1. Solve the Laplace equation with the boundary conditions ux (0, y) = u(0, y), u(x, y) = 1, u(x, 0) = 0, u(x,T) = 0 2. Find the steady-state temperature u(r, 0) in the ring shape domain: on the inner circle of radius 2 u=0, and on the outer circle of radius 4 u = f(0). 3. Solve the Laplace equation in the quarter-circular domain of radius c with the bound- ary conditions ue (r, 0) = 0, ue (r,π/2) = 0, u(c, 0) = f(0)