Unformatted text preview: z and w planes. It might be useful to check the image of z = 0. (b) Find φ ( x, y ) that satisﬁes ∇ 2 φ = 0 in { z1  < √ 2 } ∩ { z + 1  < √ 2 } with : φ = 1 on  z + 1  = √ 2 , and φ = 2 on  z1  = √ 2 . 4. [20] Let f ( x ) and g ( x ) be two absolutely integrable functions. Solve the boundaryvalue problem using Fourier transform, assuming  u ( x, y )  decays rapidly as ( x, y ) → ∞ . u xx + u yy = f ( x ) ey , ∞ < x < ∞ , < y, u ( x, 0) = g ( x ) , ∞ < x < ∞ . 5. [15] Solve the following ODE using Laplace transform and Bromwich formula: y 000 + y = 1 , ( t > 0); y (0) = y (0) = 0 , y 00 (0) = 1 . Do not replace exponential functions by trigonometric functions in your solution....
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 Winter '10
 Dr.AlejandroCortas
 Math, right half plane, absolutely integrable functions, Draw rough sketches

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