Re: Conformal Mapping
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- Subject: [mg128575] Re: Conformal Mapping
- From: Roland Franzius <roland.franzius at uos.de>
- Date: Mon, 5 Nov 2012 18:39:41 -0500 (EST)
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Am 01.11.2012 08:22, schrieb MaxJ: > Hi folks, > > I need help finding a Mobius transform such that the region: > > |z-i|< sqrt(2) > && > |z+i|< sqrt(2) > > in z-plane be mapped conformally into a unit circle in w-plane. > > Any help is appreciated very much. The boundaries are two circles with centers at +-i and radius^2 = 2. Consequently the contours are passing through the six points on the squares with vertices +-1, 2i +-1 and +-1 -2i +-1 Consequently the lens shaped area in question is bounded by two symmetric quarter circles with center at +-i intersecting at +-1 with an angle of pi/2. We conclude that the identity w=z is a conformal map of the lens into the inner of the unit circle. The construction of a conformal map onto the unit circle, transforming to straight lines the pi/2 vertices at +-1, needs square roots centered at the vertices +-1. This task could generate homework for up to one day approximately. -- Roland Franzius
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