EAN: 9783319115108

LECTURES ON SEVERAL COMPLEX VARIABLES - PAUL M ...

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 Université de Montréal  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.

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