2d curl formula

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Here we build up to the formula for computing the two-dimensional curl of a vector field, reasoning through what partial derivative information corresponds to fluid rotation.

[@danielc4267]

I am learning so much from this series. The moment I saw the positive-curl diagram you drew, I could derive the exact same curl equation you wrote at the end of the video.

[@Fai9alsq]

I have been looking for someone to explain green's theorem for me and I spend one whole day and I couldn't get it but with your 5 minuets I got it clearly

[@jlpsinde]

This is heaven on Earth for someone like me that learned this 24 years ago and just now understand!

[@edwardhartz1029]

The quintessential calculus teacher right here.

[@anonymoustraveller2254]

I cant express my joy in words

[@hermolaoutube]

[@HitomiAyumu]

God damn these videos are amazing.

[@MrHan-is1ko]

Wow finally I have a feeling of understanding it. Thank you!

[@deepakchacko5585]

Thanks Grand

[@akashgillella]

Thanks a lot!! Khan Academy

[@alibavafa2094]

Just the explanation i wanted

[@h.k.acreations2374]

Thank you so much !😍

[@anggalol]

Finally I understood why curl have that weird formula

[@ruilinzhou2532]

Thanks so much, you saved me😭

[@shenelf240]

perfect！！！

[@anonymoustraveller2254]

Bliss.

[@736939]

İ don't understand it. Why P with respect to Y must be negative? I mean that it's negative only if the vector is above the point, but it's positive when it's below. So, it's like we take the only top and right vectors, but how about the bottom and left vectors?

[@videofountain]

The letter Q is spoken. When the letter q is written by the author it looks a bit like the letter a.

[@iustinianconstantinescu5498]

Does this stay constant when you change the coordinator system.Maybe, can anyone show a link on this subject( proof or formula for the change, as you change the coordinate system, in 3D , I know it's constant, because I heard it shows up all the time in physics)?

[@loghanrowden7540]

it's 1:22 in the morning, it's to early for this.

[@arturmizuno]

3:55 here

[@sarveshpadav2881]

is'nt curl(v) a vector i.e a cross product of nabla and V??

[@greenland8376]

The cross product isn't even defined in 2 dimensions. You are thinking about the 3-dimensional case.

[@kunalmuley09]

can someone please explain, why partial(P)/partial(y) is subtracted from partial(Q)/partial(x)?

[@MrSypratt]

You are adding two cumulative effects. Illustrate it yourself: Take a large dinner plate. You take the 12:00 and 6:00 position with each of your two hands. Have a friend take the 3:00 and 9:00 position. You and your friend are going to work together to rotate the plate on a table counterclockwise. You will see that your hand at the 6:00 position must be moving to the right and your hand at the 12:00 position moves left to make its contribution. Going right to left as you go up means decreasing as you go up. We call that negative! So you subtract! Similarly your friend’s contribution is positive.

[@utof]

@@MrSypratt great explanation, thank you!

[@roronoa_d_law1075]

I thought rot = Nabla ^ G

[@atriagotler]

!!!

[@raejt610]

marry me