Professor
John Hunter
Department of Mathematics
University of California
Davis, CA 95616, USA
e-mail: jkhunter@ucdavis.edu
Phone:
- (530) 554-1397 (Office)
- (530) 752-6653 (Fax)
Office: 3230 Mathematical Sciences Building
Course Information
MAT 205B, Spring Quarter, 2014
Lectures: MWF 2:10–3:00 p.m., Physics 148
Office hours: M 3:10–4:00 p.m., W 3:10–4:30 p.m.
Text: Complex Analysis, E. M. Stein and R. Shakarchi
Announcement
The course project will consist of a paper on some topic in complex analysis. It should summarize basic definitions and give a proof of at least one selected theorem related to the topic. The paper should be roughly 10 pages long (typeset in LaTeX is strongly preferred), but mathematical content is more important that length. You can choose your own topic. Here are some possible suggestions:
- The Gamma function
- Boundary behavior of conformal maps
- Conformal equivalence of non-simply connected domains
- Moduli spaces for compact Riemann surfaces
- ODEs in the complex plane and the monodromy group
- Riemann-Hilbert problems
- The Fourier-Laplace transform
- The Picard theorem for entire functions
- Differential forms in complex analysis
Please e-mail me with your proposed topic by Wed, May 21. I'll be glad to suggest possible references or papers, or something more specific if you have a rough idea of what you're interested in but don't have a particular topic in mind.
The paper will be due Fri, Jun 9 (a pdf file by e-mail is fine).
Syllabus
The Department syllabus is here.
Here are some online notes on Complex Analysis and Riemann Surfaces by Wilhelm Schlag at the Univesity of Chicago. Chapter 5 discusses analytic continuation.
Homework
Set 1 (Fri, Apr 11)
Ch. 8, Exercises, p. 248: 1, 4, 13
Ch. 8, Problems, p. 254: 3, 4
Set 2 (Fri, Apr 18)
Ch. 8, Exercises, p. 248: 8, 12, 14, 15, 18
Set 3 (Fri, May 9)
Problems are
here.