Hypernumbers and Extrafunctions

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Extending the Classical Calculus, SpringerBriefs in Mathematics

ISBN: 1441998748
ISBN 13: 9781441998743
Autor: Burgin, Mark
Verlag: Springer Verlag GmbH
Umfang: vii, 160 S.
Erscheinungsdatum: 17.05.2012
Auflage: 1/2012
Produktform: Kartoniert
Einband: KT

Designed to introduce the reader to hypernumbers and extrafunctions, which is another rigorous mathematical approach to operations with infinite valuesShows that even in the most standard case of real analysis, hypernumbers and extrafunctions significantly extend the scope and increase the power not only of the classical calculus but of its moderngeneralizations and extensions, such as distribution theory or gauge integrationUsed for enhancing traditional courses of calculus for undergraduates, as well as for teaching a separate course for graduate students

Artikelnummer: 1629648 Kategorie:

Beschreibung

Inhaltsverzeichnis

-1. Introduction: How mathematicians solve a¿unsolvablea¿ problems.-2.  Hypernumbers(Constructive definition and algebraic properties of hypernumbers, Axiomatic definition and topological properties of hypernumbers).-3. Extrafunctions and hyperdistributions.-4.  How to differentiate any real function.-5. How to integrate any continuous real function. -6. Integration in infinite dimensional spaces and Feynman integral.-7. Conclusion: New opportunities.- Appendix.- References.

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