The Schwarz-Christoffel Transformation

 

Chapter 11. Show that the mapping [Graphics:sc10.txtgr1.gif]
maps the upper half plane onto the upper half plane plus an infinite rectangle in quadrant four.
The Schwarz-Christoffel formula for [Graphics:sc10.txtgr2.gif] is:

[Graphics:sc10.txtgr4.gif][Graphics:sc10.txtgr3.gif]

Integrate to obtain:

[Graphics:sc10.txtgr4.gif][Graphics:sc10.txtgr5.gif]

The coefficients are [Graphics:sc10.txtgr6.gif], and we obtain

[Graphics:sc10.txtgr4.gif][Graphics:sc10.txtgr7.gif]

A graph for the solution is:

Fluid flow over a step.

 

 

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(c) John Mathews, 1998, 2006