APM346-2012 > Misc Math

Mean-value theorem

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Kun Guo:
I do not quite understand step b and c(see attached) in the proof of Mean-value theorem. Did you use Green's identity or some other identity when dragging out terms from the integral?

Victor Ivrii:
b. Gauss identity (you may call it Green in 2D). We proved this before.

c. $\Sigma$ is a sphere of radius $r$ with a center $y$ so $G$ so for $x\in \Sigma$  $G(x,y)=c |x-y|^{2-n}=cr^{2-n}$ is constant and could be moved out of integral.

Ziting Zhou:
Hi Professor Ivrii. I have a question on the attachment above. In part b, after dragging out the factor, why the remainder is (partial u)/(partial v) instead of u? Thanks.

Victor Ivrii:

--- Quote from: Ziting Zhou on November 25, 2012, 04:56:23 PM ---Hi Professor Ivrii. I have a question on the attachment above. In part b, after dragging out the factor, why the remainder is (partial u)/(partial v) instead of u? Thanks.

--- End quote ---

Right, fixed and details added
http://www.math.toronto.edu/courses/apm346h1/20129/L26.html#sect-26.4

Kun Guo:
thanks professor, now it makes more sense  :)

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