Extra Examples1 (a-d).  Find a function  [Graphics:Images/DirichletProblemMod_gr_100.gif]  that is harmonic in the upper half-plane  [Graphics:Images/DirichletProblemMod_gr_101.gif]  and takes on the indicated boundary values.

Explore Solution Extra Example 1 (a).

Extra Example 1 (a).  Find a function  [Graphics:../Images/DirichletProblemMod_gr_106.gif]  that is harmonic in the upper half-plane  [Graphics:../Images/DirichletProblemMod_gr_107.gif]  and takes on the boundary values  

            [Graphics:../Images/DirichletProblemMod_gr_108.gif]  

[Graphics:../Images/DirichletProblemMod_gr_109.gif]

[Graphics:../Images/DirichletProblemMod_gr_110.gif]

 

 

[Graphics:../Images/DirichletProblemMod_gr_111.gif]

[Graphics:../Images/DirichletProblemMod_gr_112.gif]

[Graphics:../Images/DirichletProblemMod_gr_113.gif]

 

 

 

[Graphics:../Images/DirichletProblemMod_gr_114.gif]

[Graphics:../Images/DirichletProblemMod_gr_115.gif]

[Graphics:../Images/DirichletProblemMod_gr_116.gif]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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