Complex Analysis / Edition 1

Complex Analysis / Edition 1

by THEODORE GAMELIN
     
 

ISBN-10: 0387950699

ISBN-13: 9780387950693

Pub. Date: 05/18/2001

Publisher: Springer New York

An introduction to complex analysis for students with some knowledge of complex numbers from high school. It contains sixteen chapters, the first eleven of which 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.…  See more details below

Overview

An introduction to complex analysis for students with some knowledge of complex numbers from high school. It contains sixteen chapters, the first eleven of which 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 include Julia sets and the Mandelbrot set, Dirichlet series and the prime number theorem, and the uniformization theorem for Riemann surfaces, with emphasis placed on the three geometries: spherical, euclidean, and hyperbolic. Throughout, exercises range from the very simple to the challenging. The book is based on lectures given by the author at several universities, including UCLA, Brown University, La Plata, Buenos Aires, and the Universidad Autonomo de Valencia, Spain.

Product Details

ISBN-13:
9780387950693
Publisher:
Springer New York
Publication date:
05/18/2001
Series:
Undergraduate Texts in Mathematics Series
Edition description:
1st ed. 2001. Corr. 2nd printing 2003
Pages:
478
Sales rank:
814,104
Product dimensions:
1.00(w) x 6.14(h) x 9.21(d)

Table of Contents

Preface
Introduction
Ch. IThe Complex Plane and Elementary Functions1
Ch. IIAnalytic Functions33
Ch. IIILine Integrals and Harmonic Functions70
Ch. IVComplex Integration and Analyticity102
Ch. VPower Series130
Ch. VILaurent Series and Isolated Singularities165
Ch. VIIThe Residue Calculus195
Ch. VIIIThe Logarithmic Integral224
Ch. IXThe Schwarz Lemma and Hyperbolic Geometry260
Ch. XHarmonic Functions and the Reflection Principle274
Ch. XIConformal Mapping289
Ch. XIICompact Families of Meromorphic Functions315
Ch. XIIIApproximation Theorems342
Ch. XIVSome Special Functions361
Ch. XVThe Dirichlet Problem390
Ch. XVIRiemann Surfaces418
Hints and Solutions for Selected Exercises447
References469
List of Symbols471
Index473

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