<電子ブック>
Nonstandard Analysis in Practice / edited by Francine Diener, Marc Diener
(Universitext. ISSN:21916675)
版 | 1st ed. 1995. |
---|---|
出版者 | (Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer) |
出版年 | 1995 |
本文言語 | 英語 |
大きさ | XIV, 250 p. 14 illus : online resource |
著者標目 | Diener, Francine editor Diener, Marc editor SpringerLink (Online service) |
件 名 | LCSH:Functions of real variables LCSH:Mathematical logic LCSH:Geometry, Differential LCSH:Probabilities FREE:Real Functions FREE:Mathematical Logic and Foundations FREE:Differential Geometry FREE:Probability Theory |
一般注記 | 1. Tutorial -- 1.1 A new view of old sets -- 1.2 Using the extended language -- 1.3 Shadows and S-properties -- 1.4 Permanence principles -- 2. Complex analysis -- 2.1 Introduction -- 2.2 Tutorial -- 2.3 Complex iteration -- 2.4 Airy’s equation -- 2.5 Answers to exercises -- 3. The Vibrating String -- 3.1 Introduction -- 3.2 Fourier analysis of (DEN) -- 3.3 An interesting example -- 3.4 Solutions of limited energy -- 3.5 Conclusion -- 4. Random walks and stochastic differential equations -- 4.1 Introduction -- 4.2 The Wiener walk with infinitesimal steps -- 4.3 Equivalent processes -- 4.4 Diffusions. Stochastic differential equations -- 4.5 Probability law of a diffusion -- 4.6 Ito’s calculus — Girsanov’s theorem -- 4.7 The “density” of a diffusion -- 4.8 Conclusion -- 5. Infinitesimal algebra and geometry -- 5.1 A natural algebraic calculus -- 5.2 A decomposition theorem for a limited point -- 5.3 Infinitesimal riemannian geometry -- 5.4 The theory of moving frames -- 5.5 Infinitesimal linear algebra -- 6. General topology -- 6.1 Halos in topological spaces -- 6.2 What purpose do halos serve ? -- 6.3 The external definition of a topology -- 6.4 The power set of a topological space -- 6.5 Set-valued mappings and limits of sets -- 6.6 Uniform spaces -- 6.7 Answers to the exercises -- 7. Neutrices, external numbers, and external calculus -- 7.1 Introduction -- 7.2 Conventions; an example -- 7.3 Neutrices and external numbers -- 7.4 Basic algebraic properties -- 7.5 Basic analytic properties -- 7.6 Stirling’s formula -- 7.7 Conclusion -- 8. An external probability order theorem with applications -- 8.1 Introduction -- 8.2 External probabilities -- 8.3 External probability order theorems -- 8.4 Weierstrass, Stirling, De Moivre-Laplace -- 9. Integration over finite sets -- 9.1 Introduction -- 9.2 S-integration.-9.3 Convergence in SL1(F) -- 9.4 Conclusion -- 10. Ducks and rivers: three existence results -- 10.1 The ducks of the Van der Pol equation -- 10.2 Slow-fast vector fields -- 10.3 Robust ducks -- 10.4 Rivers -- 11. Teaching with infinitesimals -- 11.1 Meaning rediscovered -- 11.2 the evidence of orders of magnitude -- 11.3 Completeness and the shadows concept -- References -- List of contributors 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 HTTP:URL=https://doi.org/10.1007/978-3-642-57758-1 |
目次/あらすじ
所蔵情報を非表示
電子ブック | 配架場所 | 資料種別 | 巻 次 | 請求記号 | 状 態 | 予約 | コメント | ISBN | 刷 年 | 利用注記 | 指定図書 | 登録番号 |
---|---|---|---|---|---|---|---|---|---|---|---|---|
電子ブック | オンライン | 電子ブック |
|
Springer eBooks | 9783642577581 |
|
電子リソース |
|
EB00232481 |
類似資料
この資料の利用統計
このページへのアクセス回数:12回
※2017年9月4日以降