Extra Example 2.  Show that    maps the upper half-plane onto the domain indicated in Figure 11.78.   
Hint: Set    and  

Figure 11.78  The region with and .

Explore Extra Solution 2.

Enter the formula and integrate it to construct  f(z).

We will use this form of the integral to continue the computations.

Now solve for the coefficients  A  and  B.

Use Mathematica to graph conformal mapping  w = f(z).

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