4. (a). Use the polar coordinates r and 0 (x = rcos(0), y = rsin(e)) to transform the Laplace equation 1 u+u,, = 0 into the polar form V²u=u,, +=u₁₁ +· r 1 (b) Use the cylindrical polar coordinates x = rcos(e), y = rsin(e), z = z, to transform the 3-D 1 1 Laplace equation u+u, +u_ =0 into the form V²u=u,, +-u, +- r 200+u=0, (c) Use the spherical coordinates (r, 0, $) so that x = rsino cose, y = rsinosine, z = rcoso to transform the 3-D Laplace equation u+u,,,+u хх 0 into the form 1 1 Vuu,,+u,+ (sindu) r sing 1 sin 2 100 = 0.