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Erschienen in:
2011 | OriginalPaper | Buchkapitel
The Schwarz-Christoffel Transformation
verfasst von : Ravi P. Agarwal, Kanishka Perera, Sandra Pinelas
Erschienen in: An Introduction to Complex Analysis
Verlag: Springer US
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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.