Hypernumbers and Extrafunctions Extending the Classical Calculus /

• Main Author: Burgin, Mark (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: New York, NY : Springer New York : Imprint: Springer, 2012.
• Series: SpringerBriefs in Mathematics,
• Subjects: Mathematics.; Mathematical analysis.; Analysis (Mathematics).; Functional analysis.; Measure theory.; Partial differential equations.; Physics.; Analysis.; Functional Analysis.; Partial Differential Equations.; Measure and Integration.; Mathematical Methods in Physics.

“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 bas...

Table of Contents:

• -1. Introduction: How mathematicians solve ”unsolvable” problems.-2.  Hypernumbers(Definitions and typology,Algebraic properties,Topological properties).-3. Extrafunctions(Definitions and typology, Algebraic properties, Topological properties).-4.  How to differentiate any real function (Approximations, Hyperdifferentiation).-5. How to integrate any continuous real function (Partitions and covers, Hyperintegration over finite intervals, Hyperintegration over infinite intervals). -6. Conclusion: New opportunities
• Appendix
• References.