Rouche's Theorem and the Fundamental Theorem of Algebra

[@bugson08]

This Fundamental Theorem of Algebra proof is slick as heck! Great video, great series. Please do Real Analysis soon!

[@dcterr1]

I learned Rouche's theorem many years ago but I forgot about it, and this was a very clear and thorough explanation. Great job!

[@Alex_Deam]

I was just googling something about Rouche's Theorem, but ended up here and got a nice proof of the Fundamental Theorem of Algebra as a nice bonus, thanks!

[@yudhisthir7247]

My favourite teacher is back with an outstanding video. Thankyou very much.

[@CHRISTIANZEGARRA2018]

Please do more complex analysis videos! I'm going to take the grad version of it next Fall 2020. I took Complex variables in spring 2019 and I really liked it. Videos are smooth and very easy to understand. Keep up the good work!

[@JoelRTLCosta]

Very helpful videos. Watched them all and I'm looking forward some more! Thanks a lot!

[@eulefranz944]

When looking at complex analysis proofs I always think:" huh neat, true true. Very clear." They are so *cool* and almost straight forward, I donno they just make sense to me... Contratray to some more difficult linear algebra proofs...:]

[@fisikalectures597]

Amazing video as always.

[@shamsulkhaknurulkhakov4230]

You know men, I am deciding to throw away all my books and wait for your videos....thanks a lot.

[@maherabmurad9055]

Amazing work man.good job.keep it up.

[@xjuhox]

Can you make a video of the most simple proof of FTA that is based on the Green's theorem for circles and polynomial analyticity?

[@shamsulkhaknurulkhakov4230]

Please, make a video about evaluation of CONTOUR INTEGRATION IN THE PRESENCE OF BRANCH CUTS. It is still unclear for me to distinguish between pole and singularity.

[@FacultyofKhan]

Here you go! kzbin.info/www/bejne/rXaZZJeVm52DZ5o

[@hafizajiaziz8773]

It feels like someday you're going to talk about L-function and Modular Form.

[@Preparing_and_Testing]

pleas also mention books which you think best for complex analysis and group theory

[@mousaalsaeed9410]

Why proof is important if some theorems practically work. Why do we need their proof?

[@FacultyofKhan]

It's because a) Getting in the habit of proving theorems is an important skill in Math, b) Proofs provide important insight and intuition into mathematical concepts, and c) It feels incomplete to state a theorem without proof.

[@mousaalsaeed9410]

@@FacultyofKhan I'm mechanical engineer in the senior year, my first and second years for me in university I really cared about the proofs of the theorems now if I encountered with one and I get the intuition behind it and understand it practical aspects I really don't care about its proof and I see no difference in my understanding for the subject. Is that okay? Cause sometimes my curiosity drives me to look for the proof but I just stop it and say it's not worthy

[@FacultyofKhan]

@@mousaalsaeed9410 Don't worry, that's fine! Speaking as someone who also did an engineering degree (Chemical), I agree that knowing proofs isn't really necessary for an engineer. Having said that, not all my viewers are engineers, and many crave the rigor that comes with providing a full proof. For this reason, I usually like to prove theorems (especially important ones like Rouche's Theorem) when I teach them.

[@mousaalsaeed9410]

@@FacultyofKhan yes, I really admire your hard work and the time you spend to make these videos and to be honest sometimes the proof show some points can let you understand the whole topic, and that's really what happened to me when I watched your video in proofing Euler Lagrange equation I faced it in mechanical vibration course.