Complex Analysis with Applications pp 403-482 | Cite as

# Conformal Mappings

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## Abstract

This chapter presents a sampling of successful applications of complex analysis in applied mathematics, engineering, and physics. After laying down the theory and methods of conformal mappings we discuss Dirichlet problems; in particular, we derive Poisson’s integral formula in the upper half-plane and other regions, by performing a suitable change of variables. In Section 7.4, we broaden the scope of our applications with the Schwarz-Christoffel transformation, which is a method for finding conformal mappings of regions bounded by polygonal paths. The section contains interesting applications from fluid flow.

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