Complex Analysis 4 | Holomorphic and Entire Functions

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This is my video series about Complex Analysis. I hope that it will help everyone who wants to learn about complex derivatives, curve integrals, and the residue theorem. Complex Analysis has a lof applications in other parts of mathematics and in physics.

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00:00 Intro
00:28 How to define a holomorphic function?
02:29 Essential properties of holomorphic functions
04:21 Example 1. A complex polynomial
06:11 Example 2. A 'rational function' for polynomials

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#Analysis
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#curveintegral
#integration

(This explanation fits to lectures for students in their first or second year of study: Mathematics, Mathematics for physicists, Mathematics for the natural science, Mathematics for engineers and so on)

[brightsideofmaths]

Please do the quiz to check if you have understood the topic in this video: tbsom.de/s/ca

[mertunsal]

I love how us mathematicians make even simplest things sound extremely cool, no way not to get hyped up when you say HOLOMORPHIC 😄

[MaD]

that really is a simple definition for holomorphic functions

[alphalunamare]

6:48 'When you exclude a finte number of points' .... a Null set I suppose? I suppose one can take a path avoiding those critter's easily to get to the limit. It is not obvious however at first glance :-)

[NewDeal]

00:00 Intro

00:28 How to define a holomorphic function?

2:29 Essential properties of holomorphic functions

4:21 Example 1. A complex polynomial

6:11 Example 2. A 'rational function' for polynomials

[mikeperri]

I feel lucky to have come across your channel. Your lectures on Complex Analysis are crisp and crystal clear - excellent work. Thank you so much.

[PunmasterSTP]

Holomorphic? More like “Heck yeah!” Thanks for making and sharing your complex analysis series!

[RSLT]

I believe analytic and Holomorphic are analogous for functions with one variable like the zeta function. Is that correct?

[ivanrodionov]

Your videos are literally a life saver! Please please keep up the great work!

[jorex]

Is a real valued function with this certain property also called holomorphic?

[darthtleilaxu]

We are getting close to The Residue Theorem. 😎

[wtt]

Very clear explanation !
Thank you sir .

[shlimsady]

Why not let the set S be countably infinite? Then q could also be of degree ∞ but is that a problem?

[skogn]

Doesn’t U have to be connected to be a domain?