First video on Covariant Derivative in flat space: https://www.youtube.com/watch?v=U5iMpOn5IHw ERROR at 21:00, the 1st line, there should also be a (partial v1/partial u1)*e_1 term because of the summation over k. I neglected to add this term in. ERROR at 21:11, the 2nd line, 1st component, v2 should be multiplied by 1/2 sin(2u), not a subtraction. Minor error at 19:52; I wrote e_z instead of e_y in the last 2nd order derivative.