Math 534/535/536
Complex Analysis
Don Marshall
Autumn/Winter/Spring 2002-2003, Monday/Wednesday/Friday 10:30-11:20
This three quarter course is an introduction to complex analysis covering
the material on the PhD prelim exam: Cauchy theory and applications. Series
and product expansions of holomorphic and meromorphic
functions. Classification of isolated singularities. Theory and
applications of normal families. Riemann mapping theorem; mappings defined
by elementary functions; construction of explicit conformal maps. Runge's
theorem and applications. Picard's theorems and applications. Harmonic
functions; the Poisson integral; the Dirichlet problem. Analytic
continuation and the monodromy theorem. The reflection principle. The
third quarter will also include the uniformization theorem, elliptic
functions and fuchsian groups.
The prerequisite for the course is an
undergraduate analysis class, approximately on the level of math 424-5-6. A
detailed syllabus, and a list of prerequisite topics will be handed out on
the first day of class.
There are many suitable texts, for
example:
- Gamelin, Theodore, Complex Analysis (the bookstore has
copies)
- Ahlfors, Lars, Complex Analysis
- Sarason, Don, Notes on Complex Function Theory
From the introduction to the first book: "Complex analysis is a
splendid realm within the world of mathematics, unmatched for its
beauty and power. It has varifold elegant and often-times unexpected
applications to virtually every part of mathematics. It is broadly
applicable beyond mathematics, and in particular it provides powerful
tools for the sciences and engineering."
A more mundane observation:
Our grad web page
../Programs/recprog.html"
lists recommended programs in thirteen separate areas of research.
Twelve of them include math 534-5-6.
Feel free to drop by if you want more information.