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.
Nonstandard Analysis in Practice
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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.
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Inside This Book
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First Sentence:
Nonstandard Analysis, as is the case with Mathematics itself, can be applied to many domains; to illustrate this by means of examples is the object of this book. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
idempotent neutrix, idempotent neutrices, idealisation principle, standard uniform space, two external numbers, quadrable subsets, lower halfline, two neutrices, standard topological space, unlimited real number, whose standard elements, standard open set, unlimited integers, concentration lemma, precompact space, external interval, concentration theorem, duck value, standard metric spaces, nonstandard context, wise curve, uniform proximity, external probability, external formulas, topological proximity Key Phrases - Capitalized Phrases (CAPs): (learn more)
Tewfik Sari, Michel Goze, Eric Benoit, Berg Proposition, Standard Subset New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Nonstandard Analysis, as is the case with Mathematics itself, can be applied to many domains; to illustrate this by means of examples is the object of this book. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
idempotent neutrix, idempotent neutrices, idealisation principle, standard uniform space, two external numbers, quadrable subsets, lower halfline, two neutrices, standard topological space, unlimited real number, whose standard elements, standard open set, unlimited integers, concentration lemma, precompact space, external interval, concentration theorem, duck value, standard metric spaces, nonstandard context, wise curve, uniform proximity, external probability, external formulas, topological proximity Key Phrases - Capitalized Phrases (CAPs): (learn more)
Tewfik Sari, Michel Goze, Eric Benoit, Berg Proposition, Standard Subset New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 8
books:
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45
books
cite this book:
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- Abraham Robinson by Joseph Warren Dauben in Back Matter
- Analyse non standard by F. Diener in Back Matter
- Set-Valued Analysis (Systems & Control: Foundations & Applications) by Jean-Pierre Aubin in Back Matter
- Nonstandard Asymptotic Analysis (Lecture Notes in Mathematics) by Imme Van Den Berg in Back Matter
- Introduction to the Theory of infiniteseimals, Volume 72 (Pure and Applied Mathematics) by Author Unknown in Back Matter
See all 8 books this book cites
- Option Theory with Stochastic Analysis: An Introduction to Mathematical Finance (Universitext) by Fred Espen Benth in Back Matter
- Complex Geometry: An Introduction (Universitext) by Daniel Huybrechts in Back Matter
- p-adic Numbers: An Introduction (Universitext) by Fernando Quadros Gouvea in Back Matter
- Logic and Structure by Dirk van Dalen in Back Matter
- Theory and Numerics of Differential Equations by James F. Blowey in Back Matter
See all 45 books citing this book
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