Articoli correlati a Nonstandard Analysis: Theory and Applications: 493
Sinossi
1 More than thirty years after its discovery by Abraham Robinson , the ideas and techniques of Nonstandard Analysis (NSA) are being applied across the whole mathematical spectrum,as well as constituting an im portant field of research in their own right. The current methods of NSA now greatly extend Robinson's original work with infinitesimals. However, while the range of applications is broad, certain fundamental themes re cur. The nonstandard framework allows many informal ideas (that could loosely be described as idealisation) to be made precise and tractable. For example, the real line can (in this framework) be treated simultaneously as both a continuum and a discrete set of points; and a similar dual ap proach can be used to link the notions infinite and finite, rough and smooth. This has provided some powerful tools for the research mathematician - for example Loeb measure spaces in stochastic analysis and its applications, and nonstandard hulls in Banach spaces. The achievements of NSA can be summarised under the headings (i) explanation - giving fresh insight or new approaches to established theories; (ii) discovery - leading to new results in many fields; (iii) invention - providing new, rich structures that are useful in modelling and representation, as well as being of interest in their own right. The aim of the present volume is to make the power and range of appli cability of NSA more widely known and available to research mathemati cians.
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Contenuti
Preface. Foundations of Nonstandard Analysis: A Gentle Introduction to Nonstandard Extensions; C.W. Henson. Nonstandard Real Analysis; N.J. Cutland. Nonstandard Analysis and Topology; P.A. Loeb. Loeb Measure and Probability; D.A. Ross. An Introduction to Nonstandard Functional Analysis; M.P.H. Wolff. Applications of Nonstandard Analysis in Ordinary Differential Equations; E. Benoit. Better Nonstandard Universes with Applications; R. Jin. Internal Martingales and Stochastic Integration; T. Lindstrøm. Stochastic Differential Equations with Extra Properties; H.J. Keisler. Hyperfinite Mathematical Finance; P.E. Kopp. Applications of NSA To Mathematical Physics; L. Arkeryd. A Nonstandard Approach to Hydromechanics: Navier-Stokes Equations; M. Capinski. Index.
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Nonstandard Analysis : Theory and Applications
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Springer Netherlands, 1997
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ISBN 13: 9780792345862
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Gebunden. Condizione: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. Proceedings of the NATO Advanced Study Institute on Nonstandard Analysis and its Applications, International Centre for Mathematical Studies, Endinburgh, Scotland, 30 June-13 July 1996 1 More than thirty years after its discovery by Abraham Robin. Codice articolo 5968129
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Nonstandard Analysis: Theory and Applications (Nato Science Series C:, 493)
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Buch. Condizione: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -1 More than thirty years after its discovery by Abraham Robinson , the ideas and techniques of Nonstandard Analysis (NSA) are being applied across the whole mathematical spectrum,as well as constituting an im portant field of research in their own right. The current methods of NSA now greatly extend Robinson's original work with infinitesimals. However, while the range of applications is broad, certain fundamental themes re cur. The nonstandard framework allows many informal ideas (that could loosely be described as idealisation) to be made precise and tractable. For example, the real line can (in this framework) be treated simultaneously as both a continuum and a discrete set of points; and a similar dual ap proach can be used to link the notions infinite and finite, rough and smooth. This has provided some powerful tools for the research mathematician - for example Loeb measure spaces in stochastic analysis and its applications, and nonstandard hulls in Banach spaces. The achievements of NSA can be summarised under the headings (i) explanation - giving fresh insight or new approaches to established theories; (ii) discovery - leading to new results in many fields; (iii) invention - providing new, rich structures that are useful in modelling and representation, as well as being of interest in their own right. The aim of the present volume is to make the power and range of appli cability of NSA more widely known and available to research mathemati cians. 384 pp. Englisch. Codice articolo 9780792345862
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Buch. Condizione: Neu. Neuware -1 More than thirty years after its discovery by Abraham Robinson , the ideas and techniques of Nonstandard Analysis (NSA) are being applied across the whole mathematical spectrum,as well as constituting an im portant field of research in their own right. The current methods of NSA now greatly extend Robinson's original work with infinitesimals. However, while the range of applications is broad, certain fundamental themes re cur. The nonstandard framework allows many informal ideas (that could loosely be described as idealisation) to be made precise and tractable. For example, the real line can (in this framework) be treated simultaneously as both a continuum and a discrete set of points; and a similar dual ap proach can be used to link the notions infinite and finite, rough and smooth. This has provided some powerful tools for the research mathematician - for example Loeb measure spaces in stochastic analysis and its applications, and nonstandard hulls in Banach spaces. The achievements of NSA can be summarised under the headings (i) explanation - giving fresh insight or new approaches to established theories; (ii) discovery - leading to new results in many fields; (iii) invention - providing new, rich structures that are useful in modelling and representation, as well as being of interest in their own right. The aim of the present volume is to make the power and range of appli cability of NSA more widely known and available to research mathemati cians.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 384 pp. Englisch. Codice articolo 9780792345862
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Buch. Condizione: Neu. Druck auf Anfrage Neuware - Printed after ordering - 1 More than thirty years after its discovery by Abraham Robinson , the ideas and techniques of Nonstandard Analysis (NSA) are being applied across the whole mathematical spectrum,as well as constituting an im portant field of research in their own right. The current methods of NSA now greatly extend Robinson's original work with infinitesimals. However, while the range of applications is broad, certain fundamental themes re cur. The nonstandard framework allows many informal ideas (that could loosely be described as idealisation) to be made precise and tractable. For example, the real line can (in this framework) be treated simultaneously as both a continuum and a discrete set of points; and a similar dual ap proach can be used to link the notions infinite and finite, rough and smooth. This has provided some powerful tools for the research mathematician - for example Loeb measure spaces in stochastic analysis and its applications, and nonstandard hulls in Banach spaces. The achievements of NSA can be summarised under the headings (i) explanation - giving fresh insight or new approaches to established theories; (ii) discovery - leading to new results in many fields; (iii) invention - providing new, rich structures that are useful in modelling and representation, as well as being of interest in their own right. The aim of the present volume is to make the power and range of appli cability of NSA more widely known and available to research mathemati cians. Codice articolo 9780792345862
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Hardcover. Condizione: new. Hardcover. Presenting a detailed introduction to the methodology of nonstandard analysis and the foundations of its use in analysis, topology, probability theory and stochastic analysis, this text includes articles concerning more advanced applications in functional analysis. These include stochastic differential equations, mathematical physics and mathematical finance theory. A detailed introduction to the methodology of nonstandard analysis and the foundations of its use in analysis, topology, probability theory and stochastic analysis. Further articles expound recent, more advanced applications in functional analysis, stochastic differential equations, mathematical physics and mathematical finance theory. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. Codice articolo 9780792345862
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ISBN 13: 9780792345862
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Hardcover. Condizione: new. Hardcover. Presenting a detailed introduction to the methodology of nonstandard analysis and the foundations of its use in analysis, topology, probability theory and stochastic analysis, this text includes articles concerning more advanced applications in functional analysis. These include stochastic differential equations, mathematical physics and mathematical finance theory. A detailed introduction to the methodology of nonstandard analysis and the foundations of its use in analysis, topology, probability theory and stochastic analysis. Further articles expound recent, more advanced applications in functional analysis, stochastic differential equations, mathematical physics and mathematical finance theory. Shipping may be from our Sydney, NSW warehouse or from our UK or US warehouse, depending on stock availability. Codice articolo 9780792345862
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