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 here.