TY  - BOOK
AU  - Burgin,Mark
ED  - SpringerLink (Online service)
TI  - Hypernumbers and Extrafunctions: Extending the Classical Calculus 
T2  - SpringerBriefs in Mathematics,
SN  - 9781441998750
AV  - QA299.6-433 
U1  - 515 23
PY  - 2012///
CY  - New York, NY
PB  - Springer New York, Imprint: Springer
KW  - Mathematics
KW  - Mathematical analysis
KW  - Analysis (Mathematics)
KW  - Functional analysis
KW  - Measure theory
KW  - Partial differential equations
KW  - Physics
KW  - Analysis
KW  - Functional Analysis
KW  - Partial Differential Equations
KW  - Measure and Integration
KW  - Mathematical Methods in Physics
N1  - -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
N2  - “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
UR  - http://dx.doi.org/10.1007/978-1-4419-9875-0
ER  -