---

＜電子ブック＞
Infinitesimal Analysis / by E.I. Gordon, A.G. Kusraev, Semën Samsonovich Kutateladze
(Mathematics and Its Applications ; 544)

版	1st ed. 2002.
出版者	(Dordrecht : Springer Netherlands : Imprint: Springer)
出版年	2002
本文言語	英語
大きさ	XIV, 422 p : online resource
著者標目	*Gordon, E.I author Kusraev, A.G author Kutateladze, Semën Samsonovich author SpringerLink (Online service)
件　名	LCSH:Functional analysis LCSH:Operator theory LCSH:Measure theory LCSH:Mathematical logic FREE:Functional Analysis FREE:Operator Theory FREE:Measure and Integration FREE:Mathematical Logic and Foundations
一般注記	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 Subdifferentials -- 6. Technique of Hyperapproximation -- 7. Infinitesimals in Harmonic Analysis -- 8. Exercises and Unsolved Problems -- References -- Notation Index 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 HTTP:URL=https://doi.org/10.1007/978-94-017-0063-4

 類似資料