ENGLISH

Infinitesimal Analysis

By E. I. Gordon , A. G. Kusraev , S. S. Kutateladze (auth.)

Book information

Publisher
Springer Netherlands
Year
2002
ISBN
1402007388, 9781402007385
DOI
10.1007/978-94-017-0063-4
LCC
QA299.82 .G67 2002
Open Library ID
OL21801672M
Language
english
Format
PDF
Filesize
2 MB (2388984 bytes)
Series
Mathematics and Its Applications 544
Edition
1
Pages
422\431
Library
Kolxo3
Time added
2009-12-04 00:34:26
Functional Analysis; Operator Theory; Measure and

Description

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

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