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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Complex analysis
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Lectures on Several Complex Variables (Paperback, Softcover reprint of the original 1st ed. 2014)
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Lectures on Several Complex Variables (Paperback, Softcover reprint of the original 1st ed. 2014)
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This monograph provides a concise, accessible snapshot of key
topics in several complex variables, including the Cauchy Integral
Formula, sequences of holomorphic functions, plurisubharmonic
functions, the Dirichlet problem, and meromorphic functions. Based
on a course given at Universite de Montreal, this brief
introduction covers areas of contemporary importance that are not
mentioned in most treatments of the subject, such as modular forms,
which are essential for Wiles' theorem and the unification of
quantum theory and general relativity. Also covered is the Riemann
manifold of a function, which generalizes the Riemann surface of a
function of a single complex variable and is a topic that is
well-known in one complex variable, but rarely treated in several
variables. Many details, which are intentionally left out, as well
as many theorems are stated as problems, providing students with
carefully structured instructive exercises. Prerequisites for use
of this book are functions of one complex variable, functions of
several real variables, and topology, all at the undergraduate
level. Lectures on Several Complex Variables will be of interest to
advanced undergraduate and beginning undergraduate students, as
well as mathematical researchers and professors.
General
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