Complex Analysis 03: The Cauchy-Riemann Equations

[@sandratobias2158]

Thank you. You make more sense than my professor.

[@donyang2119]

I study in China and you sir, just saved my life. thank god

[@camilomuianga7865]

Without having any classes with my professor, however, i ready and reready so when i come to this vídeo everything wemt clearer. Here from Mozambique.

[@JonPowersDrives]

Thank you so much. But the way you write x really gets to me :D

[@timothyvarghese6335]

Thank you from India!

[@petermartin7885]

Great video, but where did you learn to write your x's?

[@godsrighteousness5003]

soo good explanation, now i know what analytic means :) keep up the great videos

[@sajateacher]

Just goes to show you, a country can start off as a penal colony and go on to build world-class universities. That's not imaginary (v), that's real (u).

[@terryphi]

How did we go from checking if CR holds to finding where it is differentiable?

[@debajyotisg]

CR relations actually test whether a complex function is analytic in a given region. So if the CR relations hold, the function is analytic (which is just a fancy word for it being complex differentiable at every point in the region)

[@gustavlotz5415]

Thanks, easy to understand

[@GraphicEngine]

Not the circle of radius 2, circle of radius sq.root 2

[@godsrighteousness5003]

no what he did there was in translating the x^2 + y^2 -2x = 1 into (x-1)^2 +y^2 = 2 when we expand the brackets of (x-1)^2 we get: x^2 - 2x +1 however because there is no +1 on the LHS of the first equation stated we have to add a +1 & -1 to the LHS so rewriting our first equation we have: x^2 + y^2 -2x +1 - 1 = 1 where the x^2 -2x +1 becomes our (x-1)^2 of expression #2; the y^2 remains where it is and our remaining -1 we translate to the RHS in equation 2 to giving: (x-1)^2 +y^2 = 2 P.S I know you probably already figured this out, but incase other people are interested

[@MegaRawraw]

@kevin horn yes of course. However, the radius is of the form r^2 = 2 in that equation. So, r = sqrt(2)

[@dpedalv]

Really good, thank you.

[@rsv25k]

Thanks ❤️❤️

[@Oliver-xt5wu]

This guy looks like maths!

[@ninosawbrzostowiecki1892]

I like the way you draw your x's, so very Welsh!

[@noe9250]

you know new south wales is in Australia? John Steele ain't Welsh

[@BubbaDoodle1998]

@@noe9250 he certainly ain't Australian you moron

[@vector8310]

Drive me nuts

[@roadiesahil]

very helpful Thank you

[@vector8310]

Much appreciated, but may I proffer two suggestions for future videos? Illustrate using shorter, simpler equations and make your x's look more like x's

[@aakhilgohain0770]

(x-1)^2 + y^2 = 2? Shouldn't it be (x-1)^2 + y^2 = 0?

[@godsrighteousness5003]

no because he added a (+1 -1) to the LHS of the equation: x^2 + y^2 -2x = 1 and he uses the +1 to get the (x-1)^2 and translates the -1 to the RHS giving the 2.

[@giikfada1435]

senin yazacağın x'i gondiklesinler

[@giikfada1435]

yinede eyv

[@anshulmathur9368]

ty 👍

[@nipunfernando6689]

wow wow wow

[@sarah_70]

But I don't understand, du/dx DOESN'T equal dv/dy. The cauchy riemann equations aren't satisfied. Why are you talking about a circle? Please someone explain this to me.

[@luismisanmartin98]

When he obtains what du/dx and dv/dy look like, there is no reason to believe those two expressions will never be the same for all values of x and y. In fact, forcing them equal to each other (du/dx = dv/dy) , we obtain that this will only be possible if x and y are constrained to the circunference centered at (1,0) with radius root2

[@sarah_70]

Thank you. Could you please explain to me the circle stuff?

[@luismisanmartin98]

The function f(z) will only be differentiable if z=x+iy has its real(x) and imaginary(y) components in the circunference. What do you actually mean by circle stuff?

[@sarah_70]

I was just confused why the function gives a circle but now I understand... sorry. Complex analysis still sucks but I’m one step closer to understanding it a bit more! Thank you for your help!

[@luismisanmartin98]

No worries, I'm glad I could help! I am also trying to understand for an upcoming exam. What are you studying? I am doing second year physics in the UoM :)

[@LD-ux4hz]

Mistake! du/dy is wrong! X^3 ,du/dy=0