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Nonstandard Analysis in Practice

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Nonstandard Analysis in Practice Cover

 

Synopses & Reviews

Publisher Comments:

This book introduces the graduate mathematician and researcher to the effective use of nonstandard analysis (NSA). It provides a tutorial introduction to this modern theory of infinitesimals, followed by nine examples of applications, including complex analysis, stochastic differential equations, differential geometry, topology, probability, integration, and asymptotics. It ends with remarks on teaching with infinitesimals. Written by members of the Reeb-school, and favouring typical examples, the results are new or give at least new insights into classical problems. Even if its first purpose is to help the readers to use NSA, it gives a taste of the research in progress in this domain.

Table of Contents

1. Tutorial / F. Diener and M. Diener — 2. Complex analysis / A. Fruchard — 3. The Vibrating String / Pierre Delfini and Claude Lobry — 4. Random walks and stochastic differential equations / Eric Benoit — 5. Infinitesimal algebra and geometry / Michel Goze — 6. General topology / Tewfik Sari — 7. Neutrices, external numbers, and external calculus / Fouad Koudjeti and Imme van den Berg — 8. An external probability order theorem with applications / I.P. van den Berg — 9. Integration over finite sets / Pierre Cartier and Yvette Perrin — 10. Ducks and rivers: three existence results / Francine Diener and Marc Diener — 11. Teaching with infinitesimals / Andre' Deledicq.

Product Details

ISBN:
3330000238464
Publisher:
Springer
Subject:
Nonstandard mathematical analysis
Author:
Diener, Francine
Author:
Diener, Marc
Subject:
Logic
Subject:
Mathematical Analysis
Subject:
Geometry - Differential
Subject:
Functional Analysis
Subject:
Duck
Subject:
infinitesimals
Subject:
neutrice
Subject:
nonstandard analysis
Subject:
Shadow
Subject:
Real functions
Subject:
Mathematical Logic and Foundations
Subject:
Differential geometry
Subject:
Probability Theory and Stochastic Processes
Subject:
Mathematics-Logic and Philosophy
Subject:
main_subject
Subject:
all_subjects
Publication Date:
1995
Binding:
ELECTRONIC
Language:
English
Pages:
250

Related Subjects

Science and Mathematics » Mathematics » Analysis General
Science and Mathematics » Mathematics » Differential Geometry
Science and Mathematics » Mathematics » Foundations and Logic
Science and Mathematics » Mathematics » Functional Analysis
Science and Mathematics » Mathematics » Probability and Statistics » General

Nonstandard Analysis in Practice
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Product details 250 pages Springer - English 3330000238464 Reviews:
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