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Unformatted text preview: z/a ) maps the semi-innite strip of width a in the z-plane shown in the diagram on the left of the gure onto the upper half of the w-plane in the manner shown in the diagram on the right. Determine the images in the w-plane of the lines x = c and y = k . Problem # 4 Find a function ( x,y ) that is harmonic, i.e. a solution of Laplaces equation, in the unit disk | z | < 1 and takes on the boundary values ( x,y ) = 0 , for z = e i , < < , ( x,y ) = 1 , for z = e i , < < 2 . 2 Use the mapping w = f ( x ) = i 1-z 1 + z to map the interior of the disk to the upper half plane Im ( w ) > 0. Problem # 5 Find the solution ( x,y ) of the Laplace equation in the upper half-plane Im ( z ) > that has the boundary values ( x, 0) = x, for-1 < x < 1 , and ( x, 0) = 0 , for | x | > 1 . 3...
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This note was uploaded on 09/24/2010 for the course MMAE 501 taught by Professor Kevincassel during the Spring '10 term at Illinois Tech.
- Spring '10