Lectures on complex analysis Norbert Steinmetz

Format:

Book

Author/Creator:

Steinmetz, Norbert, 1949- author.

Series:

Oregon State monographs. Mathematics and statistics series

Mathematics and Statistics Series

Language:

English

Subjects (All):

Functions of complex variables.

Differential equations.

Physical Description:

1 online resource

illustration

Place of Publication:

Cham Springer 2026

System Details:

text file PDF

Summary:

This elegant textbook offers a comprehensive course on one-dimensional complex analysis. It includes many topics that, in this scope, are not covered in most other textbooks, such as a detailed investigation of the Schwarzian derivative and its associated differential equation, with applications to conformal mappings of circular polygons; various proofs of the uniformisation theorem for planar domains; an introduction to the theory of ordinary differential equations in the complex domain, culminating in a proof of the Cauchy-Kovalevskaya theorem; an introduction to the theory of normal families, including Zalcman's lemma; a proof of the Paley-Wiener theorem; a complete discussion of the Laguerre-Pólya class; solution of the Dirichlet problem, with special emphasis on harmonic measure and Green's function, and applications to conformal mappings of multiply connected domains; a detailed description of the dynamics of polynomials; and the consistent use of the theory of proper mappings whenever possible

Contents:

Chapter 1. Complex Numbers and Functions

Chapter 2. Two Theorems of Cauchy

Chapter 3. The Local Theory

Chapter 4. The Residue Theorem

Chapter 5. Entire Functions

Chapter 6. Special Functions

Chapter 7. Periodic and Elliptic Functions

Chapter 8. Conformal Mappings of Simply Connected Domains

Chapter 9. Harmonic Functions

Chapter 10. Conformal Mappings of Multiply Connected Domains

Chapter 11. Analytic Continuation

Chapter 12. Ordinary Differential Equations in the Complex Domain

Chapter 13. Iterations of Polynomials

Notes:

Includes bibliographical references and index

Online resource; title from PDF title page (SpringerLink, viewed June 22, 2026)

ISBN:

9783032139962

3032139961

OCLC:

1597453259