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    Schwarz-Christoffel transformations

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    Date
    2007-12
    Author
    Bergonio, Philip Palma
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    Abstract
    The Riemann Mapping Theorem guarantees that the upper half plane is conformally equivalent to the interior domain determined by any polygon. Schwarz-Christoffel transformations provide explicit formulas for the maps that work. Popular textbook treatments of the topic range from motivational and contructive to proof-oriented. The aim of this paper is to combine the strengths of these expositions, filling in details and adding more information when necessary. In particular, careful attention is paid to the crucial fact, taken for granted in most elementary texts, that all conformal equivalences between the domains in question extend continuously to their closures.
    URI
    http://purl.galileo.usg.edu/uga_etd/bergonio_philip_p_200712_ma
    http://hdl.handle.net/10724/24360
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