# Toronto Math Forum

## APM346-2016F => APM346--Lectures => Chapter 3 => Topic started by: Shentao YANG on October 09, 2016, 01:29:01 PM

Title: Are there typos?
Post by: Shentao YANG on October 09, 2016, 01:29:01 PM
http://www.math.toronto.edu/courses/apm346h1/20169/PDE-textbook/Chapter3/S3.2.html#mjx-eqn-eq-3.2.15
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/PDE-textbook/Chapter3/S3.2.html#mjx-eqn-eq-3.2.24
I guess this one should be
${(4\pi kt)^{{{ - n} \over 2}}}$ instead of ${(2\sqrt {\pi kt} )^{{{ - n} \over 2}}}$
Title: Re: Are there typos?
Post by: Victor Ivrii on October 09, 2016, 03:26:09 PM
http://www.math.toronto.edu/courses/apm346h1/20169/PDE-textbook/Chapter3/S3.2.html#mjx-eqn-eq-3.2.15 (http://www.math.toronto.edu/courses/apm346h1/20169/PDE-textbook/Chapter3/S3.2.html#mjx-eqn-eq-3.2.15)
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 copy-paste error. Fixed.

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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.

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http://www.math.toronto.edu/courses/apm346h1/20169/PDE-textbook/Chapter3/S3.2.html#mjx-eqn-eq-3.2.24 (http://www.math.toronto.edu/courses/apm346h1/20169/PDE-textbook/Chapter3/S3.2.html#mjx-eqn-eq-3.2.24)
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).
Title: Re: Are there typos?
Post by: Shentao YANG on October 10, 2016, 06:41:32 PM
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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/PDE-textbook/Chapter3/S3.2.html#mjx-eqn-eq-3.2.14 should all have zero in the position of $y$. I guess you have already plug in the value $y = 0$ inside the integral.
Title: Re: Are there typos?
Post by: Victor Ivrii on October 11, 2016, 07:04:37 AM
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I am curious where / when this $k$ is introduced in the derivation of the final formula
It was present in   non-numbered equation before (13) but missing in (13).
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By the way, I guess the two unlabeled equations above http://www.math.toronto.edu/courses/apm346h1/20169/PDE-textbook/Chapter3/S3.2.html#mjx-eqn-eq-3.2.14 (http://www.math.toronto.edu/courses/apm346h1/20169/PDE-textbook/Chapter3/S3.2.html#mjx-eqn-eq-3.2.14) should all have zero in the position of $y$.
Indeed