Extra Example 1.  Find the electrical potential    in the crescent-shaped region that lies inside the disk   and outside the circle   that satisfies the following boundary values shown in Figure 11.41:

              

Figure 11.41  The electrical potential inside   and outside .  

Explore Extra Solution 1.

Construct the solution with a conformal mapping.  

Use Mathematica to make a contour plot of the equipotentials.

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