Nonstandard analysis [Documento eletrónico] / Martin Väth
Language: eng - inglesa.Country: Switzerland, Swiss Confederation.Publication: Basel : Birkhäuser , 2007Description: VIII, 252 p.ISBN: 978-3-7643-7774-8.Subject - Topical Name: Análise global (Matemática) Online Resources:Click here to access online| Item type | Current location | Collection | Call number | Copy number | Status | Date due | Barcode |
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| E-Books | Biblioteca da FCTUNL Online | Não Ficção | QA297. FCT 95423 (Browse shelf) | 1 | Available |
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| QA297.ELS FCT 85318 Basic structured grid generation with an introduction to unstructured grid generation | QA297. FCT 94181 Equazioni a derivate parziali | QA297. FCT 95318 Forward-backward stochastic differential equations and their applications | QA297. FCT 95423 Nonstandard analysis | QA297. FCT 95434 Control of coupled partial differential equations | QA297. FCT 95529 Piecewise-smooth dynamical systems | QA297. FCT 95542 Numerical linear algebra |
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Nonstandard analysis was originally developed by Robinson to rigorously justify infinitesimals like df and dx in expressions like df/dx in Leibniz' calculus or even to justify concepts like \delta-`functions'. However, the approach is much more general and was soon extended by Henson, Luxemburg and others to a useful tool especially in more advanced analysis, topology, and functional analysis. The book is an introduction with emphasis on those more advanced applications in analysis which are hardly accessible by other methods. Examples of such topics are a deeper analysis of certain functionals like Hahn-Banach limits or of finitely additive measures: From the viewpoint of classical analysis these are strange objects whose mere existence is even hard to prove. From the viewpoint of nonstandard analysis, these are rather 'explicit' objects. Formally, nonstandard analysis is an application of model theory in analysis. However, the reader of the book is not expected to have any background in model theory; instead knowledge of calculus is required and, although the book is rather self-contained, background in more advanced analysis or (elementary) topology is useful.
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