Use Green's function for the first quadrant of R^2 to solve Laplace's equation with boundary conditions.

Once Green's function is known for a particular domain, the solution to Laplace's equation with given boundary conditions is obtained from an integral formula (which in itself is often difficult to calculate!)  In general, determining Green's functions is non-trivial, but is often simplified for domains with a high degree of symmetry.  The solution comprises a 2 1/2 page Word document with equations written in Mathtype first determining the Green's function for R^+ x R^+ (the first quadrant of R^2) and then applying the result in two specific cases.  Each step is explained.  The solution assumes knowledge of complex integration.