Laplace Derivation

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Derivation of Laplace's Equation

In this video, I derive Laplace's equation from first principles, staring with a fluid in equilibrium and using the divergence theorem. This derivation is particularly elegant and coordinate-free. Enjoy!

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Man I love these videos. Dr. Peyam is so happy about math.

joels
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I make it a point to like your videos whether I understand them or not
Keep up the good work!

rohunse
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Dr.Peyam you should cover Sobolev Spaces!!!!, I just finished my pde class and I don't think I really understand them ):

dyer
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Dr. Peyam, could you cover Hilbert spaces please!!

alfredosepulveda
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Sir also give us the derivation for the laplace transform formula

kishores
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I prefer the "derivation" where Laplace u =0 is equivalent to minimizing || grad u ||_L2

matrixstuff
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Could you make a further video on how the integral always being zero means the inside function is the zero function?

hOREP
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What is the common name for this equation?

SLNDR