Infinitesimal analysis
著者
書誌事項
Infinitesimal analysis
（Mathematics and its applications, v. 544）
Kluwer Academic, c2002
- タイトル別名
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Инфинитезщимальный анализ
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注記
Includes bibliographical references and index
"This is a completely updated and revised translation of the original work Инфинитезщимальный анализ, Части 1 и 2, by E.I. Gordon, A.G. Kusraev and S.S. Kutateladze, published by the Sobolev Institute of Mathematics, Russian Academy of Sciences, in 2001. Translated by S.S. Kutateladze."--t.p. verso
内容説明・目次
内容説明
Infinitesimal analysis, once a synonym for calculus, is now viewed as a technique for studying the properties of an arbitrary mathematical object by discriminating between its standard and nonstandard constituents. Resurrected by A. Robinson in the early 1960's with the epithet 'nonstandard', infinitesimal analysis not only has revived the methods of infinitely small and infinitely large quantities, which go back to the very beginning of calculus, but also has suggested many powerful tools for research in every branch of modern mathematics.
The book sets forth the basics of the theory, as well as the most recent applications in, for example, functional analysis, optimization, and harmonic analysis. The concentric style of exposition enables this work to serve as an elementary introduction to one of the most promising mathematical technologies, while revealing up-to-date methods of monadology and hyperapproximation.
This is a companion volume to the earlier works on nonstandard methods of analysis by A.G. Kusraev and S.S. Kutateladze (1999), ISBN 0-7923-5921-6 and Nonstandard Analysis and Vector Lattices edited by S.S. Kutateladze (2000), ISBN 0-7923-6619-0
目次
Foreword.
1. Excursus into the History of Calculus.
2. Naive Foundations of Infinitesimal Analysis.
3. Set-Theoretic Formalisms of Infinitesimal Analysis.
4. Monads in General Topology.
5. Infinitesimals and Sub differentials.
6. Technique of Hyperapproximation.
7. Infinitesimals in Harmonic Analysis.
8. Exercises and Unsolved Problems.
Appendix. References.
Notation Index. Subject Index.
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