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Unformatted text preview: unit circle under the boundary conditions = 1 for { ( x,y ) : x 2 + y 2 = 1 and y } , and = 0 for { ( x,y ) : y = 0 and  x  > 1 } . [Hint: consider the map w = z + 1 /z and recall your solution of problem 1, Figure 3.14, in Problem Set IV.] 4. (30 pts.) Find the electrostatic potential in the slit upper halfplane, or, more precisely, solve the problem = 0 for y > 0, except the part of the yaxis axis between (0 , 0) and (0 , 1) = 0 on y = 0 = 1 on the part of the yaxis axis between (0 , 0) and (0 , 1). [Hint: Note that the map z z 2 maps both the real and the imaginary axes into the real line.] Due at 5pm on Wed. December 2nd....
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This note was uploaded on 01/14/2010 for the course ACM 1 taught by Professor Prof during the Fall '09 term at Caltech.
 Fall '09
 PROF

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