Conformal Mappings

  • Nakhlé H. Asmar
  • Loukas GrafakosEmail author
Part of the Undergraduate Texts in Mathematics book series (UTM)


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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© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of MissouriColumbiaUSA

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