Complex Analysis

Theodore W. Gamelin

478 pages, parution le 01/06/2001

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Résumé

The book provides an introduction to complex analysis for students with some familiarity with complex numbers from high school. The book consists of three parts. The first part comprises the basic core of a course in complex analysis for junior and senior undergraduates. The second part includes various more specialized topics as the argument principle, the Schwarz lemma and hyperbolic geometry, the Poisson integral, and the Riemann mapping theorem. The third part consists of a selection of topics designed to complete the coverage of all background necessary for passing Ph.D. qualifying exams in complex analysis. Topics selected 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, particularly the Interuniversity Summer School at Perugia (Italy), and also UCLA, Brown University, Valencia (Spain), and La Plata (Argentina). The author did his undergraduate work at Yale University and his graduate work at UC Berkeley. He was a Moore Instructor at MIT and held regular faculty positions at the Universidad Nacional de La Plata and at MIT, before joining the faculty at UCLA in 1968. He has spent academic years on leave to the Universidad Nacional de Buenos Aires, Argentina, and to the Universidad Autonoma de Valencia, Spain.

Contents

The Complex Plane and Elementary Functions.
Analytic Functions Line Integrals and Harmonic Functions.
Complex Integration and Analyticity.
Power Series.
Laurent Series and Isolated Singularities.
The Residue Calculus.
The Logarithmic Integral.
The Schwarz Lemma and Hyperbolic Geometry.
Harmonic Functions and the Reflection Principle.
Conformal Mapping.
Compact Families of Meromorphic Functions.
Approximation Theorems.
Some Special Functions.
The Dirichlet Problem.
Riemann Surfaces.

Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	Theodore W. Gamelin
Parution	01/06/2001
Nb. de pages	478
Format	15,5 x 23,5
Couverture	Relié
Poids	702g
Intérieur	Noir et Blanc
EAN13	9780387950693
ISBN13	978-0-387-95069-3