Ebook: Nonstandard Analysis in Practice

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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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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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.
Content:
Front Matter....Pages I-XIV
Tutorial....Pages 1-21
Complex analysis....Pages 23-50
The Vibrating String....Pages 51-70
Random walks and stochastic differential equations....Pages 71-90
Infinitesimal algebra and geometry....Pages 91-108
General topology....Pages 109-144
Neutrices, external numbers, and external calculus....Pages 145-170
An external probability order theorem with applications....Pages 171-183
Integration over finite sets....Pages 185-204
Ducks and rivers: three existence results....Pages 205-224
Teaching with infinitesimals....Pages 225-238
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.
Content:
Front Matter....Pages I-XIV
Tutorial....Pages 1-21
Complex analysis....Pages 23-50
The Vibrating String....Pages 51-70
Random walks and stochastic differential equations....Pages 71-90
Infinitesimal algebra and geometry....Pages 91-108
General topology....Pages 109-144
Neutrices, external numbers, and external calculus....Pages 145-170
An external probability order theorem with applications....Pages 171-183
Integration over finite sets....Pages 185-204
Ducks and rivers: three existence results....Pages 205-224
Teaching with infinitesimals....Pages 225-238
Back Matter....Pages 239-250
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