Complex Analysis: Cauchy's Integral Theorem

Today, we prove Cauchy's integral theorem, which states that a contour integral around a simple closed loop is 0 if the function everywhere inside the contour is holomorphic.

***Note: I forgot to mention in the video that the contour must be SIMPLE, which means it does not intersect itself.

Cauchy Riemann Equations:

[angelmendez-rivera]

The idea behind the conservative vector fields is that there exists some scalar field f such that partial(f, x) = Q and partial(f, y) = P, so that df = Q·dx + P·dy, and partial(P, x) – partial(Q, y) = partial(partial(f, y), x) – partial(partial(f, x), y). Assuming everything is nice and continuous, we have that partial(partial(f, x), y) = partial(partial(f, y), x), so the above subtraction is 0.

[datsmydab-minecraft-and-mo]

Best Complex analysis channel out there! fantastic Video

[wuyqrbt]

Dear QN³ ...
Please don't forget Green Theorem (you said you want to prove it) 😊
Thank you ❤️

[wuyqrbt]

Hello Dear QN3.
Thank you so much for your great videos (I love all of them).
Please make a video about Green Theorem too (I'm waiting).
Thank you so much

[zinzhao]

There's a typo in the thumbnail. I'll let you figure that out. Good idea!

[SimonSithole-pp]

This video made the Cauchy's so dump😂👍👍👍