Hypernumbers and Extrafunctions

Extending the Classical Calculus

Nonfiction, Science & Nature, Mathematics, Functional Analysis, Mathematical Analysis
Cover of the book Hypernumbers and Extrafunctions by Mark Burgin, Springer New York
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Mark Burgin ISBN: 9781441998750
Publisher: Springer New York Publication: May 16, 2012
Imprint: Springer Language: English
Author: Mark Burgin
ISBN: 9781441998750
Publisher: Springer New York
Publication: May 16, 2012
Imprint: Springer
Language: English

“Hypernumbers and Extrafunctions” 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 theFeynman 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 powerful tools for mathematics and its applications. Specifically, it makes it possible to solve PDE for which it is proved that they do not have solutions  in distributions. Also illustrated in this text is how this new theory allows the differentiation and integration of any real function. This text can be used for enhancing traditional courses of calculus for undergraduates, as well as for teaching a separate course for graduate students.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

“Hypernumbers and Extrafunctions” 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 theFeynman 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 powerful tools for mathematics and its applications. Specifically, it makes it possible to solve PDE for which it is proved that they do not have solutions  in distributions. Also illustrated in this text is how this new theory allows the differentiation and integration of any real function. This text can be used for enhancing traditional courses of calculus for undergraduates, as well as for teaching a separate course for graduate students.

More books from Springer New York

Cover of the book Diabetes and Viruses by Mark Burgin
Cover of the book A Longitudinal Study of Dyslexia by Mark Burgin
Cover of the book War, Community, and Social Change by Mark Burgin
Cover of the book Finance with Monte Carlo by Mark Burgin
Cover of the book Translational Approach to Heart Failure by Mark Burgin
Cover of the book Exotic Nuclear Excitations by Mark Burgin
Cover of the book Analytical Techniques in Biochemistry and Molecular Biology by Mark Burgin
Cover of the book Stem Cells Handbook by Mark Burgin
Cover of the book Exercise and Cancer Survivorship by Mark Burgin
Cover of the book Genetics and Genomics of Rosaceae by Mark Burgin
Cover of the book Pediatric Infectious Disease by Mark Burgin
Cover of the book TH17 Cells in Health and Disease by Mark Burgin
Cover of the book Reviews of Environmental Contamination and Toxicology Volume 223 by Mark Burgin
Cover of the book Cognitive Strategy Research by Mark Burgin
Cover of the book Advances in Growth Curve Models by Mark Burgin
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy