Hypernumbers and extrafunctions : extending the classical calculus
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...
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Livre numérique |
| Lenguaje: | Anglais |
| Publicado: |
New York, NY :
Springer New York
[20..].
Cham : Springer Nature |
| Edición: | 1st ed. 2012. |
| Colección: | SpringerBriefs in Mathematics
|
| Materias: | |
| Acceso en línea: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Nota: |
Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Hypernumbers and Extrafunctions, Texte imprimé, 9781441998743 • Hypernumbers and Extrafunctions, Texte imprimé, 9781441998743 • Hypernumbers and Extrafunctions, Texte imprimé, 9781441998767 |
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| 100 | 1 | |a Burgin, Mark, |d 19..- | |
| 245 | 1 | 0 | |a Hypernumbers and extrafunctions : |b extending the classical calculus |c Mark Burgin. |
| 250 | |a 1st ed. 2012. | ||
| 260 | |a New York, NY : |b Springer New York. | ||
| 260 | |a Cham : |b Springer Nature, |c [20..]. | ||
| 490 | 0 | |a SpringerBriefs in Mathematics |x 2191-8201 | |
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 505 | 1 | |a -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 | |
| 506 | |a Accès en ligne pour les établissements français bénéficiaires des licences nationales | ||
| 506 | |a Accès soumis à abonnement pour tout autre établissement | ||
| 506 | |a Conditions particulières de réutilisation pour les bénéficiaires des licences nationales. https://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 | ||
| 520 | |a 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 | ||
| 650 | |a Analyse numérique | ||
| 650 | |a Équations aux dérivées partielles | ||
| 650 | |a Intégration numérique | ||
| 776 | 0 | |t Hypernumbers and Extrafunctions |b Texte imprimé |z 9781441998743 | |
| 776 | 0 | |t Hypernumbers and Extrafunctions |b Texte imprimé |z 9781441998743 | |
| 776 | 0 | |t Hypernumbers and Extrafunctions |b Texte imprimé |z 9781441998767 | |
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