Complex Analysis 10 | Uniform Convergence

[@mansisuryawanshi9199]

@2:31 range of f should be Complex numbers. Thank you for the awesome content😊

[@brightsideofmaths]

Thank you very much :)

[@NewDeal1917]

0:00 Intro 0:40 Uniform convergence definition 2:17 Power series are coverngent and holomorphic

[@baramillseo5610]

Thank you very much for your very clear and concise explanations!

[@mastershooter64]

Thank you for all your videos!

[@Sarah-pu8un]

Awesome work, thanks!

[@brightsideofmaths]

Thank you too! :)

[@otomarjupiter45]

@brightsideofmath, I guess there is typo between 2:30 and 4:06 in f defined from open complex disk to R, then it suddenly changes to C (: I guess in order to properly define uniform convergence, you need to compare C with C at the limit. Hence R is not correct. Ah it has been already noted, sorry /: anyways, really awesome stuff!

[@brightsideofmaths]

Thanks! It's corrected in the pdf version and the book :)

[@khalidmohammadjama]

Ander nice part 👍 thanks man

[@MrSeba3936]

Am I wrong, or should it be k=1 under propertie (2) in your parentheses? When you write out f'_n(z)

[@brightsideofmaths]

Yes, that would be consistent. However, it is not an actual error because the (k=0)-term vanishes nevertheless.

[@MrSeba3936]

@@brightsideofmaths Ahh yeah I see. Thanks for the reply, and keep up the awesome work! I have just now signed up as a member on steady :))

[@brightsideofmaths]

@@MrSeba3936 Thank you very much for your support :) Very appreciated.

[@aarian4908]

Thank you Love from India 🧡🤍💚

[@kevunger]

Thank you very much for your very clear and concise explanations! PS: what presentation/drawing software do you use to make your slides ? Do you use a drawing pencil? Take care

[@brightsideofmaths]

Thanks! I use Xournal.

[@nicolamombelli2149]

Could you suggest us a textbook to follow along?

[@brightsideofmaths]

Every book on complex analysis will do the work. There are a lot of good ones out there.

[@nicolamombelli2149]

@@brightsideofmaths Thanks! 🙏