Complex Analysis:
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
New York, NY
Springer New York
1985
|
| Edition: | Second Edition |
| Series: | Graduate Texts in Mathematics
103 |
| Subjects: | |
| Online Access: | Volltext |
| Item Description: | The present book is meant as a text for a course on complex analysis at the advanced undergraduate level, or first-year graduate level. Somewhat more material has been included than can be covered at leisure in one term, to give opportunities for the instructor to exercise his taste, and lead the course in whatever direction strikes his fancy at the time. A large number of routine exercises are included for the more standard portions, and a few harder exercises of striking theoretical interest are also included, but may be omitted in courses addressed to less advanced students. In some sense, I think the classical German prewar texts were the best (Hurwitz-Courant, Knopp, Bieberbach, etc. ) and I would recommend to anyone to look through them. More recent texts have emphasized connections with real analysis, which is important, but at the cost of exhibiting succinctly and clearly what is peculiar about complex analysis: the power series expansion, the uniqueness of analytic continuation, and the calculus of residues. The systematic elementary development of formal and convergent power series was standard fare in the German texts, but only Cartan, in the more recent books, includes this material, which I think is quite essential, e. g. , for differential equations. I have written a short text, exhibiting these features, making it applicable to a wide variety of tastes. The book essentially decomposes into two parts |
| Physical Description: | 1 Online-Ressource (XIV, 370 p) |
| ISBN: | 9781475718713 9781475718737 |
| ISSN: | 0072-5285 |
| DOI: | 10.1007/978-1-4757-1871-3 |
Staff View
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Record in the Search Index
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| spelling | Lang, Serge 1927-2005 Verfasser (DE-588)119305119 aut Complex Analysis by Serge Lang Second Edition New York, NY Springer New York 1985 1 Online-Ressource (XIV, 370 p) txt rdacontent c rdamedia cr rdacarrier Graduate Texts in Mathematics 103 0072-5285 The present book is meant as a text for a course on complex analysis at the advanced undergraduate level, or first-year graduate level. Somewhat more material has been included than can be covered at leisure in one term, to give opportunities for the instructor to exercise his taste, and lead the course in whatever direction strikes his fancy at the time. A large number of routine exercises are included for the more standard portions, and a few harder exercises of striking theoretical interest are also included, but may be omitted in courses addressed to less advanced students. In some sense, I think the classical German prewar texts were the best (Hurwitz-Courant, Knopp, Bieberbach, etc. ) and I would recommend to anyone to look through them. More recent texts have emphasized connections with real analysis, which is important, but at the cost of exhibiting succinctly and clearly what is peculiar about complex analysis: the power series expansion, the uniqueness of analytic continuation, and the calculus of residues. The systematic elementary development of formal and convergent power series was standard fare in the German texts, but only Cartan, in the more recent books, includes this material, which I think is quite essential, e. g. , for differential equations. I have written a short text, exhibiting these features, making it applicable to a wide variety of tastes. The book essentially decomposes into two parts Mathematics Global analysis (Mathematics) Analysis Mathematik Funktionentheorie (DE-588)4018935-1 gnd rswk-swf Funktionalanalysis (DE-588)4018916-8 gnd rswk-swf 1\p (DE-588)4151278-9 Einführung gnd-content 2\p (DE-588)4143389-0 Aufgabensammlung gnd-content Funktionentheorie (DE-588)4018935-1 s 3\p DE-604 Funktionalanalysis (DE-588)4018916-8 s 4\p DE-604 Graduate Texts in Mathematics 103 (DE-604)BV035421258 103 https://doi.org/10.1007/978-1-4757-1871-3 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 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 4\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Lang, Serge 1927-2005 Complex Analysis Graduate Texts in Mathematics Mathematics Global analysis (Mathematics) Analysis Mathematik Funktionentheorie (DE-588)4018935-1 gnd Funktionalanalysis (DE-588)4018916-8 gnd |
| subject_GND | (DE-588)4018935-1 (DE-588)4018916-8 (DE-588)4151278-9 (DE-588)4143389-0 |
| title | Complex Analysis |
| title_auth | Complex Analysis |
| title_exact_search | Complex Analysis |
| title_full | Complex Analysis by Serge Lang |
| title_fullStr | Complex Analysis by Serge Lang |
| title_full_unstemmed | Complex Analysis by Serge Lang |
| title_short | Complex Analysis |
| title_sort | complex analysis |
| topic | Mathematics Global analysis (Mathematics) Analysis Mathematik Funktionentheorie (DE-588)4018935-1 gnd Funktionalanalysis (DE-588)4018916-8 gnd |
| topic_facet | Mathematics Global analysis (Mathematics) Analysis Mathematik Funktionentheorie Funktionalanalysis Einführung Aufgabensammlung |
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