The present book is meant as a text for a course on complex analysis at the advanced undergraduate level, or first-year graduate level. The first half, more or less, can be used for a one-semester course addressed to undergraduates. The second half can be used for a second semester, at either level. Somewhat more material has been included than can be covered at leisure in one or two terms, to give opportunities for the instructor to exercise individual taste, and to lead the course in whatever directions strikes the instructor's fancy at the time as well as extra read ing material for students on their own. 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.

Innehållsförteckning

Basic Theory -- Complex Numbers and Functions -- Power Series -- Cauchy’s Theorem, First Part -- Winding Numbers and Cauchy’s Theorem -- Applications of Cauchy’s Integral Formula -- Calculus of Residues -- Conformal Mappings -- Harmonic Functions -- Geometric Function Theory -- Schwarz Reflection -- The Riemann Mapping Theorem -- Analytic Continuation Along Curves -- Applications of the Maximum Modulus Principle and Jensen’s Formula -- Entire and Meromorphic Functions -- Elliptic Functions -- The Gamma and Zeta Functions -- The Prime Number Theorem

Detaljer

Medverkan och funktion

Serge Lang, 1927-2005 (Författare)

klassifikation

30 (msc), 30-01 (msc), 515 (DDK-klassifikation), Tdh (kssb)

Identifikator

ISBN 9780387985923, ISBN 0387985921 · alk. paper

har titel

Complex analysis

upphovsuppgift

Serge Lang

upplageuppgift

4. ed.

utgivning

New York : Springer, 1999, cop. 1999

omfång

xiv, 485 s.

Mått

25 cm

Övriga fysiska detaljer

ill.

Illustrativt innehåll

Illustrationer finns men typen specificeras ej

Seriemedlemskap

Graduate texts in mathematics · ISSN 0072-5285 · Graduate texts in mathematics ; 103

Identifikator

LIBRISIII-nummer 0387985921

kontrollnummer

4880238

Biblioteksspecifik information (bestånd)

Kungliga Tekniska högskolan · KTH Biblioteket (T)

ämne
Cauchy's theorem, Conformal mappings, Harmonic functions, Meromorphic functions, Elliptic functions, Gamma functions, Zeta functions, Mathematical analysis
klassifikation
AMS 30-XX
Mittuniversitetet · Biblioteket i Sundsvall (Mhs)

klassifikation
Tdh (kssb)
Lunds universitets bibliotek · Fysik- och astronomibiblioteket (Lfa)

ämne
Analysis
Mittag-Lefflers matematiska stiftelse · Biblioteket (Vm)

klassifikation
Tdh (kssb)
Chalmers tekniska högskola · Huvudbiblioteket (Z)

klassifikation
QA 331 (LC-klassifikation)

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