3blue1brownThis is not the Second Derivative
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Tags: calculusderivativedifferentials
In the Leibniz notation, we write differentials as fractions, e.g. . But can we really treat them as such? While it works for the first derivative, it breaks down already for the second. In this video, we find out why and rebuild the second derivative with the product rule, so that it behaves like an algebraic object. As a bonus, we arrive at the second-order inversion formula in a few steps.
This video is based on the paper “Extending the Algebraic Manipulability of Differentials” by Bartlett & Khurshudyan (2018).
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I loved how clear the most important facts were throughout the video; very nice signposting. I didn’t love the cut to reading quotes off a powerpoint; maybe it would have been appropriate to give a summary and sources for interested readers because the pacing felt cut off by the length and format of the historical aside. The examples were very easy to follow and appropriate for the audience. The payoff was very cool for a late 1st year or maybe 2nd year student in undergraduate; especially how the new understanding of the notation made perhaps difficult-to-follow results like the inversion formula more straightforward.
Motivation 3/3 Clarity 3/3 Novelty 2.5/3
I’d have to watch it again to get more of the details, but I like the idea of trying to make sure the notation is correct. I love the use of projecting equations on the walls - very creative and engaging. I started to drift when we got to the derivations on paper. I also wasn’t too clear on something like d(dx) means (other than interpreted as chain rule with t.
A very strong visual element. I was about to critise the various presentation styles, but it does keep the video engaging and this could otherwise have been a very equation dominant video. I like the novel display on the stairs and walls. Your writing is extremely neat so the writing on paper worked well. I’m not sure you need the TV display and the chalkboard. If you can make second differentials interesting then I’m sure anything you try next will be entertaining
Good video. The first 7-8 minutes are excellent, but the video starts dragging on beyond a certain point. I think the video could have been shorter to deliver the message more effectively.
Nice visuals!
projecting the formulas on walls and stairs is an interesting form.
I found the video a little bit overwhelm. That said it is a not bad start.
Motivation: 7 / 9 – This idea of second derivative not working was a nice, small thing that got me hooked up right out the gate. But apart from that, this was a moderately sized topic, maybe a little too small for my taste.
Clarity: 8 / 9 – Everything was explained very clearly and I appreciate your attention to detail. The only thing I will nitpick – I felt like the math history part wasn’t necessary, it slowed down the pace of the video and, to be honest, bored me. And it’s not like I don’t like math history, I just felt like it wasn’t entertaining enough. Maybe reading from tv wasn’t my thing to watch.
Novelty: 7 / 9 – Great, but quite simple topic. I’ve seen this derivation before somewhere and it wasn’t that fresh to me, especially since it’s just calculus. But I appreciate your efforts on finding an interesting and original topic in such broadly explained field.
Memorability: 8 / 9 – The form in which it was given (especially the first sequence on stairs) and the diversity of forms are impressive. I just think that one of them, writing on blackboard, wasn’t as entertaining as others were, probably because it is very hard to talk to camera and write on board at the same time without hiding a great portion of the text.
Overall: 7.5 / 9 – Great video! Really like how creative your submission is. Good luck in the contest!
Decent video overall but I’ll have to play it multiple times to catch everything, some of the visuals were really interesting