Example 11.7.  Find a function that is harmonic in the upper half-plane  ,  which takes on the boundary values  

              

Figure 11.6  The graph of    

            with the boundary values  , for , and , for .

Explore Solution 11.7.

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