HW52, HW53, and HW55 are due on Day 58.

This, HW55, is the last homework:

Let S be the hemisphere
{(x,y,z); x^2 + y^2 + z^2 = 5^2 and z >= 0}.

(Hint: parametrize S using spherical phi and theta.)

Give S the orientation N that points away from the origin.

Let F=<y,z,x>.

Find the circulation of F on the positively
orientated boundary of S in two different ways:

(i) directly, and

(ii) using Stokes' Theorem.

(Hint: this boundary is a circular loop of radius 5.)