Example 11.6.  Find a function    that is harmonic in the upper half-plane    and takes on the boundary values indicated in Figure 11.5.  That is

              

Figure 11.5  The boundary values for the Dirichlet problem.

Explore Solution 11.6.

Enter the boundary values and construct the  Dirichlet sum.

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

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

The function    is harmonic in the upper half-plane  ,  and takes on the desired boundary values.

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