Complex Analysis: Cauchy's Integral Theorem
Рет қаралды 20,474
2 жыл бұрынToday, 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:
• Complex Analysis: Cauc...
@angelmendez-rivera351 2 жыл бұрын
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-mo5666 2 жыл бұрын
Best Complex analysis channel out there! fantastic Video
@user-wu8yq1rb9t 2 жыл бұрын
Dear QN³ ... Please don't forget Green Theorem (you said you want to prove it) 😊 Thank you ❤️
@DavideCosmaro 2 ай бұрын
You make it look less complex ❤
@user-wu8yq1rb9t 2 жыл бұрын
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
@zinzhao8231 Жыл бұрын
There's a typo in the thumbnail. I'll let you figure that out. Good idea!
@jameyatesmauriat6116 Жыл бұрын
Why your voice is holomorphic
@qncubed3 Жыл бұрын
Bc you can differentiate it
@sudarshannelatury2882 Ай бұрын
When you pronounce the word "integrate," I seem to find it hard to integrate your accent.
@nuclearrambo3167 Ай бұрын
cOnSeRvAtIvE vEcToR fIElD
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