Green's Theorem

In this video, I present an example of Green's theorem, which is a very neat formula that allows you to calculate line integrals of any 2D vector field by converting it to a regular double integral. I also explain why it intuitively makes sense, by comparing macroscopic rotations with microscopic rotations. Enjoy!

[@kevinfung6697]

I was looking for a way to remember Green’s Theorem. It turns out that “Quixotic Peyams” is a great way to memorize this, Tq!!!

[@jessicatambo851]

Im a french student a love watching maths teaching in english. Thank you for your videos ❤

[@drpeyam]

Merci beaucoup!

[@koenth2359]

Hi dr Peyam. I followed a freshman course back in '86, (Vector calculus, textbook by Marsden & Tromba) The neat thing was that they had a picture of a golf player walking around the edge of the green, circumventing the hole. That made me remember the theorem and its name until now.

[@drpeyam]

Haha, that is amazing!!! Thanks for sharing! Oh, and Marsden was a professor at UC Berkeley, yay!!!

[@douglasstrother6584]

I took Freshman Calculus from Tony Tromba @ UC Santa Cruz in '81 ... 1981. Glad to know I'm not the only Old Geezer who watches this channel! I still have my 2nd Edition of "Vector Calculus" & remember that diagram, Figure 7.1.4.

[@RajeshYadav-re3ig]

The example of whirlpool makes everything clear. Thank you sir

[@orfeaspapaioannou2755]

by far the best exlanation!

[@soumyachandrakar9100]

Is there anything like “Peyam's theorem”?

[@simewn]

Awesome videos. Can you make a video about Green functions? Thanks!

[@tomatrix7525]

Amazing!

[@shubham1999]

Happy Belated Thanksgiving and Black Friday Dear Sir.

[@ummwho8279]

How does one prove Clairut's Theorem (ie the symmetry of second partial derivatives) using Green's theorem though? Any chance you can do a video on that Dr. Peyam?

[@ummwho8279]

Oh and Happy Thanksgiving!

[@drpeyam]

Clairaut isn’t something that follows from Green’s theorem, you prove it independently. And the proof is annoying, you just write fxy and fyx as limits and interchange them

[@ummwho8279]

@@drpeyam Haha, not according to wikipedia! The section on "Schwarz's Theorem" says that the symmetry of partial derivatives can be proved using Green's theorem. en.wikipedia.org/wiki/Symmetry_of_second_derivatives I guess I should have been clear, I was referring to Clairut's theorem of the equality of mixed partial derivatives, not the other one. sorry about that! Can you still do a video by any chance of it to prove it that way?

[@shiina_mahiru_9067]

enter some keyword into google, there's a 2-page paper to prove the 2 variable case

[@Albkiller22]

Hi Dr peyam!

[@cerio3237]

You are my only hope

[@tahamahha1465]

but inorder for the integral of the conservative field to be 0 the shape has to be differentiable

[@lorenzolevy4708]

What is path Independence?

[@MicheleCaine]

Wow, the title of the video is written with Green pen

[@drpeyam]

Blackpengreenpen 😉

[@mohammadalkhateeb2087]

I know x greater than 0 but how x less 1 where is 1 please answer me

[@borg972]

Circulation? that sounds suspiciously like physics

[@dimphucopy4344]

Where you from

[@drpeyam]

It’s complicated haha! US and Austria and Iran

[@abdonecbishop]

i Alice to Bob Gauge Holographic Transform Pardon me...Green's Theorem …smells like.....tastes like.....sounds like.....feels like.....looks like..... ............non-Abelian gauge coordinate transformation orbits X*Y*Z(c*t) ……….Bob and Alice sharing a transformed coordinate system with degree_^n .....n = 3 degrees of freedom entangling Choice(n, r), n = 4 and r= 3, P3 permutation group factorial orbits......intersecting sphere's surface coordinates (X, Y, t) .... 't' is the closed boundary edge speed of light distance converted to surface meters distance bound by quadradic formulae X^2 + Y^2 = -Z^2 solvable equation points ( (X, Y, t) } constrained by zero time mod(Pn) = 0 Schwarzschild solutions -Z^2 = Pn * t^2 surface integral with boundary characteristic Pn point solution set |{ {(X} {Y} { Pn * c * t) }| = 3