Infinitesimal Analysis
Authors: Gordon, E.I., Kusraev, A.G., Kutateladze, Semën Samsonovich
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- About this book
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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
- Table of contents (8 chapters)
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Excursus into the History of Calculus
Pages 1-9
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Naive Foundations of Infinitesimal Analysis
Pages 10-34
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Set-Theoretic Formalisms of Infinitesimal Analysis
Pages 35-115
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Monads in General Topology
Pages 116-165
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Infinitesimals and Subdifferentials
Pages 166-222
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Table of contents (8 chapters)
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Bibliographic Information
- Bibliographic Information
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- Book Title
- Infinitesimal Analysis
- Authors
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- E.I. Gordon
- A.G. Kusraev
- Semën Samsonovich Kutateladze
- Series Title
- Mathematics and Its Applications
- Series Volume
- 544
- Copyright
- 2002
- Publisher
- Springer Netherlands
- Copyright Holder
- Springer Science+Business Media Dordrecht
- eBook ISBN
- 978-94-017-0063-4
- DOI
- 10.1007/978-94-017-0063-4
- Hardcover ISBN
- 978-1-4020-0738-5
- Softcover ISBN
- 978-90-481-6070-9
- Edition Number
- 1
- Number of Pages
- XIV, 422
- Topics
