Complex Analysis - Gamelin, Theodore W.

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Résumé :
The bock provides an introduction to complex analysis for students with some familiarity with complex numbers hum high school. The book consists of three parts. The first part constitutes the basic tore 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 Julie sets and the Mandelbrot set, Dirichlet caries and the prime number theorem, and the uniformization theorem for Riemann surfaces. The three geometries-spherical, Euclidean, and hyperbolic-ore stressed. Exercises range hum 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 Plate (Argentina).

Biographie:
A native of Minnesota, the author did his undergraduate work at Yale University and his graduate work at UC Berkeley. After spending some time at MIT and at the Universidad National de La Plata (Argentine), he joined the faculty at UCIA in 1968. The author has published a number of research articles and several books on functional analysis and analytic function theory. He is currently involved in the California K-12 education scene.

Sommaire:
["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."]