Complex Analysis : In the Spirit of Lipman Bers
This book is intended for a graduate course on complex analysis, also known as function theory. The main focus is the theory of complex-valued functions of a single complex variable. This theory is a prerequisite for the study of many current and rapidly developing areas of mathematics including the...
Gespeichert in:
| Hauptverfasser: | , , |
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| Format: | Livre numérique |
| Sprache: | Anglais |
| Veröffentlicht: |
New York, NY :
Springer New York
[20..].
Cham : Springer Nature |
| Ausgabe: | 1st ed. 2007. |
| Schriftenreihe: | Graduate Texts in Mathematics
245 |
| Schlagworte: | |
| Online Zugang: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Anmerkung: |
L'impression du document génère 229 p. Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Complex analysis, in the spirit of Lipman Bers, Jane P. Gilman, Irwin Kra, Rubí E. Rodríguez, 2007, New York, Springer, 1 vol. (XIII-220 p.), Graduate texts in mathematics, 978-0-387-74714-9 • Complex Analysis, Texte imprimé, 9781441925671 • The Hamilton scales, [proceedings of the 3rd European College of Neuropsycopharmacology congress, Max Hamilton memorial symposium, held May 1989 in Gothenburg, Sweden], ed. Per Bech, Alec Coppen, Berlin, 1990, viii, 94 p., Psychopharmacology series, 3-540-52095-3 • Complex analysis, in the spirit of Lipman Bers, Jane P. Gilman, Irwin Kra, Rubí E. Rodríguez, 2007, New York, Springer, 1 vol. (XIII-220 p.), Graduate texts in mathematics, 978-0-387-74714-9 |
| Zusammenfassung: | This book is intended for a graduate course on complex analysis, also known as function theory. The main focus is the theory of complex-valued functions of a single complex variable. This theory is a prerequisite for the study of many current and rapidly developing areas of mathematics including the theory of several and infinitely many complex variables, the theory of groups, hyperbolic geometry and three-manifolds, and number theory. Complex analysis has connections and applications to many other subjects in mathematics and to other sciences. It is an area where the classic and the modern techniques meet and benefit from each other. This material should be part of the education of every practicing mathematician, and it will also be of interest to computer scientists, physicists, and engineers. The first part of the book is a study of the many equivalent ways of understanding the concept of analyticity. The many ways of formulating the concept of an analytic function are summarized in what is termed the Fundamental Theorem for functions of a complex variable. The organization of these conditions into a single unifying theorem with an emphasis on clarity and elegance is a hallmark of Lipman Bers's mathematical style. Here it provides a conceptual framework for results that are highly technical and often computational. The framework comes from an insight that, once articulated, will drive the subsequent mathematics and lead to new results. In the second part, the text proceeds to a leisurely exploration of interesting ramifications of the main concepts. The book covers most, if not all, of the material contained in Bers's courses on first year complex analysis. In addition, topics of current interest such as zeros of holomorphic functions and the connection between hyperbolic geometry and complex analysis are explored. |
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| Beschreibung: | L'impression du document génère 229 p. Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Bibliographie: | Bibliogr. Index |
| ISBN: | 9780387747156 |
| ISSN: | 2197-5612 |
| Zugangseinschränkungen: | Accès en ligne pour les établissements français bénéficiaires des licences nationales Accès soumis à abonnement pour tout autre établissement Conditions particulières de réutilisation pour les bénéficiaires des licences nationales. https://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 |