Mathematics and Its Applications

Infinitesimal Analysis

Authors: Gordon, E.I., Kusraev, A.G., Kutateladze, Semën Samsonovich

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  • ISBN 978-94-017-0063-4
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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

Table of contents (8 chapters)

  • Excursus into the History of Calculus

    Gordon, E. I. (et al.)

    Pages 1-9

  • Naive Foundations of Infinitesimal Analysis

    Gordon, E. I. (et al.)

    Pages 10-34

  • Set-Theoretic Formalisms of Infinitesimal Analysis

    Gordon, E. I. (et al.)

    Pages 35-115

  • Monads in General Topology

    Gordon, E. I. (et al.)

    Pages 116-165

  • Infinitesimals and Subdifferentials

    Gordon, E. I. (et al.)

    Pages 166-222

Buy this book

eBook $109.00
price for USA (gross)
  • ISBN 978-94-017-0063-4
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $129.00
price for USA
  • ISBN 978-1-4020-0738-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $139.00
price for USA
  • ISBN 978-90-481-6070-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Infinitesimal Analysis
Authors
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