vbid/9781441998750

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.Typham this is the title: Hypernumbers and Extrafunctions Extending the Classical Calculus