Complex analysis
The guiding principle of this presentation of ``Classical Complex Analysis'' is to proceed as quickly as possible to the central results while using a small number of notions and concepts from other fields. Thus the prerequisites for understanding this book are minimal; only elementary fac...
Gardado en:
| Auteurs principaux: | , |
|---|---|
| Formato: | Livre numérique |
| Idioma: | Anglais |
| Publicado: |
Berlin, Heidelberg :
Springer Berlin Heidelberg
[20..].
Cham : Springer Nature |
| Edición: | 1st ed. 2005. |
| Series: | Universitext
|
| Acceso en liña: | 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: | • Complex Analysis, Texte imprimé, 9783540810261 • Complex analysis, Eberhard Freitag, Rolf Busam, Berlin, Springer, 2005, 1 vol. (X-547 p.), Universitext, 978-3-540-25724-0 • Complex Analysis, Texte imprimé, 9783540810261 • Complex analysis, Eberhard Freitag, Rolf Busam, Berlin, Springer, 2005, 1 vol. (X-547 p.), Universitext, 978-3-540-25724-0 |
| Résumé: | The guiding principle of this presentation of ``Classical Complex Analysis'' is to proceed as quickly as possible to the central results while using a small number of notions and concepts from other fields. Thus the prerequisites for understanding this book are minimal; only elementary facts of calculus and algebra are required. The first four chapters cover the essential core of complex analysis: - differentiation in C (including elementary facts about conformal mappings) - integration in C (including complex line integrals, Cauchy's Integral Theorem, and the Integral Formulas) - sequences and series of analytic functions, (isolated) singularities, Laurent series, calculus of residues - construction of analytic functions: the gamma function, Weierstrass' Factorization Theorem, Mittag-Leffler Partial Fraction Decomposition, and -as a particular highlight- the Riemann Mapping Theorem, which characterizes the simply connected domains in C. Further topics included are: - the theory of elliptic functions based on the model of K. Weierstrass (with an excursions to older approaches due to N.H. Abel and C.G.J. Jacobi using theta series) - an introduction to the theory of elliptic modular functions and elliptic modular forms - the use of complex analysis to obtain number theoretical results - a proof of the Prime Number Theorem with a weak form of the error term. The book is especially suited for graduated students in mathematics and advanced undergraduated students in mathematics and other sciences. Motivating introductions, more than four hundred exercises of all levels of difficulty with hints or solutions, historical annotations, and over 120 figures make the overall presentation very attractive. The structure of the text, including abstracts beginning each chapter and highlighting of the main results, makes this book very appropriate for self-guided study and an indispensable aid in preparing for tests. This English edition is based on the fourth forthcoming German edition. |
|---|---|
| descrición da copia: | Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| ISBN: | 9783540308232 |
| ISSN: | 2191-6675 |
| Acceso: | 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 |