Legesse, Hunduma (PhD)Kassahun, Amnaye2019-09-302023-11-042019-09-302023-11-042018-08-12http://etd.aau.edu.et/handle/123456789/19242In this thesis,given a domain <n and a function f : @ ! < Dirichlet problem for laplace equation which has the form 8< : u = 0 in ; and u = f on @ is solved by using conformal mapping. Some Diriclet problems which are di cult to solve in z �� plane were simply solved by mapping(conformal mapping)in to w �� plane. The Drichlet problems of argument functions,exponential functions,sine functions and logarithmic functions were solved by using four-step method of solving Drichlet prob- lems with conformal mapping in the region with the prescribed boundary value problems.enSolving Dirichlet ProblemsConformal MappingsAnalytic FunctionsCauchy Rieman EquationThesis