Robert A. — Non-Standard Analysis :: Электронная библиотека попечительского совета мехмата МГУ

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Robert A. — Non-Standard Analysis

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Название: Non-Standard Analysis

Автор: Robert A.

Аннотация:

Infinitesimals have been hotly debated since the invention of calculus 300 years ago. This accessible treatment of nonstandard analysis (NSA) presents an elementary, yet rigorous account of the theory of infinitesimals and derives some known mathematical results in a nonclassical way. Provides recent solutions to mathematical questions which remained unsolved until the advent of NSA. Treatment is self-contained and includes exercises with detailed solutions.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 1st edition

Год издания: 1988

Количество страниц: 180

Добавлена в каталог: 12.05.2008

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Предметный указатель

Analytic (function)      5.4.2
Appreciable number      3.5.13
Archimedian field      3.1.1
Asymptotic numbers      3.5.14
Bernoulli (formulas)      6.1.2
Bernstein polynomials      8.3.1
Bernstein Robinson (theorem)      11.1.2
Best approximation Lemma      8.4.2
Cantor set      Exercise 3.5.18
Cardinal (of a set)      2.4.1
Cartesian product      2.5.2
Cesaro, solution of      Exercise 7.5.4
Classical (formula, statement)      1.2.2
Classical mathematics      1.1.3
Compact operator      11.2.6
Continuity (relation with S-continuity)      4.1.2
Continuity (relation with S-continuity), uniform      4.4
Continuous shade theorem      4.3.5
Couple      2.5.1 2.5.2
Definitions (implicit)      2.2.5
Derivatives (higher )      5.4
Difference operator $\nabla$       5.5.1
Differentiability      5.1.1
Differentiability, strict      5.3.1
Dirac function      8.1.1
Extension (axiom of )      1.1.1
Extensionality      2.2.4
External set      1.8
Fejer’s theorem      8.2.2
Finite (cardinal)      2.4.1
Finite differences      5.5.1
Fourier coefficients      8.2.1
Fractal, solution of Exercise      3.5.18
Galaxy      3.5.15
Graph of a map      2.5.2
Green function      10.1.1
Halo      3.5.15 3.5.16
Higher derivatives      5.4
Idealization axiom (I)      1.2.4
Illimited integer      1.6.1
Illimited numbers      3.1.2
Illimited vectors      3.2.5
Implicit definition of a standard map      2.5.4
Implicit definition of a subset      2.2.5

Implicit definition of continuity      4.3.1
Implicit definition of differentiability      5.1.5
Implicit definition of uniform continuity      4.4.4
Induction principle      1.5.5
Induction principle, nonstandard      Exercise 2.8.4
Infinitely near      3.1.2
Infinitesimal      3.1.2
Integral (of a function)      6.2.1
Integral part [x]      3.1.6
Invariant mean (on $\mathbb{Z}$ )      7.1.1
Kuralowski (axiom of couples)      2.5.2
Limited integers      1.6.1
Limited numbers      3.1.2
Limited vectors      3.2.5
Mean (invariant)      7.1.1
Measure      7.1.2
Near standard      3.3.1
Parseval equality      8.4.1
Power set $\mathcal{V}(E)$       1.7
Quasi-nilpotenl operator      11.1.1
Relativization {of a statement)      2.6
Robinson’s Lemma      3.4.9
Rolle’s Theorem      5.2.1
S-continuhy      4 1.1
S-differentiability      5.1.1
Safety rectangle      9.1.3
Schroedinger equation      10.3.1
Separation principle (Diener-van den Berg)      3.5.15
Set forming relation      1.5.1
Shade of a set      3.3.4
Specification axiom      1.5.2
Standard (predicate)      1.1.2
Standard finite set      2.4.2
Standard part of a function      3.2.9
Standard part of a vector      3.2.5
Standard part x*=st(.x)      3.2.1 3.3.1
Standardization axiom      2.1.1
Strict differentiability      5.3.1
Strict differentiability, standard part of a function      6.3.5
Strict standard part of a function      6.3.5
Transfer Axiom      2.1.1
Transferred extensionality      2.2.4
von Koch (curve), solution of      Exercise 3.5.
Wallis (formulas)      6.1.2
Zermelo — Fraenkel axiomatic (ZF), (ZFC)      1.1.1

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