Example 11.10.  Find a function    that is harmonic in the quarter disk  ,  which takes on the boundary values

                

            Figure 11.11  The Dirichlet problems for the domains G and H.  

Figure 11.12  The graph  .

Explore Solution 11.10.

Construct the solution via a known conformal mapping.

First use Mathematica to make a contour plot of the solution.

Then use Mathematica to make a 3D plot of the solution.

The function    that is harmonic in the quarter disk  ,  and takes on the desired boundary values.

(c) 2006 John H. Mathews, Russell W. Howell