Comments on Lesson VC.05

• I present the path independence of flow along in a gradient field by showing that the path integral is really integrating the derivative df(x(t),y(t))/dt when you expand it, so you know that the integral of the derivative is just the difference of the function at the endpoints.
• I think it is worth paying special attention to how to get from the gradient field to the function. This also shows why you need dn/dy = dm/dx to have a gradient field.
• The book is not so clear explaining that the gradient field is gradf for some function f.
• Even after explaining that flow along is only path independent in a gradient field, I got lots of answers that said, "Path integrals are independent of path," with no restrictions.