Finally a decent video on this topic. I have been through SO MANY shitty ones. Its not even that fucking hard but people make it seem soooooo hard by giving vague, half explanations and proofs. I don't want a proof i want an example!!!! Thank you so much
Excellent explanation, and the trampoline example really helps clarify the concept that once you know what is happening on the boundary of an analytic function f(z), you also know everything that is happening inside the function within the region C. That is mind blowing. The boundary contains all the information of the function! Cool. Thank you, Michael Barrus!
For 10:02, on the LHS with the second integrand, could we also do a substitution z |----> z-1 to make the denominator have a singularity at -1 and apply the Cauchys Integral Formula much like for the first integral?
Sir u are really awesome... Great teaching...bt I hv only one doubt sir, that how do paramerise all types of curves?? I'm unable to find paramerzation of curves..pls tell me
Mujy ya pouchna tha k mod k andar jo value di hoti hai us sy diagarm kasy draw karne hai or agr factorize kar k 2 values aye hain un my sy kis ko z0 banana hai or kis ko f(z) boly gain...
why do f(z) must be analytic inside a closed curve for Cauchy integral theorem. the integral is taken along the path not inside then why points inside curve matter. an intuitive explanation plz .
Because it is derived from the Cauchy-Goursat theorem and CG requires f(z) to be everywhere analytic in a simply connected domain. I.e. you can't prove Cauchy's integral formula without f(z) being analytic in a simply connected domain.
Finally a decent video on this topic. I have been through SO MANY shitty ones. Its not even that fucking hard but people make it seem soooooo hard by giving vague, half explanations and proofs. I don't want a proof i want an example!!!! Thank you so much
I'm so happy I found this channel. Your job is awesome, Michael. Really helped me, thank you!
What do you study?
Wow didn’t know it was that easy! 😄
Appreciate how easy and simple you make complex analysis!
Excellent explanation, and the trampoline example really helps clarify the concept that once you know what is happening on the boundary of an analytic function f(z), you also know everything that is happening inside the function within the region C. That is mind blowing. The boundary contains all the information of the function! Cool. Thank you, Michael Barrus!
Really enjoyed it, thank you.
Wow!!! this is amazing. Thanks Michael
Very clear, thank you!
Thank you!
Thanks Professor!!!!!!!!!!!!
Great video, thanks!
🙏🙏
Gracias
Does anybody know which textbook he was using or this course? His lectures are amazing Professor Michael Barrus.
how do you know how many times to differentiate
For 10:02, on the LHS with the second integrand, could we also do a substitution z |----> z-1 to make the denominator have a singularity at -1 and apply the Cauchys Integral Formula much like for the first integral?
Sir u are really awesome... Great teaching...bt I hv only one doubt sir, that how do paramerise all types of curves?? I'm unable to find paramerzation of curves..pls tell me
Mujy ya pouchna tha k mod k andar jo value di hoti hai us sy diagarm kasy draw karne hai or agr factorize kar k 2 values aye hain un my sy kis ko z0 banana hai or kis ko f(z) boly gain...
Tq sir
On besoin explications sur formule de Cauchy pompeiu
why do f(z) must be analytic inside a closed curve for Cauchy integral theorem. the integral is taken along the path not inside then why points inside curve matter. an intuitive explanation plz .
Because it is derived from the Cauchy-Goursat theorem and CG requires f(z) to be everywhere analytic in a simply connected domain.
I.e. you can't prove Cauchy's integral formula without f(z) being analytic in a simply connected domain.