Example 10.2.  Show that the mapping [Graphics:Images/ConformalMappingMod_gr_122.gif] maps the unit square [Graphics:Images/ConformalMappingMod_gr_123.gif] onto the region in the upper half-plane [Graphics:Images/ConformalMappingMod_gr_124.gif], which lies under the parabolas  

            [Graphics:Images/ConformalMappingMod_gr_125.gif]   and   [Graphics:Images/ConformalMappingMod_gr_126.gif]

as shown in Figure 10.4.

Figure 10.4  The mapping  [Graphics:Images/ConformalMappingMod_gr_128.gif].

Explore Solution 10.2.

Enter the function  [Graphics:../Images/ConformalMappingMod_gr_145.gif]  and graph the mapping.

[Graphics:../Images/ConformalMappingMod_gr_146.gif]





[Graphics:../Images/ConformalMappingMod_gr_147.gif]

[Graphics:../Images/ConformalMappingMod_gr_148.gif]

[Graphics:../Images/ConformalMappingMod_gr_149.gif]

[Graphics:../Images/ConformalMappingMod_gr_150.gif]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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