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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"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)