68
Plot of a function 55
Poincare 20
Pointwise convergence 464
Polar coordinate system 396
Polynomial 61
Polynomial, Bernstein 517
Polynomial, binomial 513
Polynomial, coefficients 61
Polynomial, constant 62
Polynomial, degree of a 62
Polynomial, interpolation problem 543
Polynomial, linear 62
Polynomial, quadratic 62
Polynomial, Taylor's representation of a 528
Polynomial, zero 62
Polynomials, basis for 544
Polynomials, equality of 67
Polynomials, Lagrange basis for 545
Polynomials, linear combination of 65
Polynomials, long division of 79
Polynomials, monomials 65 68 89 248
Polynomials, piecewise 68
Polynomials, product of 66
Polynomials, sum of 63
Population growth 370
Population model 33 231
Positive integers 22
Power function 171 187 362—363
Powers, natural numbers 17
Predation 560
Prime number 127
Principle of Induction 31—32
Principle of Uniform Continuity 451
Product of differentiable functions 261
Product of functions 76
Product of Lipschitz continuous functions 94
Product of polynomials 66
Product of polynomials and numbers 64
Product rule 262
Pythagoreans 128
Quadratic convergence 208 415
Quadratic polynomial 62
Quadratic, approximation of a function 525
Quasi-Newton method 427
Quotient function 76
Quotient of differentiable functions 265
Quotient of Lipschitz continuous functions 95
Quotient rule 266
Radioactive decay 370 375
RANGE 52
Raphson 422
Rate of change, average 241
Rate of change, instantaneous 241
ratio 37
Rational coordinate plane 58
Rational function 78
Rational number line 47
Rational numbers 23 37 39 45
Real Number Theorem 148
Real numbers 143
Real numbers, sequences of 144
Refinement of a mesh 485
Regula falsi method 213
Relative change 369
Relative rate of change 370
Remainder 24
Remainder of a Taylor polynomial 528
Rescale 166
Residual 422
Restriction of a function 183
Riemann 334
Riemann sum 335
Right derivative 254
Right linearization 254
Rocket propulsion, model of 357 364—365
Rolle 272 456
Rolle, Rolle's Theorem 271 456
Roots, computing 165 171
Roots, ill-conditioned 423
Round-off error 119
Secant line 238 269
Secant method 428
Second derivative 267
Second order rate of convergence 415
Separable 524
Separable differential equation 290
Separation of variables 563
SEQUENCE 100
Sequence of functions 323 463
Sequence of functions, limit of a 463
Sequence of functions, pointwise convergence of a 464
Sequence of functions, uniform convergence of a 323 464
Sequence of real numbers 144
Sequence, arithmetic 111
Sequence, bounded 112
Sequence, Cauchy 144
Sequence, convergence of a 101—103 144
Sequence, divergence of a 107 324
Sequence, divergence to infinity 107
Sequence, element of a 100
Sequence, extracting a subsequence from a 452
Sequence, fundamental 136
Sequence, index of a 100
Sequence, limit of a 101—103
Sequence, limit point of a 452
Sequence, subsequence of a 452
Sequence, uniform Cauchy 325
Series, convergence of a 110
Series, geometric 109 145
Series, harmonic 62 119
Series, infinite 109
Series, limit of a 110
Series, partial sum of a 110
Set 53
Set of natural numbers 19
Set of real numbers 143
Set, greatest lower bound of a 454
Set, infimum of a 454
Set, least upper bound of a 454
| Set, maximum of a 455
Set, minimum of a 455
Set, supremum of a 454
Set, upper bound of a 454
Short time existence 564
Sigma notation 62
Simpson 422
Single precision 118 120
Size of a set of numbers 89 454
Solubility 46 166 201 205
Spaces of functions 570
Spring constant 389
Spruce budworm 560 585
Stable equilibrium point 233
Step function 69 84
Stopping criterion for Newton's method 424
Strictly monotone function 182
Strong differentiability and differentiability 242
Strongly differentiable 223
Strongly differentiable on an interval 245
Strongly differentiable on the left 254
