Summer of Math Exposition

Very well spoken, animated, and organized. I appreciate that you emphasize that the viewer take a moment and really absorb the information that you’re giving to make sure that it sinks in. Sometimes people just let information wash over them without really thinking about it, even though they think they’re thinking about it.

Your visuals are clean as always. You built quite a good intuition for applying calculus in the context of physics.

Pihedron

Great animations. The idea is useful but I feel like I didn’t get a good big picture.

This video is about as clean as it is clear. The visuals are amazing; the story telling is clean, the problem is interesting; and when it’s all tied together like this it becomes instantly as memorable as 3blue1brown videos. The presented math problems aren’t that novel, but instead the way you’ve explained them is novel in the sense that the style is visually unique and outstanding.

Honestly, this is the best video for a classroom context that I’ve seen so far. Especially because it addresses the viewers directly at some points with questions and food for thought. Well done!

Whether this is the “most important” concept in physics is debatable, but it is definitely an essential and interesting one.

The real-world problems motivate the concept, and the animation and explanation work together well. My one suggestion would be to start with a simpler example. The wave example requires viewers to get their heads around shifting reference frames and circular motion on top of understanding the infinitesimals, which is a lot all at once.

Very geeky. Lovely animations.

Great video very clear explanations, I remember that first problem in Morin haha. I would say the novelty is probably the biggest potential drawback since most of these are standard physics problems, but I think it’s a great explanation for a fundamental physics topic that any physics student struggling with this should watch.

This is a good one maybe not for a layman but for math majors?

The physics problems are clearly explained, and the pacing is good. It’s also clear that a lot of work was put into the animations. They’re super slick! Of course it’s always easier to find problems with things:

It’s confusing that when we’re moving with the wave, at 3:12, the absorbing boundary appears to be moving with us.

Around 6:39, why isn’t theta infinitesimal?

I’m not sure it’s fair to say we’ve solved the string wavespeed problem without calculus. When using the small angle approximation, but then getting an equality instead of an approximate solution, you’re implicitly taking a limit. It also relies on prior knowledge about uniform circular motion. Of course a lot of students who don’t know calculus know the formulas, but in a cursory google search I didn’t find any non-calculus arguments that don’t at least use ideas about rates of change or small angles.

You say the barometric model is very accurate. How accurate? It would be nice to include real data on the plot so we could see. It’s also not clear what you mean when you say that you can use a different lapse rate to model higher layers in the atmosphere. What does the dotted extension to the curve mean? Do you just change the lapse rate to make the curve match the data better, or is it a piecewise kind of thing?

Longitudinal is spelled wrong at 20:54.

A rope wrapped around a pole is always my favourite example for a differential equation!

I think the video would have greatly benefited from some kind of… punchline or lesson or overall arc that tied the examples together. Beyond “infinitesimals are cool and important”.

While there are many videos dealing with infinitesmals, I have rarely come across videos any videos that properly explain their usefulness in physics concepts in such a good way. High school me would have found this very very useful.

Nice video! Examples are really well motivated and the visuals are beautiful. My main complaint is that the video seems to be rendered at a low frame rate. I’m not sure if this was a stylistic choice, but I thought the animations would have looked smoother at 60 FPS.

I’ve watched this video twice, but unfortunately some of the calculations still went over my head and I couldn’t follow. It’s mostly a vague sense of not understanding, but there are some specifics I can point out

1. The picture at 4:18. if $\delta x$ is infinitesimally small, then shouldn’t $\theta$ be virtually zero? Why does $T$ have a downward component at all?
2. In all the rope-and-pulley problems I did in first year physics, the tension in a taut string is the same everywhere. But the setup at 7:35 makes it look like the tension are different at the two ends. Why are they not the same?

The parallel plate capacitor example at the end is neat though. I also think the visuals in this visual are quite polished, but there was one thing that bothered me: at 3:06, if I’m in a moving frame of reference such that the wave appears still, then the blue end point should not be stationary.

Brilliant video with brilliant visuals. I personally enjoyed this video very much. I do not agree that this video is for middle school or high school students. If he switched the tags to undergraduate only, I would have given it maybe over 8.