Complex Analysis in One Variable:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Boston, MA
Birkhäuser Boston
2001
|
| Ausgabe: | Second Edition |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | This book presents complex analysis in one variable in the context of modern mathematics, with clear connections to several complex variables, de Rham theory, real analysis, and other branches of mathematics. Thus, covering spaces are used explicitly in dealing with Cauchy's theorem, real variable methods are illustrated in the Loman-Menchoff theorem and in the corona theorem, and the algebraic structure of the ring of holomorphic functions is studied. Using the unique position of complex analysis, a field drawing on many disciplines, the book also illustrates powerful mathematical ideas and tools, and requires minimal background material. Cohomological methods are introduced, both in connection with the existence of primitives and in the study of meromorphic functionas on a compact Riemann surface. The proof of Picard's theorem given here illustrates the strong restrictions on holomorphic mappings imposed by curvature conditions. New to this second edition, a collection of over 100 pages worth of exercises, problems, and examples gives students an opportunity to consolidate their command of complex analysis and its relations to other branches of mathematics, including advanced calculus, topology, and real applications |
| Beschreibung: | 1 Online-Ressource (XIV, 381 p) |
| ISBN: | 9781461201755 9781461266471 |
| DOI: | 10.1007/978-1-4612-0175-5 |
Internformat
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| 650 | 4 | |a Functions of a Complex Variable | |
| 650 | 4 | |a Algebraic Geometry | |
| 650 | 4 | |a Analysis | |
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Datensatz im Suchindex
| _version_ | 1804153090127953920 |
|---|---|
| any_adam_object | |
| author | Narasimhan, Raghavan |
| author_facet | Narasimhan, Raghavan |
| author_role | aut |
| author_sort | Narasimhan, Raghavan |
| author_variant | r n rn |
| building | Verbundindex |
| bvnumber | BV042419467 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)879621363 (DE-599)BVBBV042419467 |
| dewey-full | 515.9 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.9 |
| dewey-search | 515.9 |
| dewey-sort | 3515.9 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4612-0175-5 |
| edition | Second Edition |
| format | Electronic eBook |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:04Z |
| institution | BVB |
| isbn | 9781461201755 9781461266471 |
| language | English |
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| spelling | Narasimhan, Raghavan Verfasser aut Complex Analysis in One Variable by Raghavan Narasimhan, Yves Nievergelt Second Edition Boston, MA Birkhäuser Boston 2001 1 Online-Ressource (XIV, 381 p) txt rdacontent c rdamedia cr rdacarrier This book presents complex analysis in one variable in the context of modern mathematics, with clear connections to several complex variables, de Rham theory, real analysis, and other branches of mathematics. Thus, covering spaces are used explicitly in dealing with Cauchy's theorem, real variable methods are illustrated in the Loman-Menchoff theorem and in the corona theorem, and the algebraic structure of the ring of holomorphic functions is studied. Using the unique position of complex analysis, a field drawing on many disciplines, the book also illustrates powerful mathematical ideas and tools, and requires minimal background material. Cohomological methods are introduced, both in connection with the existence of primitives and in the study of meromorphic functionas on a compact Riemann surface. The proof of Picard's theorem given here illustrates the strong restrictions on holomorphic mappings imposed by curvature conditions. New to this second edition, a collection of over 100 pages worth of exercises, problems, and examples gives students an opportunity to consolidate their command of complex analysis and its relations to other branches of mathematics, including advanced calculus, topology, and real applications Mathematics Geometry, algebraic Global analysis (Mathematics) Functions of complex variables Differential equations, partial Functions of a Complex Variable Algebraic Geometry Analysis Several Complex Variables and Analytic Spaces Mathematik Funktion Mathematik (DE-588)4071510-3 gnd rswk-swf Komplexe Variable (DE-588)4164905-9 gnd rswk-swf Funktionentheorie (DE-588)4018935-1 gnd rswk-swf Mehrere komplexe Variable (DE-588)4169285-8 gnd rswk-swf Komplexe Variable (DE-588)4164905-9 s Funktionentheorie (DE-588)4018935-1 s 1\p DE-604 Funktion Mathematik (DE-588)4071510-3 s Mehrere komplexe Variable (DE-588)4169285-8 s 2\p DE-604 Nievergelt, Yves Sonstige oth https://doi.org/10.1007/978-1-4612-0175-5 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Narasimhan, Raghavan Complex Analysis in One Variable Mathematics Geometry, algebraic Global analysis (Mathematics) Functions of complex variables Differential equations, partial Functions of a Complex Variable Algebraic Geometry Analysis Several Complex Variables and Analytic Spaces Mathematik Funktion Mathematik (DE-588)4071510-3 gnd Komplexe Variable (DE-588)4164905-9 gnd Funktionentheorie (DE-588)4018935-1 gnd Mehrere komplexe Variable (DE-588)4169285-8 gnd |
| subject_GND | (DE-588)4071510-3 (DE-588)4164905-9 (DE-588)4018935-1 (DE-588)4169285-8 |
| title | Complex Analysis in One Variable |
| title_auth | Complex Analysis in One Variable |
| title_exact_search | Complex Analysis in One Variable |
| title_full | Complex Analysis in One Variable by Raghavan Narasimhan, Yves Nievergelt |
| title_fullStr | Complex Analysis in One Variable by Raghavan Narasimhan, Yves Nievergelt |
| title_full_unstemmed | Complex Analysis in One Variable by Raghavan Narasimhan, Yves Nievergelt |
| title_short | Complex Analysis in One Variable |
| title_sort | complex analysis in one variable |
| topic | Mathematics Geometry, algebraic Global analysis (Mathematics) Functions of complex variables Differential equations, partial Functions of a Complex Variable Algebraic Geometry Analysis Several Complex Variables and Analytic Spaces Mathematik Funktion Mathematik (DE-588)4071510-3 gnd Komplexe Variable (DE-588)4164905-9 gnd Funktionentheorie (DE-588)4018935-1 gnd Mehrere komplexe Variable (DE-588)4169285-8 gnd |
| topic_facet | Mathematics Geometry, algebraic Global analysis (Mathematics) Functions of complex variables Differential equations, partial Functions of a Complex Variable Algebraic Geometry Analysis Several Complex Variables and Analytic Spaces Mathematik Funktion Mathematik Komplexe Variable Funktionentheorie Mehrere komplexe Variable |
| url | https://doi.org/10.1007/978-1-4612-0175-5 |
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