Hypernumbers and extrafunctions: extending the classical calculus
Author:
Publisher:
Springer
Pub. Date:
[2012]
Language:
English
Description
?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.
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Contributors:
ISBN:
9781441998750
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Grouping Information
Grouped Work ID | 7b6b90ad-5a47-c74f-332a-892b11a08705 |
---|---|
Grouping Title | hypernumbers and extrafunctions extending the classical calculus |
Grouping Author | m s burgin |
Grouping Category | book |
Grouping Language | English (eng) |
Last Grouping Update | 2024-05-16 18:07:41PM |
Last Indexed | 2024-05-17 23:34:36PM |
Solr Fields
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author
Burgin, M. S. (Mark Semenovich)
author2-role
SpringerLink (Online service)
author_display
Burgin, M. S.
available_at_ccu
CCU Electronic Resources
detailed_location_ccu
CCU Electronic Resources
display_description
?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.
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eBook
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eBook
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7b6b90ad-5a47-c74f-332a-892b11a08705
isbn
9781441998750
itype_ccu
E-book
last_indexed
2024-05-18T05:34:36.522Z
lexile_score
-1
literary_form
Non Fiction
literary_form_full
Non Fiction
owning_library_ccu
Colorado Christian University Online
owning_location_ccu
CCU Electronic Resources
primary_isbn
9781441998750
publishDate
2012
publisher
Springer
recordtype
grouped_work
series
SpringerBriefs in mathematics
series_with_volume
SpringerBriefs in mathematics|
subject_facet
Calcul infinitésimal
Calculus
Cálculo
MATHEMATICS -- Calculus
MATHEMATICS -- Mathematical Analysis
Matemáticas
Mathematics
Mathématiques
calculus
Calculus
Cálculo
MATHEMATICS -- Calculus
MATHEMATICS -- Mathematical Analysis
Matemáticas
Mathematics
Mathématiques
calculus
title_display
Hypernumbers and extrafunctions : extending the classical calculus
title_full
Hypernumbers and extrafunctions : extending the classical calculus / Mark Burgin
title_short
Hypernumbers and extrafunctions
title_sub
extending the classical calculus
topic_facet
Calcul infinitésimal
Calculus
Cálculo
MATHEMATICS
Matemáticas
Mathematical Analysis
Mathematics
Mathématiques
calculus
Calculus
Cálculo
MATHEMATICS
Matemáticas
Mathematical Analysis
Mathematics
Mathématiques
calculus
Solr Details Tables
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