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Estep D.J. — Practical Analysis in One Variable
Estep D.J. — Practical Analysis in One Variable

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Название: Practical Analysis in One Variable

Автор: Estep D.J.

Аннотация:

The book is well suited for an honors calculus sequence typically taken by first-year undergraduates planning to major in engineering, mathematics, and science and for an introductory course in rigorous real analysis offered to mathematics majors.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 1st edition

Год издания: 2002

Количество страниц: 624

Добавлена в каталог: 11.06.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$C^q([a, b])$      570
$e^X$      372
$log_b$      363
$\cdots$      17
$\infty$      18 48
$\int$      302
$\mathbb{N}$      19
$\mathbb{Q}$      23 37 39 45
$\mathbb{R}$      143
$\rightarrow$      52
$\Sigma$      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 $-\infty$      494
Function, converges at $\infty$      493
Function, converges to $-\infty$      495
Function, converges to $\infty$      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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