Example 11.5.  Show that the function  

(11-4)              

is harmonic in the upper half plane    and has boundary values  

              

Explore Solution 11.5.

For illustration, set  .  

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 has the desired boundary values.

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