Senior Project Advisor
Smit Vega Garcia, Mariana
Conformal maps are functions from subsets of the complex plane to the complex plane that locally preserve angles. Our goal is to understand conformal maps that pass to and from polygonal domains. In order to do so, we derive some of the basic theory of harmonic functions on simply connected domains. In particular, our goal with the first few sections is to prove the Schwarz Reflection principle. Using this, as well as other tools from complex analysis, we give an in-depth explanation of Tao’s proof of the Schwarz-Christoffel formula. This is a differential equation that allows one to compute a conformal map from either a half plane or a disk into the interior of a polygonal domain. We apply the result to some basic examples in the analysis of fluid flow.
Albert, Michael, "Conformal Geometry of Polygons" (2020). WWU Honors College Senior Projects. 361.
Subjects - Topical (LCSH)
Conformal mapping; Schwarz function; Christoffel-Darboux formula; Polygons
student projects; term papers
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