Schwarz-Christoffel transformations
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چکیده
It is helpful to have available systematic ways to find a variety useful conformal mappings. Our text treats one such method: bilinear transformations. Here we study a second: Schwarz-Christoffel transformations. These are discussed in many references; I recommend particularly [1], a lovely book on complex variable theory which has a decided applied slant. The Schwarz-Christoffel transformations solve the following problem: we are given a certain polygon lying in the w-plane, and we want to find a conformal mapping w = f(z) which carries the real axis onto the boundary of the polygon and the upper half plane D into the interior D of the polygon. Figure 1 shows the basic set-up, assuming that the polygon has five vertices:
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