Compute the gradient and Laplacian of the function T = r (cos θ + sin θ cos ϕ). Check th...

Compute the gradient and Laplacian of the function T = r (cos θ + sin θ cos ϕ). Check the Laplacian by converting T to Cartesian coordinates and using Eq. 1.42. Test the gradient theorem for this function, using the path shown in Fig. 1.41, from (0, 0, 0) to (0, 0, 2).

Eq. 1.42