The Argument Principle | Complex Variables

[@FacultyofKhan]

Quick addendum that I think is worth mentioning: I didn't really define the concepts of winding number and meromorphic functions here. I originally planned to include those definitions/explanations in this video but 1) after looking at those explanations again, I didn't think they were very good and 2) including those explanations in this video would have made it really long (above 15 min). I've posted a separate video defining and explaining those concepts here: kzbin.info/www/bejne/qoeUq2edfqqHbqs

[@ruchi9917]

I'm sorry but I couldn't understand the part at 6:44, sorry if it's dumb but how can you take you the z-zi part from the f(z) ... Assuming you're factoring out from the Laurent transf of f(z)

[@avdrago7170]

I love your videos and wish you could upload more frequently, but I know that life is complicated. As a high school student who is inclined in math, I would love if you continued your real analysis and differential geometry playlists. Thank you for uploading these videos!

[@NicolasSchmidMusic]

I like your videos because all the informations you give are relevant. So I know that if I miss 10 seconds of it, I'll miss something important, and when I know I have to be concentrated to watch a video, I will learn much more from it. I have to rewind back a few times, but at no point I feel like "mh I don't learn anything from what he's saying, I should go forward in the video". Thank you, you are in my favourite math teacher list next to 3Blue1Brown!

[@cesareduardogarza3446]

Welcome back. I’ve missed you

[@dr.ambiguous4913]

Haha that opening line cracked me up

[@darkseid856]

How do mathematicians even do this ? How do they even think that integrating this particular function will give us this result ? Seems like a ALOT of trial and error (which is highly likely) but still how ? This is breathtaking .

[@TheNiTeMaR3]

I know nothing about winding numbers but I could still follow the proof! Such a nice proof and I like your clear and concise explanations. Although sometimes I have to rewind back a few times haha..

[@ytjoemoore94]

at 7:30 there is some weird switching from i to k for the index of the zeros

[@ChessedGamon]

Wait a second this is a new video!

[@FacultyofKhan]

It is!

[@Ksdpm]

physicist sneaking in here

[@jamesbra4410]

These videos are the best, there isn't a lot of content on Complex Variables. Now do some Poisson Integral examples lol

[@agyro3978]

Small question regarding counting the number of Poles and Zeros. Do you count the zeros of both the numerator and the denumerator? Do you also count the poles of both? I am asking since you say to find P and Z from f(z). Do you mean the denumerator or the whole equation when you mean to count the poles and zeros of f(z)?

[@siweifeng8953]

How do you know only zeros and poles of f make contributions to the residue of f'(x)/f(x)? What if f'(x)/f(x) has a pole at z when z is neither the zero nor the pole of f?

[@priyaverma3247]

Could you provide video of Lioueville and Morera's theorem ...

[@thetheandrein]

I thought you died. :( I love your videos, although I can't understand some things. Would you stay?

[@alwayssamar2929]

Thanks sir for this amezing explanation

[@joshlaubach3380]

Love your videos, do you know when you're gonna continue with real analysis or if you're going to start abstract algebra?

[@makispetrakov6024]

what kind of program you use to write?

[@yilanh6167]

great explanation! should summary of -k_j from 1 to p be -P insteaf of P?

[@FacultyofKhan]

Thank you! The index j is supposed to denote the pole I'm talking about. There are p poles (p obviously can't be a negative number), so j runs from 1 to p. Hope that helps!

[@hafizajiaziz8773]

Long time no see

[@eulefranz944]

Nice and easy:)

[@TawpeeBoyshuck]

Genius!