The Cauchy-Riemann Equations - Complex Analysis By A Physicist

In this video we do 8 examples where we test complex functions for complex differentiability with the Cauchy-Riemann Equations. The Cauchy-Riemann equations are crucial in testing for complex differentiability, and are incredibly important in complex analysis.
Intro Song: Mirror Mind - Bobby Richards, Obtained through the CZcams Audio Library

[@MichaelMarteens]

FELLOW MATH MAJORS: Hi, I am also a math major, and I'm nearing the end of my complex analysis course. I can vouch that these videos are great and applicable to those interested in pure mathematics. Don't let the title scare scare you away. Do well!

[@douglasstrother6584]

"Complex Variables" by John W. Dettman is a great read: the first part covers the geometry/topology of the complex space from a Mathematician's perspective, and the second part covers application of complex analysis to differential equations and integral transformations, etc. from a Physicist's perspective.

[@nspace-cowboy]

I'll have to check that out. I recall getting that title recommended to me before.

[@CreamyFucker]

I love you. Thank you for saving my grade

[@rookie2128]

HUGE thanks man this video allowed me to understand the topic 1 hour right before a test from this very thing so it really saved my ass

[@nspace-cowboy]

Glad it helped!

[@KaranSharma-ew7io]

why talented guy like you have to struggle on youtube . Your content is lit man

[@dantethunderstone5766]

Nice job with this Nick. A much clearer presentation than the other videos I've seen. Physicists really do make better teachers than mathematicians :)

[@nspace-cowboy]

Thanks! I'm glad it helped.
I've had probably a equal amount of both good and bad math teachers as I have had physics teachers. I just think people from different fields think about things differently, so explaining things from a different perspective might help sometimes.

[@ayeflippum]

10:07 Exponent should be -2, not 2.

[@strugglingP6student]

thanks a lot! I didn't understand the discussion of this topic in math methods by arfken but this video gave me many insights. thanks again!

[@nspace-cowboy]

Glad it helped!

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[@sherrywang4233]

thank u for saving my life

[@nspace-cowboy]

Glad I could help "save your life"

[@KhangLe-hc4sw]

thank for your lesson

[@crystal_royal3405]

remember me when you get famous

[@yurigansmith]

I like the analogy where analicity is equivalent to rotation freeness. Then it's very intuitive that closed path integrals must vanish, as long as the region is simply connected.

[@yanisberger1476]

Thank you, seems really easy the way you explained it now! Something my professor couldn‘t do.

[@nspace-cowboy]

Glad I could help.

[@midnightmadness1714]

WOW sir, really mad emy life easier. Thank you so much, please keep on posting.

[@brandonhines9816]

great vid man, thank you

[@nspace-cowboy]

No problem!

[@lasithathilakarathne3205]

In the second example, you say 3 = 3xy^2 is only possible for x=1 and y=+1 or y=-1, what if x = 4 and y = 1/2? something like that?

[@nspace-cowboy]

There are plenty of possibilities that we could consider that would satisfy the equation. I just chose the first one that I noticed. If I'm recalling the example you are referring to correctly, all this told us was that we could move on and test the second Cauchy-Riemann equation, which ended up telling us that the function was not complex differentiable.

[@lasithathilakarathne3205]

@@nspace-cowboy in that case, no issue. Thank you

[@Hadeerkhafagy24699]

Excuse me please, may you answer this question please.
I really need the answer.💔
Express the Cauchy Remainn equation in the complex form.
If f(z) is an analytic function, express f`(z) in the complex form.

[@nickmcstuffins1836]

no

[@Hadeerkhafagy24699]

@@nickmcstuffins1836
OK, no problem.

[@nopepae]

how 'bout z^n

[@adiba5237]

Please remove bg music