Complex Analysis / Edition 4

Complex Analysis / Edition 4

by Serge Lang
     
 

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ISBN-10: 0387985921

ISBN-13: 9780387985923

Pub. Date: 12/07/1998

Publisher: Springer New York

Now in its fourth edition, the first part of this book is devoted to the basic material of complex analysis, while 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 is found in other texts, and the resulting proofs often shed more light on

Overview

Now in its fourth edition, the first part of this book is devoted to the basic material of complex analysis, while 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 is found in other texts, and the resulting proofs often shed more light on the results than the standard proofs. While the first part is suitable for an introductory course at undergraduate level, the additional topics covered in the second part give the instructor of a gradute course a great deal of flexibility in structuring a more advanced course.

Product Details

ISBN-13:
9780387985923
Publisher:
Springer New York
Publication date:
12/07/1998
Series:
Graduate Texts in Mathematics Series, #103
Edition description:
4th ed. 1999. Corr. 3rd printing 2003
Pages:
489
Sales rank:
1,119,680
Product dimensions:
6.10(w) x 9.25(h) x 0.04(d)

Table of 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.

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