Nonstandard Analysis in Practice

  • Francine Diener
  • Marc Diener

Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages I-XIV
  2. F. Diener, M. Diener
    Pages 1-21
  3. A. Fruchard
    Pages 23-50
  4. Pierre Delfini, Claude Lobry
    Pages 51-70
  5. Michel Goze
    Pages 91-108
  6. Tewfik Sari
    Pages 109-144
  7. Fouad Koudjeti, Imme van den Berg
    Pages 145-170
  8. Pierre Cartier, Yvette Perrin
    Pages 185-204
  9. Francine Diener, Marc Diener
    Pages 205-224
  10. André Deledicq
    Pages 225-238
  11. Back Matter
    Pages 239-250

About this book

Introduction

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.

Keywords

Martingale Riemannian geometry curvature differential geometry duck infinitesimals neutrice nonstandard analysis proof random walk set shadow

Editors and affiliations

  • Francine Diener
    • 1
  • Marc Diener
    • 1
  1. 1.Laboratoire CNRS de MathématiquesUniversité de NiceFrance

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-57758-1
  • Copyright Information Springer-Verlag Berlin Heidelberg 1995
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-60297-2
  • Online ISBN 978-3-642-57758-1
  • Series Print ISSN 0172-5939
  • Series Online ISSN 2191-6675
  • About this book