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Infinitesimal Analysis

  • E. I. Gordon
  • A. G. Kusraev
  • S. S. Kutateladze

Part of the Mathematics and Its Applications book series (MAIA, volume 544)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. E. I. Gordon, A. G. Kusraev, S. S. Kutateladze
    Pages 1-9
  3. E. I. Gordon, A. G. Kusraev, S. S. Kutateladze
    Pages 10-34
  4. E. I. Gordon, A. G. Kusraev, S. S. Kutateladze
    Pages 35-115
  5. E. I. Gordon, A. G. Kusraev, S. S. Kutateladze
    Pages 116-165
  6. E. I. Gordon, A. G. Kusraev, S. S. Kutateladze
    Pages 166-222
  7. E. I. Gordon, A. G. Kusraev, S. S. Kutateladze
    Pages 223-280
  8. E. I. Gordon, A. G. Kusraev, S. S. Kutateladze
    Pages 281-366
  9. E. I. Gordon, A. G. Kusraev, S. S. Kutateladze
    Pages 367-379
  10. Back Matter
    Pages 380-422

About this book

Introduction

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

Keywords

functional functional analysis harmonic analysis vector lattice

Authors and affiliations

  • E. I. Gordon
    • 1
  • A. G. Kusraev
    • 2
  • S. S. Kutateladze
    • 3
  1. 1.Eastern Illinois UniversityCharlestonUSA
  2. 2.Vladikavkaz State UniversityVladikavkazRussia
  3. 3.Sobolev Institute of MathematicsSiberian Division of the Russian Academy of SciencesNovosibirskRussia

Bibliographic information

  • DOI https://doi.org/10.1007/978-94-017-0063-4
  • Copyright Information Springer Science+Business Media B.V. 2002
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Print ISBN 978-90-481-6070-9
  • Online ISBN 978-94-017-0063-4
  • Buy this book on publisher's site
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