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1. (a) Find the Green's function for the quarter-space D - {(x,y,z) ix> 0, >0}. (b) Solve the Dirichlet problemi Au - 0 in D and u(0.y,z) - 0, u(x,0,z) - h(x,z). 2. Suppose that u is a harmonic function in the three dimensional ball (in spherical coordinates) D - 2} and that u - 3sin0+2co54p+1 on the boundary ad - {r - 2, 0 s s IT, 0 s 2w}. (a) Find the maximum value of u in D - DU aD. (b) Calculate the value of u at the origin. 3. Let u(x,y) be a function in two dimensions such that auar - r + 0 (when written in polar coordinates). Find Rn Audx where D is the disc {x2+y2c 4}

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