Complex Analysis 25 | Cauchy's Theorem (general version)

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This is my video series about Complex Analysis. I hope that it will help everyone who wants to learn about complex derivatives, curve integrals, and the residue theorem. Complex Analysis has a lof applications in other parts of mathematics and in physics.

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(This explanation fits to lectures for students in their first or second year of study: Mathematics, Mathematics for physicists, Mathematics for the natural science, Mathematics for engineers and so on)

[elitewarrior]

Whoa...! After all these years, your face appear on the video, thanks Sir for giving us a figure to remember and refer to whenever we encounter difficulties in Mathematics.

[nirmalbajiya]

Hello sir I am from INDIA and I am a BTech student in IIT Kanpur one of the most premiere engineering institutes around the country still I was not able to understand the concept by studying from our professor but you're such a wonderful teacher that you explained everything from basic to the core.Thank you So much sir

[zwazwezwa]

No way I imagined you look like this. Great look sir!

[eamon_concannon]

I have considerable familiarity with most of what you cover in this playlist. However, I enjoy getting your take on this subject, which I think is one of the most interesting of mathematical subjects.
Subscribed and considering membership.

[nm-debw]

Couldn't we just aproximate the closed curve integral with closed polygon integrals and show that in the limit the value is still 0?

[hyperduality]

Inside is dual to outside, interior is dual to exterior.
Union is dual to intersection.
Convex (convergent, syntropy, homology) is dual to concave (divergent, entropy, co-homology).
Inclusion is dual to exclusion -- the Pauli exclusion principle for Fermions.
Bosons (inclusion or the same state) are dual to Fermions (exclusion or different states) -- atomic duality!
Waves are dual to particles -- quantum duality.
"Always two there are" -- Yoda.

[yololololo]

i had an off topic doubt related to foundations of mathematics, ive noticed that logic uses notions of set theory for its axioms and set theory uses logic in a similar way, isnt this a kind of circular reasoning? and ive always been told that circular reasoning is generally "bad". how should i be thinking about this? it bugs me a lot.