2D divergence theorem | Line integrals and Green's theorem | Multivariable Calculus | Khan Academy

Using Green's Theorem to establish a two dimensional version of the Divergence Theorem

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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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[adityaprasad]

14:02 "Hopefully it makes a little bit of complete sense" lol

[phylton]

YES! I love these calculus videos.
This one came out in a specially great timing for me, since I have a task due monday on Stokes and Divergence Theorem.
This is really great!

[abhips]

Yes! FINALLY!!! Please update your site with this too! It has a better interface than youtube!

[dalisabe]

F.n is the active component of F in the direction of n. The other component doesn’t matter because it is orthogonal to n.

[miceblue]

Wow thanks for the video. My math class just went over Stoke's Theorem and we're going to cover the Divergence Theorem next week. :D

[LAnonHubbard]

I've gotta agree with you. Although the essence of Khan Academy is whatever it means to Salman (and his advisors), THIS is the sort of stuff I need to learn and Sal: you're better at getting these difficult concepts into my head than anyone else.

[HAWXLEADER]

you can also view green's theorm as just multiplying and dividing by dxdy...

the - is because of the region...

[zaheersuhabuth]

What is your reasoning behind choosing dr= dy i - dx j instead of dr= - dy i + dx j ????

[andersjaevel]

Yes please! More advanced math and physics!

[Badroucl]

Very brilliant and a straightforward explanation, thanks mister^^. It can be explained in a physical manner rather than mathematical but math's way is stronger and more satisfying. btw without George Green we were doomed^^.

[TTTiton]

you have gotten really better at drawing.

[LAnonHubbard]

I agree, and hello as I recognise your username from the comments and Q/A section of the KA website.

[pqxh]

I'm curious about how the units check out...It seems as though when you take that integral you get units of distance squared over

[keledjuarez]

cooking, runing, sleeping, driving etc

[JeaneAdix]

lol, someones gotta do it. props to informing yourself then by watching khana

[linuxisbetter]

Wow I completely forgot this; I think I learned this in multivariable calculus.

[arthursb]

"Hopefully that makes a little bit of complete sense". hahaha, gotta love Mr. Khan.

[pnogas]

watch the TED talk: Arthur Benjamin's formula for changing math education
(Note this is coming from an electrical engineer who LOVES calculus)

[abhips]

Calculus is very important. He can make economy videos anytime, but Calculus, rules!

[abhips]

We need balance, but these days Khan's making too much economy videos.

Now,

THE GREAT KHAN HAS RETURNED!