Complex Analysis 3 | Complex Derivative and Examples

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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
00:34 The [geometric] intuition for complex derivative
04:11 Producing the formal definition
05:19 Example 1: A linear polynomial in ℂ
07:34 Example 2: A conjugate function

#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)

[brightsideofmaths]

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

[NewDeal]

00:00 Intro

00:34 The [geometric] intuition for complex derivative

4:11 Producing the formal definition

5:19 Example 1. A linear polynomial in C

7:34 Example 2. A conjugate function

[jaimelima]

Cool! BTW, another way to show how crazy this limit in the second example gets is to put the limit in the polar format using our old boy Euler's formula. The function that measures distance in the metric space returns a real number, and this is good because we want ordering. However, the price to pay, and the phantom that will haunt us forever on this, is that the phase(argument) information collapses and is lost, and strange things the average normal human mind has trouble accept at first start to happen.

[PunmasterSTP]

Complex derivative and examples? More like "Completely dynamite and expansive!" Thanks for helping to shatter our old ways of thinking and broadening our horizons.

[BariScienceLab]

My brain is completely fried and I love it. Thank you for this series!

[Hold_it]

Nice to see the next video so soon.
I really appreciate it.

[LuukeFX]

Just discovered your videos now as I have to refresh my memory on this topic. Wish this existed during my study! Super clear explanation, thanks for sharing this for free!

[reptilewithsadhumaneyes]

Great video as always, excited for the series

[ADCtEADCtE]

This is BULLSHIT. No one has shown a complex number on a complex axis.

[blind_vigilante.murdock]

wouldn t the last example give the same results in a function that mirrors dots in cartesian plane because none of the process included some unique complex property or anything?? i rlly need an answer

[baramillseo]

Great video as always, excited for the series

[alejrandom]

3:54 shouldn't there be an error term for f(z)?

[darthtleilaxu]

Haa ! Je viens justement de finir mon thé ☕.
Bonne pause en perspective. 👌

[codeo]

Incredible videos!!! Thank you so much!

[kaursingh]

SIR - WHETHER CONTOUR IS DOMAIN OF FUNCTION ? THANK U SIR

[juancarlosperez]

if delta is defined so f(z)=f(z0)+(z-z0)*Delta(z), then why isn't Delta (z)= (f(z)-f(z0))/(z-z0) instead of the limit of that expression? I mean the derivative as the slope would still work if it is defined as the limit of delta and not delta itself. f(z)=f(z0)+(z-z0)*f'(z) is not correct in general.

[acf]

Why is this form linear aproximation before z is fixed to z0? Delta is just hiding nonlinearity until it is evaluated, this nomenclature confuses me.

[kitstudent]

really interesting, will you be covering modular forms?

[geoglyphproject]

I love this playlist thanks for sharing

[Canda-fhxc]

We will really appreciate it 🙏 🙌
if you can teach us
Geometric Analysis