Green's Theorem, explained visually

This video aims to introduce green's theorem, which relates a line integral with a double integral.

For the example at 5:07, the equation of the vector field has the x equation and y equation flipped. It should be F=(-yx + x^3, 6y-9x).

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#calculus #multivariable #greenstheorem

[vcubingx]

CORRECTIONS

For the example at 5:07, the equation of the vector field has the x equation and y equation flipped. It should be F=<-yx + x^3, 6y-9x>

[brogcooper]

Keep it up dude. The more videos like this, the less people will struggle with math and the more people will learn to enjoy it.

[poiboipi]

Excellent video! For a field F=<P, Q>, my understanding is that the 2D curl = dQ/dx - dp/dy . For this field, 2Dcurl = 3x^2 - y - 6

[twakilon]

That is Stoke's theorem though. Stokes and Green are the same in 2D anyway.

[macprc]

I've taken a class on advanced engineering mathematics that was heavily focused on vector spaces and green's theorem etc. a year ago. I passed the class. But now I'm looking at this video and wondering, how the hell did I actually pass I do not know any of this. So I will watch your videos to actually learn the subjects this time Thanks a lot for the quality videos !

[annothree]

I guess there is a mistake.. when I calc curl from the example mentioned (5:39) I get: -y+3(x^2)-6 !?

[jadenephrite]

Regarding 2:48 adding the line integral around a closed curve; a planimeter is a mechanical instrument that is used to trace around the perimeter of a closed curve. What a planimter does is to calculate the area inside of the closed curve based on the principle of Green's Theorem.

[timgeldof]

Very nice visualization. Your explanation "clicked" for me at 2:38 :) Finally a video where they actually explain what it is rather than just apply it. You just earned yourself a subscriber.

[Laufield]

Elementary: I love math! It’s easy
College: I want to die

[CuongNguyen-tkgq]

Hope u will keep making such videos. I believe that learning math visually is much better for applied mathematicians, engineers, and physicists because those math practitioners needs to know what that math does, not what is its definition!

[DoDzillanator]

Wow. This along with the video about the divergence theorem are pure gold! Thanks!

[HassHansson]

Thank you, I had never considered that the line integral of a surface is the integral of the curl of an infinite amount of areas approximating the surface.

[michaelgonzalez]

That is where the mobius vector is time placement {p~n}3.14`1

[hooya]

I don't remember who made this analogy of Green's theorem, but it stuck with me: Imagine laying out the whole of the Sunday New York Times on the floor of a gymnasium. By reading every word on the edges, you know the content of the whole newspaper. Not a perfect analogy, but it conveys the profound nature of this theorem.

[luizestilo]

Hey dude, amazing channel, keep coming with these!
Just a constructive criticism, if you don't mind. When you explained the cutting the section in two parts, it'd be cool to go in a bit more detail on why it works (I'm guessing it's because the line integral of a small square approaches its curl as it gets smaller, and the fact that since the line integral cancels inside, the curl also cancels, leaving only the “outside curl”, so, the line integral... but I don't really know, just a guess), as, at least for me, it was not clear why the curl of the small pieces should approximate its line integral (it's understandable that the sum of their line integrals would do it, since they cancel, but it only makes sense for the curl to approximate as well if the curl approximates the line integral for those small pieces)

But other than that, great video man, hard to find such intuitive and understandable explanations out there, people like you make math much easier and fun, keep it up!

[itswakke]

Just found this channel randomly. I’ve been trying to learn different math visualization software like manim because this looks amazing. I absolutely love this video and your explanations!

[Arbmosal]

I would add that a physical way of thinking about this theorem, is that if you know the in and outflows at the edge of your area, the flow and curliness on the inside is basically already determined.

[mr.ketchup]

I finally found my new favorite channel

[mokouf]

Thank you. I can't fully understand this before your video!
Universities need you as a lecturer!

[backyardmachinist]

I like this. It's like Vice is giving me a calculus lecture, wonderful!