Harmonic functions: Mean value theorem

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  1. Dr Chris Tisdell
  2. Mean Value Theorem
  3. harmonic function
  4. partial differential equation
  5. Chris Tisdell
  6. math
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Комментарии
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Learned more than the class I paid $1200 to attend...  Thanks

npr
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Exciting... I'm seeing all of these ideas I know about and heaps I have no idea about and understanding how all this fits together is a boggle. Can't wait till the holidays :D

porkypine
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My question to you, Chris, is why did you change "r" (radius of the ball), for "R", in the proof.

gustavobagu
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Minute 10:28 ... an R should come out in front of the partial d/dr ... Right?

gustavobagu
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I think it would be easier to introduce the directional derivative of direction of radial vector instead of parameterising.

minhokim
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thanks, can You please explain why the solutions of Laplace's equations are continuous?

zeinabashtab
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9:40 if you use "chain rule" R disapear, you will have ux cost+uy sint, doesn't it?

АртемПоляков-жю
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why is it Ux*dy -Uy*dx and not Ux*dx + Uy*dy ??

good video!

matthiasstahli
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Something isn't quite right. at 9:40 you claim that d/dR by the chain rule would give you the integrand but it doesn't. You have an extra R in the integrand. I think the reason is that you didn't divide by |r'(t)| = R which is necessary to give you the unit normal since you are not parameterizing by arc length. Or, I could be wrong.

finweman