Example 23.  The conformal mapping    .  
The image of the portion of the unit disk    that lies in the upper half-plane   is the upper half-plane  .  Furthermore, the upper semicircular portion of the boundary is mapped onto the line negative u-axis, and the segment    is mapped onto the positive u-axis.

            Figure 10.12  The composite transformation  .

Details 23.

Under Construction

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(c) 2008 John H. Mathews, Russell W. Howell