The Schwarz-Christoffel Transformation

Ravi P. Agarwal (), Kanishka Perera () and Sandra Pinelas ()
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Ravi P. Agarwal: Florida Institute of Technology, Department of Mathematics
Kanishka Perera: Florida Institute of Technology, Department of Mathematical Sciences
Sandra Pinelas: Azores University, Department of Mathematics

Chapter Lecture 41 in An Introduction to Complex Analysis, 2011, pp 275-280 from Springer

Abstract: Abstract In this lecture, we shall provide an explicit formula for the derivative of a conformal mapping that maps the upper half-plane onto a given bounded or unbounded polygonal region (boundary contains a finite number of line segments). The integration of this formula (often a formidable task unless done numerically) and then its inversion (another nontrivial task) yields a conformal mapping that maps a polygonal region onto the upper halfplane. Such mappings are often applied in physical problems such as in heat conduction, fluid mechanics, and electrostatics.

Keywords: Heat Conduction; Line Segment; Real Axis; Explicit Formula; Conformal Mapping (search for similar items in EconPapers)
Date: 2011
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DOI: 10.1007/978-1-4614-0195-7_41

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