Math 534, Complex Analysis
Autumn 2013
Instructor: Steffen Rohde
Office Hours: M 1:30-2:20 and by appointment, in PDL-C337
Course Description:
While being
a classical, well developed and elegant theory that provides indispensible
tools for many areas of mathematics, complex analysis is
at the same time a
very active field of modern mathematical research. This
entry level graduate course
covers the basic theory of functions of one complex
variable.
The topics
covered include complex numbers, analytic
functions and power series, integral representation and
Cauchy’s theorem, sequences of
analytic functions, simply connected domains and the
Riemann mapping theorem,
approximation theory, analytic continuation, entire and meromorphic functions,special
functions, harmonic functions, Riemann surfaces and the uniformization
theorem.
Prerequisite
is Real Analysis such as Math 424-426.
There are
several excellent
textbooks available”. I have put the classic, “Complex Analysis”
by Lars Ahlfors (McGraw-Hill),
as well as “Functions of
one complex variable” by John Conway (Springer) and
“Complex
Analysis” by Ted Gamelin (Springer) on the course reserve in the math
library.
However, we
will follow Don Marshall’s excellent notes that he wrote for his last years
Math 534-5 course. You can get them from his
course page .
Grades will
be determined from homework (40%), the midterm exam on November
3 (20%), and
the final exam (40%).