Nonstandard Analysis in Practice

Language: English

Published by Springer, Springer Vieweg Dez 1995, 1995

3540602976 / 9783540602972

Series: Book 129 of 261 - Universitext

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This item is printed on demand - Print on Demand Titel. Neuware -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.Springer-Verlag KG, Sachsenplatz 4-6, 1201 Wien 268 pp. Englisch.…

Seller Inventory # 9783540602972

Title
Nonstandard Analysis in Practice
Author
Francine Diener
Publisher
Springer, Springer Vieweg Dez 1995
Publication year
1995
Condition
Neu
Binding
Taschenbuch
Language
English
ISBN 10
3540602976
ISBN 13
9783540602972
Item weight
411 grams
Dimensions
235x155x15 mm
Series
Book 129 of 261: Universitext

buchversandmimpf2000

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