Green's theorem proof part 1 | Multivariable Calculus | Khan Academy

Part 1 of the proof of Green's 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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[sanihasan]

when you realize that you were never bad at maths, but the way it was taught to you was too much bs. I am crying right now.

[seathblood]

just discovered you last night in frantically studying for my calc test. In a few minutes online, you have made more sense than my prof has all semester. A bit too late to do well in the class, but I will be watching your videos from now on! =)

[tiggerbouces]

@Liaomiao When he puts Y1 and Y2, he is saying that the whole Y vector field equation is made up of two separate functions; one is Y1 and one is Y2. It's like drawing two half circles to make a whole circle [for example, in graphing a circle it would be Y1(x)=squareroot(x^2+y^2) and Y2(x)=-squareroot(x^2+y^2) ]. Hopefully that helped :)

[ScottMar]

Great video. Unfortunately my current maths course does not have time to prove Greens theorem but this more than make up for it.

[harishli]

this example was very didnt get how we get dx from dr in the previous videos but now its Khan.

[Dgrt]

Depends on your definition of "understand".

[hurlicane]

Nice Green's Theorem proof. I find that a lot of professors don't take the time to explain the "why" behind these multifaceted theorems.

[carmelpule]

At 12:44 I rather preferred to not have heard the word "Volume" as the line integral would have been seen as " an area"

The single line integral would be equated to a double integral which is an " area". I guess,

[hedonism]

@rakurai19
He uses smooth draw, if you were wondering...
from 11 months ago :\

[shmiy]

Very good!!! But it was a little difficult to follow the pointer position at the last section of describing what the result equation was, so I repeated that a few times.

[dungvu-dwsy]

can someone tell me whether this is the original proof or just the unofficial proof ?

[tomfahey]

Very good, clear example, but a slight criticism for you - at around 7:45, when you're talking about swapping the two functions in the integral, you go to quite exhaustive detail about how how this requires a minus sign on the outside - clarity is always commendable, but given that the subject nature is vector calculus, I think you can assume your watchers have got basic negative multiplying operations covered ;)

[gobberpooper]

@rakurai19 he used to use MS paint, like in the older calc and physics videos

[gobberpooper]

@kylemartin3 oh you should definitely go through the rest of the calc videos. I got a 5 on my BC exam without finishing the precalc class in my school. people were confused

[rikteembhowmick]

I haven't got yet, why have you chosen to pull out a negative sign of the expression?
Is this because you wanted to match the results? Or is there some genuine notion behind the same!
SOmeone pls help me with the query. Ur response will be gratefully appreciated

[placid]

haven't even finished learning derivatives and your understanding vector integral calculus....hmmm find that hard to believe :p

[Liaomiao]

hmm, dont really see how you can just throw in Y1 and Y2 into the Y part of the respective vector field equation. Sigh, I've been through all the calculus vids and only follow about 95% of it. I think there's still something fundamental about the f(x, y) or f(g(x)) notation that I dont get. I must be slow or something.

[camilatrigoso]

I'm going crazy trying to find the video where you explain where dr comes from. Can someone help me please?

[yli]

So here the path you drew defines a convex set. What happens if the set is not convex? Taking the max and min points and dividing the path into two will still not get you a function right?

[黃信維-tc]

Will it be different if it's clockwise?