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220B Winter 2022


Instructor: Peter Ebenfelt

Office: APM 6161.

Email: pebenfelt [at] ucsd .edu

Lectures: MWF 1-1:50, APM B402A

Office hours: W 2-3pm

TA: Soumya Ganguly

Office: APM 5712.

Email: s1gangul [at] ucsd .edu

Office hours: Thu 6-8pm


COURSE DESCRIPTION

Complex numbers and functions. Cauchy theorem and its applications, calculus of residues, expansions of analytic functions, analytic continuation, conformal mapping and Riemann mapping theorem, harmonic functions. Dirichlet principle, Riemann surfaces;

Prerequisites: Undergraduate analysis

Text Book: Functions of One Complex Variable, Second Edition by J. B. Conway

Additional reading: There are a numerous books on complex variable. A classic is Complex Analysis by L. Ahlfors.

QUALIFYING EXAM CONTENT

In Conway: Chapters TBA


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