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Nonstandard Analysis in Practice

  • Textbook
  • © 1995

Overview

Editors:
  1. Francine Diener

    1. Laboratoire CNRS de Mathématiques, Université de Nice, France

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    You can also search for this editor in PubMed   Google Scholar

  2. Marc Diener

    1. Laboratoire CNRS de Mathématiques, Université de Nice, France

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    You can also search for this editor in PubMed   Google Scholar

Part of the book series: Universitext (UTX)

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Table of contents (11 chapters)

  1. Front Matter

    Pages I-XIV
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  2. Tutorial

    • F. Diener, M. Diener
    Pages 1-21

  3. Complex analysis

    • A. Fruchard
    Pages 23-50

  4. The Vibrating String

    • Pierre Delfini, Claude Lobry
    Pages 51-70

  5. Random walks and stochastic differential equations

    • Eric Benoît
    Pages 71-90

  6. Infinitesimal algebra and geometry

    • Michel Goze
    Pages 91-108

  7. General topology

    • Tewfik Sari
    Pages 109-144

  8. Neutrices, external numbers, and external calculus

    • Fouad Koudjeti, Imme van den Berg
    Pages 145-170

  9. An external probability order theorem with applications

    • I. P. van den Berg
    Pages 171-183

  10. Integration over finite sets

    • Pierre Cartier, Yvette Perrin
    Pages 185-204

  11. Ducks and rivers: three existence results

    • Francine Diener, Marc Diener
    Pages 205-224

  12. Teaching with infinitesimals

    • André Deledicq
    Pages 225-238

  13. Back Matter

    Pages 239-250
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Keywords

About this book

The purpose of this book is to provide an effective introduction to nonstandard methods. A short tutorial giving the necessary background, is followed by applications to various domains, independent from each other. These include complex dynamical systems, stochastic differential equations, smooth and algebraic curves, measure theory, the external calculus, with some applications to probability. The authors have been using Nonstandard Analysis for many years in their research. They all belong to the growing nonstandard school founded by G. Reeb, which is attracting international and interdisciplinary interest.

Editors and Affiliations

  • Laboratoire CNRS de Mathématiques, Université de Nice, France

    Francine Diener, Marc Diener

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