24: Divergence - Valuable Vector Calculus

[@jahdz4244]

This channel is so underrated, some of the best explanations I’ve found on KZbin

[@tanvirfarhan5585]

I have learned more from this channel than I have in several year's worths of schooling. I can’t believe this is free content. Thank you so much. world's best channel

[@BuddyNovinski]

Our distinguished young man has once again taught me something I missed before taking linear algebra. This one was not only well explained, but also stimulated my imagination and interest.

[@wmeisel]

I am embarrassed at how much better your explanation of divergence is compared to any explanation I have given when I teach Calc III. Bravo.

[@eswyatt]

Don't be so hard on yourself. I don't think these videos would be the best resource for the first pass through the material. Sometimes you've just got to do it the standard way before you can appreciate the deeper understanding. It seems backward to say you've got to learn how to do it correctly first, and only later do you know what you're doing! When I find a novel way to see something, and try to teach it to a novice thinking I can skip over the usual stuff, I find they're more confused than anything else. So I came to realize epiphanies aren't transferable.

[@zplays4347]

This keeps getting exciting :p

[@diegolopez6418]

Thanks for explaining....in college i didnt get to truly understand the meaning of curl and divergence

[@eswyatt]

Something tells me you're going to abandon the usual rubrics of "Stokes'" and "Green's Theorems" and those ideas will appear as incidents of the broader picture. Hope I'm right! Either way I can't wait.

[@RahulSharma-oc2qd]

ds in area integral and ds in line integral are same? And dividing the expression by Area and taking it to zero, wouldn’t that make divergence to be of infinite value?

[@MuPrimeMath]

dS in the area integral is a small area. ds in the line integral is a small length. When we take the area going to zero, it also causes the value of the integral to go to zero. Therefore we get a 0/0 indeterminate form, which can evaluate to a finite value.

[@kingbeauregard]

Still a fan of the beard. Keep that! Oh, the math's good too. Lookit all the letters and squiggly lines!

[@Michallote]

Hey man, I didn't realize I was so early. Congratulations! Great explanation, but I believe this is Gauss's divergence theorem, am I right? Or is this actually how the concept emerged? (That's why I went mad when I couldn't go to watch that other video you mentioned, cuz it is still in development) Anyway great explanation hahahaha you gave me some insight I hadn't seen before :).

[@MuPrimeMath]

This video is about the definition of divergence, and it doesn't talk about the divergence theorem. See, for example: mathworld.wolfram.com/Divergence.html I have a separate video on the divergence theorem that's almost ready to publish! Also, the "coming soon" video will be published tomorrow :)