Math 445: Theory of Functions of a Complex Variable, II
- Instructor: Richard Laugesen
- e-mail:
laugesen@illinois.edu
- Homepage:
www.math.uiuc.edu/~laugesen
- Office: 376 Altgeld Hall
Phone: 333-1329
- Class meets: MWF 1 pm, in 343 Altgeld Hall
Course outline
The course covers topics important for contemporary
research in complex analysis and related fields.
- Conformal mapping: Riemann mapping theorem, groups of Mobius
transformations, Schwarz-Christoffel mapping onto polygonal domains, reflection
principle
- Coefficient estimates: area theorem, Bieberbach's estimate on
|a2|, Koebe's 1/4-theorem, distortion theorems
- Infinite products: Weierstrass and Hadamard factorizations,
Nevanlinna theory, the Gamma function, Stirling's formula in the plane
- Analytic continuation, covering surfaces, statement of uniformization
theorem, Picard theorems on omitted values
- Hyperbolic metric: distance decreasing property of analytic functions
- Elliptic functions and integrals
- Brief introduction to complex dynamics, Fatou and Julia sets, Mandelbrot
set
Text
- There is no required text. Several books will be put on reserve at the
library.
Prerequisite
Math 440: Theory of Functions of a Complex Variable, I.
If you have any inquiries or concerns,
please contact me by e-mail at
laugesen@illinois.edu.
- Richard Laugesen