Buch, Englisch, Band 544, 422 Seiten, Format (B × H): 161 mm x 240 mm, Gewicht: 1750 g
Buch, Englisch, Band 544, 422 Seiten, Format (B × H): 161 mm x 240 mm, Gewicht: 1750 g
Reihe: Mathematics and Its Applications
ISBN: 978-1-4020-0738-5
Verlag: Springer Netherlands
Infinitesimal analysis, once a synonym for calculus, is now viewed as a technique for studying the properties of an arbitrary mathematical object by discriminating between its standard and nonstandard constituents. Resurrected by A. Robinson in the early 1960's with the epithet 'nonstandard', infinitesimal analysis not only has revived the methods of infinitely small and infinitely large quantities, which go back to the very beginning of calculus, but also has suggested many powerful tools for research in every branch of modern mathematics.
The book sets forth the basics of the theory, as well as the most recent applications in, for example, functional analysis, optimization, and harmonic analysis. The concentric style of exposition enables this work to serve as an elementary introduction to one of the most promising mathematical technologies, while revealing up-to-date methods of monadology and hyperapproximation.
This is a companion volume to the earlier works on nonstandard methods of analysis by A.G. Kusraev and S.S. Kutateladze (1999), ISBN 0-7923-5921-6 and Nonstandard Analysis and Vector Lattices edited by S.S. Kutateladze (2000), ISBN 0-7923-6619-0
Zielgruppe
Research
Autoren/Hrsg.
Fachgebiete
- Mathematik | Informatik Mathematik Mathematische Analysis Reelle Analysis
- Mathematik | Informatik Mathematik Mathematische Analysis Harmonische Analysis, Fourier-Mathematik
- Mathematik | Informatik Mathematik Mathematik Allgemein Grundlagen der Mathematik
- Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis
Weitere Infos & Material
1. Excursus into the History of Calculus.- 2. Naive Foundations of Infinitesimal Analysis.- 3. Set-Theoretic Formalisms of Infinitesimal Analysis.- 4. Monads in General Topology.- 5. Infinitesimals and Subdifferentials.- 6. Technique of Hyperapproximation.- 7. Infinitesimals in Harmonic Analysis.- 8. Exercises and Unsolved Problems.- References.- Notation Index.
