2. (a) Solve the boundary value problem on the exterior of a disk 1 2400 = Urr +-Ur + 0, r>p>0,- <<π, T u(p, 0) = f(0), - TT. (b) State the mathematical and physical boundary conditions for this problem. (c) Justify the orthogonality of the eigenfunctions used in (a). (d) Suppose p = 2 and f(0)=5101. Find (numerically) the smallest value of N such that the Nth partial sum of the series solution has L² error of than 10-1. (e) Plot the solution surface and polar contour plot for the N found in (d). less