Cauchy's Integral Formula with Proof | Complex Integration | Complex Analysis #15

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How to prove Cauchy's Integral Formula in Complex Analysis with the help of deformation of contours.

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Cauchy's Integral Formula: 00:00 - 00:21
Proof of the Theorem: 00:21 - 03:25
Outro: 03:25 - 03:47

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Комментарии
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Honestly the best Complex Analysis playlist on youtube by far, the simplicity of explanations and always demonstrating everything intuitively through explanations or diagrammatically is amazing. Thank you.

ranimahassen
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Another incredible video, and I have to say again that the writing on the board is so neat and clean; it helps amplify the message and never takes away from it! I also think it is criminal that this video only has a bit over 500 views (as of May/2021). Criminal, and a damn shame...

PunmasterSTP
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Another day, another video! Next week we will continue with the Residue Theorem and its application!

TheMathCoach
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Wonderful explanation. The only detail missing is an explanation of exactly why one can move the limit for r->0 from outside the integral to inside the integral at 2:34. It is not entirely obvious.

individuoenigmatico
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great series. thanks for your effort. 🧡

yman_kh
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What if z0 was in a region in D that the function was not analytic? What would be the result? Thanks in advance.

ZenMan
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Sorry this may be a stupid question.

Why is region D a simply connected region if z0 causes the denominator of the integrand to be infinite, which means z = z0 must be excluded from the region?

winstonong