Math 952 - Advanced Topics in Numerical Analysis, Spring 2010, 3 credit hours,
MW, 5:35 to 6:50 PM, 335 Jabara Hall
This course will be mainly devoted to numerical methods for compurting
conformal maps. The first part of the course will concentrate on an
introduction to methods based on Fourier series, especially the Fornberg-like
methods developed by the instructor and his students and coauthors.
The remainder of the course will be decided later and may include such
topics as Schwarz-Christoffel mapping (including D. Crowdy's approach via
Schottky-Klein prime fucntions and relations to Riemann surfaces),
Riemann-Hilbert problems, inverse problems, use of explicit (osculation and
power) maps, various applications, relations to integral equations methods for
solving potential theory problems, conformal invariants and theoretical
estimates of the so-called crowding, etc.
There is no required text. Notes will be provided. I have ordered
the Dover edition of N. Muskhelishvilli's book ``Singular Integral
Equations", which should provide an affordable source of some theoretical
material which we will use. P. Henrici's book ``Applied and Computational
Complex Analysis, vol. 3", will be a key reference. Also, T. Driscoll and
L. N. Trefethen's book ``Schwarz-Christoffel Mapping", may be used later.
More information will be posted soon...
Some demo MATLAB mfiles are available