This video is amazing and deserves a lot more views! I wish it would begin with a little discourse on topology and continuity in the multivariate setting, but it's awesome already as it is :) Thank you!
Also: The illustration around 3:14:56 might be a little confusing. The bottom and top edge of the surface go from left to right, from t0 to t0+dt. While the left and right edges go from bottom to top, from s0 to s0+ds. This had me confused, especially because r has these variables flipped, opposite to the (x,y) convention, where x is horizontal and y the vertical dimension. That also explains why there's the partial derivative in respect to t, instead of s.
1:31:30 Does he adjust the interval wrong? 0 < t < 2π if s=5t then multiply all t values by 5 to get s values right? 0*5=0 t*5=s 2π*5=10π Right? But he wrote it as 2π/5? (Hold alt and press 2 2 7 on your num pad to type the "π" symbol.)
Why do you insist on making x come forward let x go to the right always before and let y go onward into the page and let z go up. Xy is the same old plan view we've alway had like a piece Paper on the desk. What's with the clock wise rotation about z?
