Complex Analysis L10: Cauchy Integral Formula 

Many thanks for these videos, they are truly entertaining and brilliant.

You are a very gifted teacher

ah i used a similar but less rigorous argument for I_2. i just taylor expanded f(z) around a (because f(z) is analytic there) and said that for a sufficiently small circle f(z) \approx f(a). then the numerator is 0 and the whole integral is 0. it's pretty much exactly what you did but not as rigorous as the epsilon delta stuff. i like what you did better. thanks for the videos they have been great for helping me prepare for my exam.

Been searching for a video like this for a while. Great job

Oh I remember this topic when taking Mathematical Methods for Physicists, by Arfken back in the mid 90s. I wish I had RU-vid videos like this back then! So jealous 😁

"Analytic functions are continuous on steroids" man😂🔥

2:59! That’s why! I never knew that but have always been wondering. Cool.

You can also write f as a Taylor series to prove the theorem.

Gracias 👍

Great🎉🎉🎉

Thank you for this video Remember people, "Don't drink and derive"😂

These are great! Thank you for sharing and... is this okay? integral over closed curve of [f(z) / (z-a)]dz = I = I₁+ I₂ as shown about 7:09 By linearity of integral operator on I₂ the numerator f(z) - f(a) over common denominator (z-a) can be split into two parts wlog f(z)/(z-a) and -f(a)/(z-a) and this is negative result to I₁ so sum to zero And so integral I = I₁+ I₂₍₁₎ - I₂₍₂₎ becomes integral over closed curve of [f(z)/(z-a)]dz =f(a)2πi from Cauchy Integral Formula since second part of integral in I₂ is negative value in I₁ Equivalently I₂ = I₂₍₁₎ + I₂₍₂₎ and I₂₍₂₎ = -I₁ I cannot help but wonder at some Newtonian things happening here such as the center of gravity of a sphere equals sum of all its 'parts'. When these are summed up the value is zero.

“Don’t drink and derive”. Seriously? 😂😂

Dear sir, as you have established the inequality I2 is less than or equal to 2pi*iota*epsilon. But we know that "iota" does not obey order relations .

The link you solved the exercise on Matlab (I didn't find any code in python): Started at time 40:22 on ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-NZ25MQ5W2eA.html.

Axel Walter in Lund

For I2 didn't you just prove that the integral will be zero for the smaller circle. How can we be sure that the integral along the curve will be zero from that???

In time 5:08: Don't drink in drive 😂😂😂.

“It’s koh-shee, not 🛋y” 👁👄👁🪄

For I2 didn't you just prove that the integral will be zero for the smaller circle. How can we be sure that the integral along the curve will be zero from that???

For I2 didn't you just prove that the integral will be zero for the smaller circle. How can we be sure that the integral along the curve will be zero from that???