Strongly differentiable on the right 254
Subscript 34
Subsequence 452
Substitution 305 312
Subtraction 21
Sum of polynomials 63
Summation notation 62
Sup 454
Supremum 454
Tangent 222
Tangent line 222 223 238 269
Taylor 539
Taylor polynomial 528
Taylor polynomial, integral form of the remainder 531
Taylor polynomial, Lagrange's form of the remainder 532
Taylor polynomial, remainder 528
Taylor series 538
Taylor's representation of a polynomial 528
Theorem, Arithmetic Properties of Numbers 140
Theorem, Arzela's 591
Theorem, Bernstein Approximation 518
Theorem, Binomial Expansion 511
Theorem, Bolzano's 169 444
Theorem, Cauchy Criterion for Convergence 147
Theorem, Chain Rule 264
Theorem, Contraction Mapping Principle 205 573
Theorem, Denseness of the Rational Numbers 147
Theorem, Error Bound for Interpolation 550
Theorem, Error Formula for Interpolation 549
Theorem, Error Formulas for Taylor Polynomials 533
Theorem, Existence of the Polynomial Interpolant 548
Theorem, Existence Result of Cauchy, Lipschitz, and Peano 599
Theorem, Extremum Principle for a Continuous Function 456
Theorem, Fundamental Theorem of Calculus 333 334 343 481 487
Theorem, General Order Rolle's 548
Theorem, Generalized Integral Mean Value 531
Theorem, Generalized Mean Value 499
Theorem, Gronwall's Lemma 598
Theorem, implicit function 581
Theorem, intermediate value 170 444
Theorem, Inverse Function 183 186 444
Theorem, L'Hopital's rule 498
Theorem, Law of Large Numbers 515
Theorem, Least Upper Bound Principle 455
Theorem, Linearity of Differentiation 260
Theorem, Linearity of Integration 304
Theorem, Local Convergence for Newton's method 418
Theorem, Local Convergence for the Fixed Point Iteration 410
Theorem, mean value 269 451 456
Theorem, Monotonicity of Integration 340
Theorem, Order Properties of Numbers 142
Theorem, Picard existence 577
Theorem, Principle of Uniform Continuity 451
Theorem, Product Rule 262
Theorem, Quotient Rule 266
Theorem, Real Number 148
Theorem, Rolle's 271 456
Theorem, Uniform Cauchy Criterion for Sequences of Functions 326
Theorem, Uniqueness for an Ordinary Differential Equation 598
Theorem, Weierstrass Approximation Theorem 510
Theorem, Weierstrass' Principle 453
Theorem, Weierstrass's Characterization of a Limit of a Function 161
Three components of mathematical modeling 11
Transformation 53 158
Trial and error strategy 129
Trial-and-error strategy 8 9 11 12
Triangle inequality 25
Truncated decimal expansion 44
Truncated decimal expansion, error 100
Uniform Cauchy Criterion for Sequences of Functions 326
Uniform, Cauchy sequence 325
Uniform, continuity 446
Uniform, convergence 323 464
Uniformly, differentiable 450
Uniformly, Lipschitz continuous 326
Uniformly, strongly differentiable 251
Unique linear combination 75
Uniqueness for an Ordinary Differential Equation 598
Uniqueness for first order, separable, linear differential equations 295
Uniqueness of a solution of a differential equation 292
Uniqueness of an infinite decimal expansion 111
UNKNOWN 8
Unstable equilibrium point 233
Upper bound 454
Upper Darboux integral 491
Upper estimate 87
Upper limit 62 312
v with remainder 23
Variable 52
Variable, dependent 53
Variable, dummy 62 101 303 308
Variable, independent 53
Velocity 241
Verhulst 46 560
Verhulst population model 45—46 114 115
Vertical Line Test 181
Viete 421
Wallis 44 436
Weak form of a differential equation 572
Weierstrass 106 437 442 453 456
Weierstrass, Weierstrass Approximation Theorem 510
Weierstrass, Weierstrass' Principle 453
Weierstrass, Weierstrass's Characterization of a Limit of a Function 161
Weight 287
Weight function 352
Weighted average of a function 352
Weighted average of numbers 352
Weights 352
Weyl 20
Zeno 122
Zero polynomial 6
| | 24 69
~ 137
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