Answer Happy

b. Check whether or not the following coordinate system x = a cosh(s) cos(t), y = a sinh(s) sin(t), z = 2, is orthogonal. In addition determine its scale factors. In particular, write the two scale factors h, and he as functions of sinh(s) and sin(t) only. c. Consider the vector field a = tye, + yze, + rze, and compute the line integral (without using Stokes' theorem) I != 5.4.4, (1) where is the closed curve defined by r² + y2 = R2 (and z=0). d. Building upon Eq. (1) verify Stokes' theorem with the aid of the surface element ds derived in part (b). e. The Laplacian in orthogonal curvilinear coordinates uin three dimensions reads 1 h2 hs hh2 v2f hi h2 Deduce the corresponding formula for two dimensions by particularisation. Use your result to write down the Laplacian in two dimensional polar coordinates. hshi In this has {... (1498 0,5) + 2, (, 0, 1) + , ou (suha .) -} да + duz aus hi