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Table of contents (8 chapters)
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Front Matter
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Back Matter
Keywords
About this book
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
Authors and Affiliations
Bibliographic Information
Book Title: Infinitesimal Analysis
Authors: E. I. Gordon, A. G. Kusraev, S. S. Kutateladze
Series Title: Mathematics and Its Applications
DOI: https://doi.org/10.1007/978-94-017-0063-4
Publisher: Springer Dordrecht
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eBook Packages: Springer Book Archive
Copyright Information: Springer Science+Business Media Dordrecht 2002
Hardcover ISBN: 978-1-4020-0738-5Published: 30 June 2002
Softcover ISBN: 978-90-481-6070-9Published: 15 December 2010
eBook ISBN: 978-94-017-0063-4Published: 14 March 2013
Edition Number: 1
Number of Pages: XIV, 422
Topics: Functional Analysis, Operator Theory, Measure and Integration, Mathematical Logic and Foundations