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A Course in Complex Analysis (Hardcover)
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A Course in Complex Analysis (Hardcover)
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A comprehensive graduate-level textbook that takes a fresh approach
to complex analysis 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 Moebius 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.
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. 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. Presenting a wealth of material in a single
volume, A Course in Complex Analysis will be a valuable resource
for students and working mathematicians.
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