Comments by "SmallSpoonBrigade" (@SmallSpoonBrigade) on "Part V: Multiple Integration, Lec 3 | MIT Calculus Revisited: Multivariable Calculus" video.

  1. Herb Gross No problem, I've been tutoring students for many years, so my perspective is a bit different from that of teachers. Why is a more complicated and more sophisticated question than what, so most students really need the what/how before the why. If you can wrap the why into the how without losing the comprehensibility, then that's even better. But, I find that if I do enough problems correctly that I tend to understand the why without much extra help. This is a great video in large part because it successfully folds the why into the lesson without making the material hard to understand. It's unfortunate that it's so hard to do that on a regular basis.
    2
  2. Hi Herb, That's just the way it is. I'll generally look at the region I've been given and the formulas I've been given and pay attention to how the parts interact. Unfortunately, you're right that this is more art than science it's not like integration by parts or u substitution where you can generally identify it via formula. By default I'll go with the form that gives me the simplest possible limits of integration such as x=(y^2)-1 rather than sqrt(x+1)=y, and I'll try to imagine what the equation is going to look like after each integration, but there's a huge amount of guessing involved and sometimes you're left with two equally complicated choices. BTW, this is a really nice video, I'd never seen anybody explicitly explain the u-substitution like that before. I wish we could go back and do more math in this sort of formal way rather than the flashier stuff that passes for math now.
    1