Complex Analysis 9 | Power Series

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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
00:57 Why are power series important? Example of exp(z)
02:05 General definition
04:03 Example. Geometric series + conditions for convergence
09:06 Cauchy-Hadamard theorem

#ComplexAnalysis
#Analysis
#Calculus
#Mathematics
#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)

[rob]

It would be great to see the details of the proof you reference in the video

[leonilsonnunes]

I always stay anxious for next video of this channel. These videos are true Math classes.

[thermrm]

Thank you so much for making these videos. I'm a physics student, and these concepts aren't taught this well.
Also, your handwriting is so neat!
love from Palestine <3

[darrenpeck]

I would very much like to see the proof.

[omkardwivedi]

HEY NICE JOB . I AM YOUR GREAT ADMIRER.
PLEASE MAKE VIDEOS FOR GEOMETRY FROM (EUCLID TO COORDINATE TO MODERN ONE)

[TrongNguyen-szwr]

thanks very much, teacher. Its really help me a lot :)

[mariolemelin]

As always, great videos. Could you give us a link here to the proof of the nice result (8:48) as a pdf. Thank you in advance!

[darthtleilaxu]

Power Series...?! Haaaa ! "Séries entières" !
Thanks for the video!

[masteroogway]

Does anyone know how he makes these presentation?

[JojiThomas]

Good videos. Really understood the concept

[manswind]

Hey! Fantastic video, really well-made and comprehensive, and easy to understand as well. I have one request tho, if possible please include proofs of the theorems you mention (such as Cauchy Hadamard, or that power series converge in a ball), or at least provide some links for the same. Much appreciated, thanks!

[higifnr]

I have a friend that is studying abroad in Germany and when he showed me the Cauchy-Hadamard limit I was kinda confused because we use the d'Alembert rule and it seems to be a lot simpler. Any reason why to use C-H over it?

[NewDeal]

00:00 Intro
0:57 Why power series are important? Example of exp(z)
2:05 General definition for C
4:03 Example. Geometric series + conditions for convergence
9:06 Cauchy-Hadamard theorem

[hyperduality]

Convergent is dual to divergent -- power series are dual!
Syntropy is dual to increasing entropy --the 4th law of thermodynamics!
Analysis or wholes become parts is an entropic process or reductionist process -- divergent.
Synthesis or parts become wholes is a syntropic process, or a holistic process -- convergent.
Noumenal (analytic, rational) is dual to phenomenal (synthetic, empirical) -- Immanuel Kant.
"Always two there are" -- Yoda.

[ayaayout]

Hello
May i have your email ? I would like to ask you few questions .