Overview
Written with exceptional clarity and insightful style, A Course in Complex Analysis is accessible to beginning graduate students and advanced undergraduates with some background knowledge of analysis and topology. A Course in Complex Analysis explores a central branch of mathematical analysis, with broad applications in mathematics and other fields such as physics and engineering. Ideally designed for a year-long graduate course on complex analysis and based on nearly twenty years of classroom lectures, this modern and comprehensive textbook is equally suited for independent study or as a reference for more experienced scholars. Saeed Zakeri guides the reader through a journey that highlights the topological and geometric themes of complex analysis and provides a solid foundation for more advanced studies, particularly in Riemann surfaces, conformal geometry, and dynamics. He presents all the main topics of classical theory in great depth and blends them seamlessly with many elegant developments that are not commonly found in textbooks at this level. They include the dynamics of Mobius transformations, Schlicht functions and distortion theorems, boundary behavior of conformal and harmonic maps, analytic arcs and the general reflection principle, Hausdorff dimension and holomorphic removability, a multifaceted approach to the theorems of Picard and Montel, Zalcman's rescaling theorem, conformal metrics and Ahlfors's generalization of the Schwarz lemma, holomorphic branched coverings, geometry of the modular group, and the uniformization theorem for spherical domains. Zakeri includes more than 350 problems, with problem sets at the end of each chapter, along with numerous carefully selected examples. This well-organized and richly illustrated book is peppered throughout with marginal notes of historical and expository value.
Full Product Details
Author: Saeed Zakeri
Publisher: Princeton University Press
Imprint: Princeton University Press
ISBN: 9780691207582
ISBN 10: 0691207585
Pages: 448
Publication Date: 02 November 2021
Audience:
College/higher education
,
Professional and scholarly
,
Tertiary & Higher Education
,
Professional & Vocational
Format: Hardback
Publisher's Status: Active
Availability: Temporarily unavailable
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Reviews
A no-nonsense, clearly written graduate level textbook . . . . far more approachable than many other books on complex analysis ---Jonathan Shock, Mathemafrica
Author Information
Saeed Zakeri is professor of mathematics at Queens College and the Graduate Center, City University of New York. He is the author of Rotation Sets and Complex Dynamics.
