It only takes a minute to sign up. I know this is an application of Schwarz—Christoffel mappings, but do not know how to it works with these complex numbers. Sign up to join this community. The best answers are voted up and rise to the top. Home Questions Tags Users Unanswered.
Conformal mapping from upper half plane to a triangle Ask Question. Asked 1 year, 11 months ago. Active 1 year, 11 months ago.
Viewed times. Bumblebee Bumblebee 9, 1 1 gold badge 26 26 silver badges 52 52 bronze badges. Furthermore, if is an analytic function such that. Conformal transformations can prove extremely useful in solving physical problems. By letting , the real and imaginary parts of must satisfy the Cauchy-Riemann equations and Laplace's equation , so they automatically provide a scalar potential and a so-called stream function.
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If a physical problem can be found for which the solution is valid, we obtain a solution--which may have been very difficult to obtain directly--by working backwards. For ,. This solution consists of two systems of circles , and is the potential function for two parallel opposite charged line charges Feynman et al. Arfken, G.
Orlando, FL: Academic Press, pp. Bergman, S. The Kernel Function and Conformal Mapping. New York: Amer. Conformal Representation. New York: Dover, Carrier, G. Functions of a Complex Variable: Theory and Technique. New York: McGraw-Hill, Churchill, R. Complex Variables and Applications, 5th ed. Coxeter, H. Geometry Revisited. Washington, DC: Math. Feynman, R. The Feynman Lectures on Physics, Vol. Greene, R.
Little Mathematics Library – Complex Numbers and Conformal Mappings | Mir Books
Function Theory of One Complex Variable. New York: Wiley, Katznelson, Y. An Introduction to Harmonic Analysis. Kober, H. Dictionary of Conformal Representations. Krantz, S. Kythe, P.
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Computational Conformal Mapping. Lamb, H.