Complex Analysis L07: Analytic Functions Solve Laplace's Equation
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- čas přidán 11. 09. 2024
- This video shows that the real and imaginary parts of analytic complex functions solve Laplace's equation. These are known as harmonic functions.
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I am truly riveted by this series. It's all stuff I've seen before, but I love how you can pull it all together in these lectures.
These lectures make this material very easy to understand. I wish CZcams and content like this existed 20 years ago
Professor, I think the equation in 18:37 should be Ur = 1/R V theta (without the negative notation).
I chuckled a little every time Steve mentioned "hairy integral" xD
Thankyou professor for these lectures. I love how you connect everything in your lectures. and like pieces of puzzle that completes a picture it starts to make sense !
Hi professor Brunton, thanks for doing these lecture series on CZcams. How can analytic functions be generalized to real-valued functions, and how can the contour integration be useful for real-valued functions?
Fascinating stuff! Excellent explanation and motivation.
I think many of us have seen this theory before, but I never got how beautiful it is, and more importantly, I never managed to like it as you make us do.
18:59 thanks for explaining different notations, sometimes this is one of the biggest issues to understanding some math paper
Thanks very much for explaining the notations! It’s very helpful for me to catch up the ideas.
The polar derivation has defeated me for now, but perhaps I will come back to it after giving my brain time to grow...
8:29 but 0! = 1, n'est-ce pas?
It does take a few hours of mine to derive the polar system C.R.Conditions. And It's hard to imagine how could we approach a point with a fixed radius but only the infinitesimal angle is changed for somebody who graduated 10 years ago! LOL
Analytic convergence (syntropic) is dual to analytic divergence (entropic) -- Taylor series..
Analytic or predictable domains require the Taylor series to converge -- a syntropic process, complex differentiable or holomorphic.
Conformal maps are complex differentiable or holomorphic hence analytic and their Taylor series converges -- a syntropic process, teleological.
"Always two there are" -- Yoda.
It's not just a log function that has levels.
The numbers themselves have levels.
exp(i t) = exp(i (t + 2 pi k))
for all integer k
It seems to me that any complex valued function also has levels.
Why is the Log function singled out as special? Is it because it has a singularity?
The theorem of Goursat was amazing...🤩🤩🤩.
Wow! My head is spinning 😮 .....but I'm
learning a lot ! 😊
You are a genius! Thanks a lot
Rational, analytic functions are calculable or computable and hence predictable functions -- syntropic functions!
Analytic functions are syntropic or predictable -- algorithms or software programs.
Syntropy (predictable) is dual to entropy -- the 4th law of thermodynamics!
"Always two there are" -- Yoda.
Real is dual to imaginary -- complex numbers are dual.