Multivariable Calculus | Vector forms of Green's Theorem.

We present two vector forms of Green's Theorem.

[TheMauror]

This is one of the best maths channels on YouTube, it's up there with blackpenredpen and Dr peyam! Congrats!

[technoguyx]

Form #1 is how most people usually think of Green's theorem, but I had never seen form #2 before. Informative stuff.

[Hiltok]

@ 9:40 small blip in answer for curl(F). You said, "... z minus x-squared" but wrote z - y^2 instead of z - x^2.
@ 16:20 Explaining why (del X F) dot k is just (Qx - Py) you said "... k dot k is obviously zero." Should have said "... k dot k is obviously just one." (Qx - Py)<0, 0, 1> dot <0, 0, 1> = (Qx - Py)
@ 19:25 T dot n = x'y' / ||r|| - x'y' / ||r|| = 0 Should be x'y' / ||r||^2 - x'y' / ||r||^2 = 0

[vtynianski]

Hey Michael, what "bigger" theorem are you talking about at 1:00 that Green's theorem is a part of? Is it already covered on your channel in later videos?

[junxionglu]

Form 1 is to calculate the total work done alone the curve
and
Form 2 is to calculate the total flux through the curve
Am I right?

[levprotter]

Pretty sure at 5:20 you wrote Q_y - P_x instead of Q_x - p_y