Complex Analysis

Beschreibung

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 exer cises 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.
Written by a well-known and somewhat controversial Springer author whose writing style has achieved a considerable following Unique approach should appeal to those who want to obtain new results in this field Goes beyond the basic material to present special topics of current interest Additional topics covered in the second part give readers a great deal of flexibility in structuring their learning of the subject Extensively revised edition, includes new examples and exercises, and hundreds of minor improvements throughout
This is the fourth edition of Serge Lang's Complex Analysis. The first part of the book covers the basic material of complex analysis, and the second covers many special topics, such as the Riemann Mapping Theorem, the gamma function, and analytic continuation. Power series methods are used more systematically than in other texts, and the proofs using these methods often shed more light on the results than the standard proofs do.

Autor*in

Serge Lang

Themen in »Complex Analysis«

Cauchy's integral formula Complex analysis Jensen's formula Meromorphic function calculus differential equation gamma function maximum

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"The very understandable style of explanation, which is typical for this author, makes the book valuable for both students and teachers."
EMS Newsletter, Vol. 37, Sept. 2000

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