3D divergence theorem intuition | Divergence theorem | Multivariable Calculus | Khan Academy

Intuition behind the Divergence Theorem in three dimensions

Missed the previous lesson?

Multivariable Calculus on Khan Academy: Think calculus. Then think algebra II and working with two variables in a single equation. Now generalize and combine these two mathematical concepts, and you begin to see some of what Multivariable calculus entails, only now include multi dimensional thinking. Typical concepts or operations may include: limits and continuity, partial differentiation, multiple integration, scalar functions, and fundamental theorem of calculus in multiple dimensions.

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[rktiwa]

Today is teacher's day in India. You are the one teacher who has shaped the future of the world to the extent that we only wish we could have a formula to measure. Did you ever think about it? I thank you for all that you have taught me since nearly a decade.

[Captain_Rhodes]

what is the order of these lectures??? he keeps referring to other ones but they are not numbered!

[mariumali]

sal khan is a saviour. May good bless him with a long, healthy, happy life so that he can continuo gracing us with his knowledge.

[Martin-iwll]

The physical interpretation of divergence is best gleamed from the continuity equation in terms of the material derivative of rho

[HoussamRachdi]

I wish that I had I professor like You !

[jmm]

i got an exam tomorrow about all this that u have been uploading the last few days, i feel so lucky lol, its like you uploaded them right on time for me. These theorems pretty hard to understand but your videos make it much easier, they help me loads, thanks.

[danidino]

Thank you so much. I've been watching your videos for year and you have always succeeded in making me understand the subject clearly. Your voice is also soothing, so listening to your videos makes me feel calm instead of impatient.
And now I was in the middle of watching your video because I was stuck on a question (Physics Bachelor) when all of a sudden I realited that I used a 1D integral instead of 2 for the flux accross the surface. I've successfully completed the question. Thanx a lot!!!

[citrus]

I totally understand some of these words.

[grovestreet]

i didn't even watch your previous videos spends 3 lectures in collagenothing happens but sir you made this clear to me thanks

[kurkawodna]

I can't thank you enough for this (and all of your other videos that have helped my countless times)

[forrest]

An amazing gift to students ! Love you kind sir !

[sangeetaish]

THIS IS SO BEAUTIFUL THANK YOU SO MUCHHHH

[mohammadabdulkhalid]

I request khan academy to please explain vector potential..

[ucasvb]

"Right over harrrr."

Your pirate is showing, Salman. :P

[tahiarahman]

thank u so much sir for the excellent video

[yli]

5:00 what do you mean by "regions that bend back on themselves"?

[Ferrus]

You know, I am kind of sensing fourier series are next after this.

[subs]

I wish you wouldn't assume previous knowledge. Your videos are very good and helpful but if you just approached everything from the basics (I know its more difficult and more time consuming) then this would be even more helpful. E.g. don't assume we know what 2D divergence is..

[eduardomuller]

I don't understand the first equation: Why the integral of (F . n) along the curve is the double integral of the divergence of F? Is something like Green's Theorem?

[estefalo]

i cant see any of your vedeos, i can hear everything but there is no image, it only happens with yours.