• Conformal mappings and the Schwarz-Christoffel transformation 

    Heinen, Rebecca (University of Missouri--Columbia, 2017)
    Let ? be an open and connected set in the complex plane. A mapping f : ? ? C is said to be conformal at a point z0 if it preserves angles and orientation between curves intersecting at z0. We discuss tangent lines and their ...
  • Harmonic functions and the Dirichlet problem 

    Mayfield, Caleb James (University of Missouri--Columbia, 2017)
    Let ? be an open and connected subset of the complex plane. A real valued function u : ? ? R is said to be harmonic if it has continuous first and second partial derivatives and satisfies Laplaces equation ?u = ? 2u ?x2 + ...