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.
About the Author
Lennart Carleson, (born March 18, 1928, Stockholm, Swed.), Swedish mathematician and winner of the 2006 Abel Prize “for his profound and seminal contributions to harmonic analysis and the theory of smooth dynamical systems.” These include his work with Swedish mathematician Michael Benedicks in 1991, which gave one of the first rigorous proofs that strange attractors exist in dynamical systems and has important consequences for the study of chaotic behaviour.
Solutions Manual of Complex Analysis by Gamelin | 1st edition ISBN 9780387979427
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Solutions Manual of Complex Analysis by Gamelin
|T. W. Gamelin