| 书目名称 | Hypernumbers and Extrafunctions | | 副标题 | Extending the Classi | | 编辑 | Mark Burgin | | 视频video | | | 概述 | 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 rea | | 丛书名称 | SpringerBriefs in Mathematics | | 图书封面 |  | | 描述 | .“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 | | 出版日期 | Book 2012 | | 关键词 | differentiation; extrafuntion; hypernumber; integration; topology; partial differential equations | | 版次 | 1 | | doi | https://doi.org/10.1007/978-1-4419-9875-0 | | isbn_softcover | 978-1-4419-9874-3 | | isbn_ebook | 978-1-4419-9875-0Series ISSN 2191-8198 Series E-ISSN 2191-8201 | | issn_series | 2191-8198 | | copyright | Mark Burgin 2012 |
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发表于 2025-3-21 19:19:06
