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Field name	Details
Dewey Class	515
Title	Hypernumbers and Extrafunctions ([Ebook]) : Extending the Classical Calculus / by Mark Burgin.
Author	Burgin, Mark
Other name(s)	SpringerLink (Online service)
Publication	New York, NY : Springer
Publication	, 2012.
Physical Details	VII, 160 pages : online resource.
Series	SpringerBriefs in Mathematics 2191-8198
ISBN	9781441998750
Summary Note	âHypernumbers and Extrafunctionsâ presents a rigorous mathematical approach to operate with infinite values. First, concepts of real and complex numbers are expanded to include a new universe of numbers called hypernumbers which includes infinite quantities. This brief extends classical calculus based on real functions by introducing extrafunctions, which generalize not only the concept of a conventional function but also the concept of a distribution. Extrafucntions have been also efficiently used for a rigorous mathematical definition of the Feynman path integral, as well as for solving some problems in probability theory, which is also important for contemporary physics. This book introduces a new theory that includes the theory of distributions' as a subtheory, providing more powerfulÂ tools for mathematicsÂ andÂ itsÂ applications. Specifically it' makes it possible to solve PDE for which it is proved that they do not have solutions Â in distributions. Also illustrated in this text is how this new theory allows the differentiation and integration of any real function. This text canÂ be used for enhancing traditional courses of calculus for undergraduates, as well as for teaching a separate course for graduate students.:
Contents note	-1. Introduction: How mathematicians solve âunsolvableâ problems.-2.Â Hypernumbers(Definitions and typology,Algebraic properties,Topological properties).-3.Â Extrafunctions(Definitions and typology, Algebraic properties, Topological properties).-4.Â How to differentiate any real function (Approximations, Hyperdifferentiation).-5.Â How to integrate any continuous real function (Partitions and covers, Hyperintegration over finite intervals, Hyperintegration over infinite intervals). -6. Conclusion: New opportunities -- Appendix -- References.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users. with VPN connection).
Internet Site	http://dx.doi.org/10.1007/978-1-4419-9875-0
Links to Related Works	Subject References: Differential equations, Partial . Functional Analysis . Global analysis (Mathematics) . Mathematical Methods in Physics . Mathematical Physics . Measure and Integration . Partial differential equations . Authors: Burgin, Mark . Corporate Authors: SpringerLink (Online service) . Series: SpringerBriefs in Mathematics . Classification: 515 . 515 (DDC 23) .

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Hypernumbers and Extrafunctions: Extending the Classical Calculus

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