The Cauchy-Riemann Equations - Complex Analysis By A Physicist
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- čas přidán 20. 08. 2024
- 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
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!
"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.
I'll have to check that out. I recall getting that title recommended to me before.
I love you. Thank you for saving my grade
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
Glad it helped!
why talented guy like you have to struggle on youtube . Your content is lit man
Nice job with this Nick. A much clearer presentation than the other videos I've seen. Physicists really do make better teachers than mathematicians :)
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.
10:07 Exponent should be -2, not 2.
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!
Glad it helped!
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thank u for saving my life
Glad I could help "save your life"
thank for your lesson
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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.
Thank you, seems really easy the way you explained it now! Something my professor couldn‘t do.
Glad I could help.
WOW sir, really mad emy life easier. Thank you so much, please keep on posting.
great vid man, thank you
No problem!
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?
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.
@@nspace-cowboy in that case, no issue. Thank you
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.
no
@@nickmcstuffins1836
OK, no problem.
how 'bout z^n
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