Infinitesimal analysis

Author(s)

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

Bibliographic Information

Infinitesimal analysis

by E.I. Gordon, A.G. Kusraev and S.S. Kutateladze

(Mathematics and its applications, v. 544)

Kluwer Academic, c2002

Other Title

Инфинитезщимальный анализ

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Note

Includes bibliographical references and index

"This is a completely updated and revised translation of the original work Инфинитезщимальный анализ, Части 1 и 2, by E.I. Gordon, A.G. Kusraev and S.S. Kutateladze, published by the Sobolev Institute of Mathematics, Russian Academy of Sciences, in 2001. Translated by S.S. Kutateladze."--t.p. verso

Description and Table of Contents

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

Table of Contents

Foreword. 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 Sub differentials. 6. Technique of Hyperapproximation. 7. Infinitesimals in Harmonic Analysis. 8. Exercises and Unsolved Problems. Appendix. References. Notation Index. Subject Index.

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Details

  • NCID
    BA58234849
  • ISBN
    • 1402007388
  • Country Code
    ne
  • Title Language Code
    eng
  • Text Language Code
    eng
  • Original Language Code
    rus
  • Place of Publication
    Dordrecht
  • Pages/Volumes
    xiii, 422 p.
  • Size
    25 cm
  • Parent Bibliography ID
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