Complex Analysis

• Serge Lang
Textbook

Part of the Graduate Texts in Mathematics book series (GTM, volume 103)

1. Front Matter
Pages i-xiv
2. Basic Theory

1. Front Matter
Pages 1-1
2. Serge Lang
Pages 3-37
3. Serge Lang
Pages 38-86
4. Serge Lang
Pages 87-122
5. Serge Lang
Pages 123-143
6. Serge Lang
Pages 144-164
7. Serge Lang
Pages 165-195
8. Serge Lang
Pages 196-223
9. Serge Lang
Pages 224-251
3. Various Analytic Topics

1. Front Matter
Pages 253-253
2. Serge Lang
Pages 255-275
3. Serge Lang
Pages 276-291
4. Serge Lang
Pages 292-306
5. Serge Lang
Pages 307-323
6. Serge Lang
Pages 324-339
7. Serge Lang
Pages 340-358
4. Back Matter
Pages 359-370

Introduction

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 recom­ mend to anyone to look through them. More recent texts have empha­ sized connections with real analysis, which is important, but at the cost of exhibiting succinctly and clearly what is peculiar about complex anal­ ysis: 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.

Keywords

Analysis Complex analysis Meromorphic function calculus complex number differential equation elliptic function integral maximum real analysis residue

Authors and affiliations

• Serge Lang
• 1
1. 1.Department of MathematicsYale UniversityNew HavenUSA

Bibliographic information

• DOI https://doi.org/10.1007/978-1-4757-1871-3
• Copyright Information Springer-Verlag New York 1985
• Publisher Name Springer, New York, NY
• eBook Packages
• Print ISBN 978-1-4757-1873-7
• Online ISBN 978-1-4757-1871-3
• Series Print ISSN 0072-5285
• Buy this book on publisher's site
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