Comments by "TinLeadHammer" (@TinLeadHammer) on "3Blue1Brown" channel.

  1. Is this supposed to show how smart or how dumb you are? There is nothing hard in the ideas behind calculus. The details are more boring and hard, but the ideas are simple.
    4
  2. Should not it be the area of a disk, not a circle?
    1
  3. Infinitesimals vs limits.
    1
  4. There is no division by 0, but there is a limit when Δt approaches 0. As he said in the beginning of the video, there are subtleties.
    1
  5. These paradoxes assume constant time slices, while in reality a smaller bit of movement require a smaller bit of time.
    1
  6. How a difference of two function values can be equal to an argument value?
    1
  7. Slope is the tangent of the angle between a line and the X axis, see here an example with exactly the same slope, 12: https://en.wikipedia.org/wiki/Slope#Examples_2
    1
  8. That is the second derivative.
    1
  9. You say: "Note, that I do not say that dt is infinitely small" thereby disregarding the approach of infinitesimals and sort of reinforcing the idea of limits as the only correct way of doing calculus. This is how I did it at school too. But lately I've read a bunch of articles and books that revived the infinitesimals and cleared them from that sheen of heresy, so it is a perfectly valid approach as well. I wish you mentioned these subtle - yes, as you mentioned in the beginning - differences in phrasing which lead to two distinctly different approaches: infinitesimals vs limits, and that the latter has been a preferred for the last hundred-something years. As for notation, you could have mentioned different approaches too, where in some "dx" means a little bit of x, in other it means "x approaches 0". You could mention prime, as well as dot. In particular, at 10:34 you would be better off if you used delta on the right, like this: ds/dt = (s(t +Δt)-s(t))/Δt, where Δt->0, which would avoid the ambiguity of what dx is: it is Δt when Δt->0. Also, when you moved from the ratio of ds/dt to derivative, you simply said "slope" without even mentioning the right triangle, the ds being the opposite side and dx being the adjacent line of the triangle, the slope being the hypotenuse. And yes, one is supposed to know that the angle of slope is the tangent of the angle... and here two tangents mix, the tangent of the angle and the tangent line, confusing some even more. Anyway, I think that going from the ratio of the sides to the tangent of the angle and THEN to the slope is a simpler transition. The above are minor niggles for the overall lovely presentation. This is what the current generation wants, they don't want to read textbooks, then want visuals.
    1