Cauchy's Integral Formula and Proof

In this video, I state and derive the Cauchy Integral Formula. In addition, I derive a variation of the formula for the nth derivative of a complex function.

If you have any questions, ask in the comments!

[JustDoIt-yhuz]

this is the best video on Cauchy's integral on YouTube... Thanks

[Abhinav_]

One of the most effective videos I've come across lately. You deserve a lot of appreciation. Amazing work!

[musawwirahmad]

I have not seen a more succinct and comprehensive treatment of the topic. PERIOD

[syeddaniyalali]

Loving how you become non-serious suddenly like "Once again I'm gonna man up and give you a proof of this formula", lol. Keeps one entertained 👌

[AbhishekSachans]

What a proof! I like these tightly packed videos which miss nothing! The style of teaching is very efficient!

[ghosthunter]

Ladies and gentlemen,
here is "The best clarification of Couchy Integral formula" in youtube!

[philipchristiansen]

I'm loving this playlist, thanks for uploading.

[hiZarki]

You're honestly a life safer. I like it how you are not as slow as others, I never lose my focus

[tariqandrea]

These videos put complex analysis withing reach of the common man.

[Jordan-sl]

The proof illustrating the application of Green's theorem was very helpful. Thank you

[archiboldpatsanza]

i have an eng math exam tmrw and you have just saved my butt....your explanation is priceless....

[ozzyfromspace]

At the end, you could also think in terms of how f(z) is holomorphic at z=a, which means that the value of the function at a location a+dz should look pretty much the same regardless of the path you take in a tiny neighborhood of z=a...otherwise the function is not holomorphic, as claimed. This would make it clear that the value of f(z) converges to f(a), which is a constant that can be pulled out of the integral sign. Your way of understanding it is good too, I was just giving another way to think about it

Edit: another way. You said z = a + r*e^(i*theta). As a->0, z->a, which is what you correctly concluded :) Every time I watch the video, I realize something new

Edit 2: you can use the derivatives of f(a) to construct the Laurent Series 😮🔥

[alishibli]

THANK YOU!
SO USEFUL AND WELL EXPLAINED

[anupamas]

Thank You so much sir....There is only two days left for my university exam and i was really shattered and fed up with the long derivations on my note book.... This is somehow a blessing.... So easy to deduce the expression....

[akarshchaturvedi]

Couldn't find it anywhere else, thank you very much.

[hossainahd]

Thanks for the lecture. It really helps

[youxizhang]

That's really helpful, thank you, I've learnt a lot!

[NicolasSchmidMusic]

That was nice, you exactly covered what I didn't fully understood!

[josephzicaro]

Much better than my book. Much thanks!

[leob]

Oh I see! Thanks for the clarification and also for the nice complex analysis material.