The Schwarz-Christoffel Transformation

 

Chapter 11. Show that the mapping
[Graphics:sc6.txtgr1.gif]
maps the upper half plane onto the domain that is a sector in the first quadrant with an infinite rectangle in the second quadrant attached.
The Schwarz-Christoffel formula for [Graphics:sc6.txtgr2.gif] is:

[Graphics:sc6.txtgr4.gif][Graphics:sc6.txtgr3.gif]

Integrate to obtain:

[Graphics:sc6.txtgr4.gif][Graphics:sc6.txtgr5.gif]

The coefficients are [Graphics:sc6.txtgr6.gif], and we obtain

[Graphics:sc6.txtgr4.gif][Graphics:sc6.txtgr7.gif]

A graph for the solution is:

Mapping onto a channel plus sector.

 

 

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(c) John Mathews, 1998, 2006