Complex Analysis / by Serge Lang.

Format:

Book

Author/Creator:

Lang, Serge, author.

Contributor:

SpringerLink (Online service)

Series:

Graduate texts in mathematics 0072-5285 ; 103.

Graduate Texts in Mathematics, 0072-5285 ; 103

Language:

English

Subjects (All):

Mathematical analysis.

Analysis (Mathematics).

Analysis.

Local Subjects:

Analysis.

Physical Description:

1 online resource.

Edition:

Fourth edition 1999.

Contained In:

Springer Nature eBook

Place of Publication:

New York, NY : Springer New York : Imprint: Springer, 1999.

System Details:

text file PDF

Summary:

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.

Contents:

One Basic Theory

I Complex Numbers and Functions

II Power Series

III Cauchy's Theorem, First Part

IV Winding Numbers and Cauchy's Theorem

V Applications of Cauchy's integral Formula

VI Calculus of Residues

VII Conformal Mappings

VIII Harmonic Functions

Two Geometric Function Theory

IX Schwarz Reflection

X The Riemann Mapping Theorem

XI Analytic Continuation Along Curves

Three Various Analytic Topics

XII Applications of the Maximum Modulus Principle and Jensen's Formula

XIII Entire and Meromorphic Functions

XIV Elliptic Functions

XV The Gamma and Zeta Functions

XVI The Prime Number Theorem

§1. Summation by Parts and Non-Absolute Convergence

§2. Difference Equations

§3. Analytic Differential Equations

§4. Fixed Points of a Fractional Linear Transformation

§6. Cauchy's Theorem for Locally Integrable Vector Fields

§7. More on Cauchy-Riemann.

Other Format:

Printed edition:

ISBN:

9781475730838

Access Restriction:

Restricted for use by site license.