Toronto Math Forum
APM3462016F => APM346Lectures => Chapter 3 => Topic started by: Shentao YANG on October 09, 2016, 01:29:01 PM

http://www.math.toronto.edu/courses/apm346h1/20169/PDEtextbook/Chapter3/S3.2.html#mjxeqneq3.2.15
I guess the second term should be ${G_N}(...)$ instead of ${G_N}_y(...)$. As far as I can understand, we have already cancelled out the ${G_N}_y(...)$ term under the context of Neumann Boundary condition.
By the way, I cannot understand why there is a $k$ in this equation, can any one explain it to me?
http://www.math.toronto.edu/courses/apm346h1/20169/PDEtextbook/Chapter3/S3.2.html#mjxeqneq3.2.24
I guess this one should be
${(4\pi kt)^{{{  n} \over 2}}}$ instead of ${(2\sqrt {\pi kt} )^{{{  n} \over 2}}}$

http://www.math.toronto.edu/courses/apm346h1/20169/PDEtextbook/Chapter3/S3.2.html#mjxeqneq3.2.15 (http://www.math.toronto.edu/courses/apm346h1/20169/PDEtextbook/Chapter3/S3.2.html#mjxeqneq3.2.15)
I guess the second term should be ${G_N}(...)$ instead of ${G_N}_y(...)$. As far as I can understand, we have already cancelled out the ${G_N}_y(...)$ term under the context of Neumann Boundary condition.
You are correct, it was a copypaste error. Fixed.
By the way, I cannot understand why there is a $k$ in this equation, can any one explain it to me?
Factor $k$ comes from the same factor in $ku_{xx}$ term in the heat equation.
http://www.math.toronto.edu/courses/apm346h1/20169/PDEtextbook/Chapter3/S3.2.html#mjxeqneq3.2.24 (http://www.math.toronto.edu/courses/apm346h1/20169/PDEtextbook/Chapter3/S3.2.html#mjxeqneq3.2.24)
I guess this one should be
${(4\pi kt)^{{{  n} \over 2}}}$ instead of ${(2\sqrt {\pi kt} )^{{{  n} \over 2}}}$
Fixed. There was another misprint in the same formula (also fixed).

By the way, I cannot understand why there is a $k$ in this equation, can any one explain it to me?
Factor $k$ comes from the same factor in $ku_{xx}$ term in the heat equation.
I guess I know this $k$ is the same factor in $ku_{xx}$ term in the heat equation, I am curious where / when this $k$ is introduced in the derivation of the final formula (I cannot see any hint from the textbook...)
By the way, I guess the two unlabeled equations above http://www.math.toronto.edu/courses/apm346h1/20169/PDEtextbook/Chapter3/S3.2.html#mjxeqneq3.2.14 should all have zero in the position of $y$. I guess you have already plug in the value $y = 0$ inside the integral.

I am curious where / when this $k$ is introduced in the derivation of the final formula
It was present in nonnumbered equation before (13) but missing in (13).
By the way, I guess the two unlabeled equations above http://www.math.toronto.edu/courses/apm346h1/20169/PDEtextbook/Chapter3/S3.2.html#mjxeqneq3.2.14 (http://www.math.toronto.edu/courses/apm346h1/20169/PDEtextbook/Chapter3/S3.2.html#mjxeqneq3.2.14) should all have zero in the position of $y$.
Indeed