Hypernumbers and extrafunctions: extending the classical calculus
(eBook)
?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.
Burgin, M. S. (2012). Hypernumbers and extrafunctions: extending the classical calculus. New York, NY, Springer.
Chicago / Turabian - Author Date Citation (style guide)Burgin, M. S. 2012. Hypernumbers and Extrafunctions: Extending the Classical Calculus. New York, NY, Springer.
Chicago / Turabian - Humanities Citation (style guide)Burgin, M. S, Hypernumbers and Extrafunctions: Extending the Classical Calculus. New York, NY, Springer, 2012.
MLA Citation (style guide)Burgin, M. S. Hypernumbers and Extrafunctions: Extending the Classical Calculus. New York, NY, Springer, 2012.
Notes
Record Information
Last Sierra Extract Time | May 01, 2024 10:09:12 AM |
---|---|
Last File Modification Time | May 01, 2024 10:11:05 AM |
Last Grouped Work Modification Time | May 01, 2024 10:09:19 AM |
MARC Record
LEADER | 04872cam a2200889 a 4500 | ||
---|---|---|---|
001 | 794176804 | ||
003 | OCoLC | ||
005 | 20240329122006.0 | ||
006 | m o d | ||
007 | cr cnu---unuuu | ||
008 | 120523s2012 nyu ob 001 0 eng d | ||
020 | |a 9781441998750|q (electronic bk.) | ||
020 | |a 1441998756|q (electronic bk.) | ||
020 | |z 9781441998743 | ||
035 | |a (OCoLC)794176804 | ||
040 | |a GW5XE|b eng|e pn|c GW5XE|d ZMC|d COO|d E7B|d CDX|d YDXCP|d OCLCQ|d OCLCF|d TPH|d OCLCQ|d Z5A|d ESU|d VT2|d IOG|d N$T|d OCLCO|d REB|d OCLCO|d OCLCQ|d OCLCO|d CEF|d U3W|d OCLCO|d WYU|d OCLCA|d YOU|d LEAUB|d OL$|d OCLCQ|d AJS|d OCLCQ|d OCLCO|d OCLCQ|d OCLCO|d OCL|d INARC|d OCLCQ|d OCLCO|d OCLCL|d S9M|d OCLCL | ||
049 | |a COM6 | ||
050 | 4 | |a QA303.2|b .B87 2012 | |
060 | 4 | |a Online Book | |
072 | 7 | |a MAT|x 005000|2 bisacsh | |
072 | 7 | |a MAT|x 034000|2 bisacsh | |
082 | 0 | 4 | |a 515|2 23 |
100 | 1 | |a Burgin, M. S.|q (Mark Semenovich)|1 https://id.oclc.org/worldcat/entity/E39PCjtTxGDy9kkhjwTJbjp8bq | |
245 | 1 | 0 | |a Hypernumbers and extrafunctions :|b extending the classical calculus /|c Mark Burgin. |
260 | |a New York, NY :|b Springer,|c ©2012. | ||
300 | |a 1 online resource (vii, 160 pages) | ||
336 | |a text|b txt|2 rdacontent | ||
337 | |a computer|b c|2 rdamedia | ||
338 | |a online resource|b cr|2 rdacarrier | ||
490 | 1 | |a SpringerBriefs in mathematics,|x 2191-8198 | |
504 | |a Includes bibliographical references and index. | ||
505 | 0 | 0 | |t Introduction: How Mathematicians Solve "Unsolvable" Problems /|r Hypernumbers /|r Extrafunctions /|r How to Differentiate Any Real Function /|r How to Integrate Any Real Function /|r Conclusion: New Opportunities. |
520 | |a ?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. | ||
650 | 0 | |a Calculus. | |
650 | 0 | |a Mathematics. | |
650 | 1 | 2 | |a Mathematics |
650 | 6 | |a Calcul infinitésimal. | |
650 | 6 | |a Mathématiques. | |
650 | 7 | |a calculus.|2 aat | |
650 | 7 | |a MATHEMATICS|x Calculus.|2 bisacsh | |
650 | 7 | |a MATHEMATICS|x Mathematical Analysis.|2 bisacsh | |
650 | 7 | |a Cálculo|2 embne | |
650 | 7 | |a Matemáticas|2 embne | |
650 | 7 | |a Mathematics|2 fast | |
650 | 7 | |a Calculus|2 fast | |
653 | 4 | |a Global analysis (Mathematics) | |
653 | 4 | |a Functional analysis. | |
653 | 4 | |a Differential equations, partial. | |
653 | 4 | |a Mathematical physics. | |
653 | 4 | |a Analysis. | |
653 | 4 | |a Partial Differential Equations. | |
653 | 4 | |a Measure and Integration. | |
710 | 2 | |a SpringerLink (Online Service) | |
830 | 0 | |a SpringerBriefs in mathematics. | |
907 | |a .b35559809 | ||
948 | |a MARCIVE Comp, in 2022.12 | ||
948 | |a MARCIVE Over, 07/2021 | ||
948 | |a MARCIVE Comp, 2019.12 | ||
948 | |a MARCIVE Comp, 2018.05 | ||
948 | |a MARCIVE August, 2017 | ||
948 | |a MARCIVE extract Aug, 5 2017 | ||
989 | |1 .i71773435|d cceb|g j|m |h 0|x 0|t 0|i 0|j 188|k 120614|o -|w SpringerLink CCU Owned|u http://ezproxy.ccu.edu/login?url=http://dx.doi.org/10.1007/978-1-4419-9875-0 | ||
989 | |1 .i151360972|d cueme|g -|m |h 0|x 0|t 0|i 0|j 200|k 240404|o -|w SpringerLink|u http://ezproxy.coloradomesa.edu/login?url=https://link.springer.com/10.1007/978-1-4419-9875-0 | ||
994 | |a 92|b COM | ||
995 | |a Loaded with m2btab.elec in 2024.04 | ||
995 | |a Loaded with m2btab.ltiac in 2022.12 | ||
995 | |a Loaded with m2btab.ltiac in 2021.07 | ||
995 | |a Loaded with m2btab.elec in 2021.06 | ||
995 | |a Loaded with m2btab.ltiac in 2019.12 | ||
995 | |a Loaded with m2btab.ltiac in 2018.06 | ||
995 | |a Loaded with m2btab.ltiac in 2017.08 | ||
995 | |a Loaded with m2btab.elec in 2016 | ||
995 | |a Loaded with m2btab.elec in 2016 | ||
995 | |a OCLC offline update by CMU | ||
998 | |e -|f eng|a cue|a cc|a cu | ||
999 | |e z | ||
999 | |a cue |