• Conformal mappings and the Schwarz-Christoffel transformation 

    Heinen, Rebecca (Rebecca Lynn) (University of Missouri--Columbia, 2017)
    [ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT REQUEST OF AUTHOR.] Let [omega] be an open and connected set in the complex plane. A mapping f : [omega] [right arrow] C is said to be conformal at a point z0 if it ...
  • Counting theorems and inverse function theorems for analytic functions 

    Delibas, Hakan (University of Missouri--Columbia, 2017)
    [ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT REQUEST OF AUTHOR.] In this master's thesis, we discuss the counting and Rouche's theorems. These theorems are used to find the roots of complex analytic functions.Also, ...
  • Harmonic functions and the Dirichlet problem 

    Mayfield, Caleb James (University of Missouri--Columbia, 2017)
    [ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT REQUEST OF AUTHOR.] Let [omega] be an open and connected subset of the complex plane. A real valued function u : [omega] [right arrow] R is said to be harmonic if it has ...