New video! What they won't teach you in calculus

Nice

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I use manim to create the clips, not the full full video, then I edit them together in a video editor.

3blue1brown

Hi, Grant! I am currently doing a student competition project, and I really want to make some beautiful animations with manim as my main content. I could run the code to generate clips now, but I am still having no idea how to actually make a video with manim. How did you make full-length videos like those on YouTube, rather than generating a few clips of the animation? Is there a special procedure? How should I run your video projects or even use manim to create my own video?

Some people have put together demos now. For example: <a href="https://www.desmos.com/calculator/mjxhds6p8q" rel="nofollow noopener" target="_blank">https://www.desmos.com/calculator/mjxhds6p8q</a>

3blue1brown

Thanks! Glad you enjoyed it :)

3blue1brown

Indeed, having a better presentation of the complex derivative ideas is one of the main motivations for this project. I agree that such diagrams don't expose critical points the way others do as easily, which is a good example of how having multiple visuals/perspectives in a student toolbelt can be helpful.

3blue1brown

Not the usual view you see written about such titles :). I think I may write up a blog post or something on my view of "clickbait" like this; you may be able to guess what those thoughts are.

3blue1brown

Loops? You mean all this time I've been hitting enter 40 times when I need to create those sample dots and arrows, and then over and over to have them iterate, and all this time I could have automated this? Man, that would have saved a *ton* of time :P

3blue1brown

Hmm, interesting. I might play around with how that looks.

3blue1brown

Great video Grant! Quick question - is there software to produce such a visualization for any function? Obviously for graphing functions there are tons of solutions, but I'm looking for a Desmos-like tool for this kind of graphing.

Edan Maor

Hi, Grant! I really liked this last video. Calculus is one of subjects in Math that Ia l like it. Intuitively, I can understand everything you teach, My difficulty is on probability. :-/

jab*

Jacob Mirra

I see that you’re taking another job at something you tried long ago: explaining why the derivative of a complex function is a complex number - by thinking of it as complex multiplication. I think you stand to arrive at a more accessible explanation with this more gradual approach from “single-variable derivative revisited” that you’ve done here. The “emergent ellipse” in this video was really lovely and stimulated my thinking about critical points. However, I’d be concerned that your diagrams did a pretty poor job highlighting where the critical points were. They turned out to be lined up with the “vertical tangents” of the aforementioned ellipse. But I wonder how many viewers will miss that!

Jacob Mirra

I second the point about the title.

Nice video, thanks. Thinking of a derivative as an inverse measure of density is very useful with probability distributions and also the rainbow effect. In the latter, incident light rays are scattered in all directions but perceived at the angle of maximum (infinite) density.

Dan Steinitz

Hi, the concept of derivative as measure of density is useful when dealing with probability distributions. Also, when explaining the rainbow effect. Rays are deflected in many angles. The rainbow forms at the angle of max (infinite) density. Thanks for the nice video.

Dan Steinitz

Extremely rad

RHüz

*Love* the clickbait title!!! Seriously - I appreciate the excitement you bring to this...*and* you are absolutely correct, they do not teach you this view. Bring ti!

Grant, don't tell me you are a serious python programmer. You don't even know loops :D No really, that was a great video and I am really looking forward to the next few follow-ups, especially the Jacobian (hope you include something on why it's useful on it, as it (like so often with things in linear algebra) seems like you just throw some numbers together and out comes gradient descent.)

I liked the visualization; but it might have been nice to stack a few of these vertically to visualize how a point moves across multiple iterations. Of course, that's probably only useful for one or two dimensions.

Hmm, I hope you don't stoop to these sort of click bait type titles, I understand the temptation but your brilliant material stands on its own merits I think. In terms of conformal maps, I've used them to transform moving boundaries to finite intervals, in fluid flow problems that simplify to solving laplace's equation on the interior of a bubble. It allows you to write the PDE as an integro-differential equation on [0,1].

The oval at 10:30 looks like a dual of a Steiner conic.

cinder_block