Further mobi transforms problem

Find a Mobius Transform w = (z) from D = {|z| 1} to W = {lul 0}, where z = x try and w = utiv. (d) Find the harmonic function h on D subject to the boundary conditions h = 0 on the top two arcs and h = cos 2(1 - y) on the lower arc. Proceed as follows: (i) Derive the corresponding boundary conditions on W. (ii) Solve V2H = 0 on W with these boundary conditions using separation of variables H(u, v) = f(u)g(v). You should also require H -+ 0 as v - too to obtain a well-behaved solution in W. (iii) Hence, using H, find the harmonic function h(x, y) on D satisfying the required boundary conditions. (iv) Using computer software of your choice, plot the contours 0, 0.05, . .., 1 of h on D. [If using Mathematica, you might use ContourPlot [. .., RegionFunction- Function [{x, y,z}, ...]] to restrict the region plotted.]