SpringerBriefs in Mathematics

Hypernumbers and Extrafunctions

Extending the Classical Calculus

Authors: Burgin, Mark

  • Designed to introduce the reader to hypernumbers and extrafunctions, which is another rigorous mathematical approach to operations with infinite values
  • Shows 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 integration
  • Used for enhancing traditional courses of calculus for undergraduates, as well as for teaching a separate course for graduate students
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eBook $34.99
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  • ISBN 978-1-4419-9875-0
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  • Immediate eBook download after purchase
Softcover $49.95
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  • ISBN 978-1-4419-9874-3
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About this book

“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 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 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.

Reviews

From the reviews:

“Burgin (UCLA) provides an introduction to the theory of hypernumbers in this short book, part of the ‘SpringerBriefs in Mathematics’ series. The (real) hypernumbers are an extension of the real numbers that permits operations with infinite quantities; a real general extrafunction is a partial map from the set of real hypernumbers to itself. … Summing Up: Recommended. Advanced upper-division undergraduates, graduate students, and researchers/faculty.” (D. Robbins, Choice, Vol. 50 (3), November, 2012)

Table of contents (6 chapters)

Buy this book

eBook $34.99
price for USA (gross)
  • ISBN 978-1-4419-9875-0
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $49.95
price for USA
  • ISBN 978-1-4419-9874-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Hypernumbers and Extrafunctions
Book Subtitle
Extending the Classical Calculus
Authors
Series Title
SpringerBriefs in Mathematics
Copyright
2012
Publisher
Springer-Verlag New York
Copyright Holder
Mark Burgin
eBook ISBN
978-1-4419-9875-0
DOI
10.1007/978-1-4419-9875-0
Softcover ISBN
978-1-4419-9874-3
Series ISSN
2191-8198
Edition Number
1
Number of Pages
VII, 160
Topics