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 (d).

Extra Example 1 (d).  Find a function  [Graphics:../Images/DirichletProblemMod_gr_139.gif]  that is harmonic in the upper half-plane  [Graphics:../Images/DirichletProblemMod_gr_140.gif]  and takes on the boundary values

            [Graphics:../Images/DirichletProblemMod_gr_141.gif]  

[Graphics:../Images/DirichletProblemMod_gr_142.gif]

[Graphics:../Images/DirichletProblemMod_gr_143.gif]

 

 

[Graphics:../Images/DirichletProblemMod_gr_144.gif]

[Graphics:../Images/DirichletProblemMod_gr_145.gif]

[Graphics:../Images/DirichletProblemMod_gr_146.gif]

 

 

 

[Graphics:../Images/DirichletProblemMod_gr_147.gif]

[Graphics:../Images/DirichletProblemMod_gr_148.gif]

[Graphics:../Images/DirichletProblemMod_gr_149.gif]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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