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Unformatted text preview: U ( x; 0) = 2 for x > and U ( x; 0) = ± 1 for x < : Hint: you can take U ( x; y ) = a + bu ( x; y ) with appropriate constants a and b: C. Let D 1 and D 2 be complex domains. Suppose f : D 1 ! D 2 is analytic and & : D 2 ! R is harmonic. De±ne g by g ( x; y ) = & ( u ( x; y ) ; v ( x; y )) where f ( x + iy ) = u ( x; y ) + iv ( x; y ) : Verify that g is harmonic on D 1 : 1...
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This note was uploaded on 09/16/2011 for the course MATH 380 taught by Professor Staff during the Spring '11 term at S.F. State.
- Spring '11