Example 11.28.  Show that    maps the upper half plane    onto the right angle channel in the first quadrant, which is bounded by the coordinate axes and the rays  , as depicted in Figure 11.74(b).

Figure 11.74  The region with and .

Explore Solution 11.28.

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

This is one, formula for the integral.   However, we will use the following 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).

We see that    maps the upper half plane    onto the channel in the right half plane bounded by the coordinate axes and rays  .  

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