Complex Analysis / Edition 1

by Theodore W. Gamelin

Overview

The book provides an introduction to complex analysis for students with some familiarity with complex numbers from high school. It conists of sixteen chapters. The first eleven chapters are aimed at an Upper Division undergraduate audience. The remaining five chapters are designed to complete the coverage of all background necessary for passing PhD qualifying exams in complex analysis. Topics studied in the book include Julia sets and the Mandelbrot set, Dirichlet series and the prime number theorem, and the uniformization theorem for Riemann surfaces. The three geometries, spherical, euclidean, and hyperbolic, are stressed. Exercises range from the very simple to the quite challenging, in all chapters. The book is based on lectures given over the years by the author at several places, including UCLA, Brown University, the universities at La Plata and Buenos Aires, Argentina; and the Universidad Autonomo de Valencia, Spain.

Product Details

ISBN-13:	9780387950938
Publisher:	Springer New York
Publication date:	05/18/2001
Series:	Undergraduate Texts in Mathematics
Edition description:	2001
Pages:	480
Product dimensions:	6.10(w) x 9.25(h) x 0.04(d)

Table of Contents

First Part.- I The Complex Plane and Elementary Functions.- II Analytic Functions.- III Line Integrals and Harmonic Functions.- IV Complex Integration and Analyticity.- V Power Series.- VI Laurent Series and Isolated Singularities.- VII The Residue Calculus.- Second Part.- VIII The Logarithmic Integral.- IX The Schwarz Lemma and Hyperbolic Geometry.- X Harmonic Functions and the Reflection Principle.- XI Conformal Mapping.- Third Part.- XII Compact Families of Meromorphic Functions.- XIII Approximation Theorems.- XIV Some Special Functions.- XV The Dirichlet Problem.- XVI Riemann Surfaces.- Hints and Solutions for Selected Exercises.- References.- List of Symbols.