Nonstandard Analysis in Practice

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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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.

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

• Laboratoire CNRS de Mathématiques, Université de Nice, France

  Francine Diener, Marc Diener

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