Elliptic coordinates (u, v) are related to Cartesian through the position vector r = (cosh*u cos*v)i +(sinh*u sin*v)j, u [0, 1], v [0, 2].

a) Find the unit vectors e_u, e_v and the scaling factors of the elliptical coordinates. Are the unit vectors orthogonal?

b) Given a scalar-field f and a vector w = w_ue_u + w_ve_v. Give f, w, and w in elliptical coordinates. Also provide the Laplace operator ².