Hypernumbers and Extrafunctions: Extending the Classical Calculus (SpringerBriefs in Mathematics) - Tapa blanda

Libro 9 de 155: SpringerBriefs in Mathematics

Burgin, Mark

 
9781441998743: Hypernumbers and Extrafunctions: Extending the Classical Calculus (SpringerBriefs in Mathematics)
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ISBN 10: 1441998748 ISBN 13: 9781441998743
Editorial: Springer, 2012

Sinopsis

“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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Críticas

From the reviews:

“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)

Reseña del editor

This rigorous approach to operating with infinite values expands concepts of real and complex numbers to include a new universe of numbers called hypernumbers which includes infinite quantities, and extends classical calculus by introducing extrafunctions.

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Editorial
Springer
Año de publicación
2012
Idioma
Inglés
ISBN 10 
1441998748
ISBN 13 
9781441998743
Encuadernación
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Número de páginas
168
Contacto del fabricante
no disponible
Persona responsable
CMN Printpool Inh. Mathis Neumann
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Friedrich-Karl-Str. 9
Hamburg
Alemania

Otras ediciones populares con el mismo título

9781441998767: Hypernumbers and Extrafunctions: Extending the Classical Calculus

Edición Destacada

ISBN 10:  1441998764 ISBN 13:  9781441998767
Editorial: Springer, 2012
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