Summer of Math Exposition

There is no text in the video which makes it pretty hard to follow. It was also not really clear straight-away what the plots were, why are there several colors?

Compared to the numerous Taylors Expansion videos on Youtube this does not seem novel and this was not really memorable.

I don’t think this video is for me. It’s been a while since I took calculus, and so I had no intuition for what the Taylor series or the radius of convergence was. I expect that the average undergrad would also have trouble understanding, let alone a high school student who just started calculus. It would have been helpful to display a single equation on screen at any point in the video, either the main functions being plotted, or their expansions.

I also feel like I didn’t get a sense of how imaginary numbers are “required” to solve this problem. The video says that they “control the radius of convergence”, but there’s no link to how that helps us solve a problem, or estimate a function. I was also a bit confused by having a green line represent the real numbers, superimposed on the (x,y) plane, where both x and y are real. I was expecting that green line to be extended into the complex plane, where i finally shows up, but if that ever happened, I missed it.

I liked the smoothness of the animation and the voice was pleasant to listen to and at a good pace. However, I believe there is too much left to interpret. I would advise to at least add somewhere on the animation the definition of the function being interpolated (I only noticed at the end that it was on the name of the chapters of the video) and the depth of the expansion used to approximate it. And while it is a nice visual representation of how Taylor expansions work, always having several approximations done at the same time makes it more difficult (at first) to understand what is happening.

So, overall a pleasant video to watch, but only useful given a certain level of familiarity with the topic, and not as a way to introduce these concepts.

Can’t completely get what’s going on

I liked the visualizations, but the deliver was very bland.

You should insert some written comment, useful for students. At the moment is difficult to follow, if I have to think about it from an ‘avarage student’ perspective.

It’s a cool result, I would’ve loved a more in depth analysis of the underlying algebra for why this is.