APM346-2016F > Chapter 3

Are there typos?

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Shentao YANG:
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 ${(2\sqrt {\pi kt} )^{{{ - n} \over 2}}}$

Victor Ivrii:

--- Quote from: 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.

--- End quote ---
You are correct, it was a copy-paste error. Fixed.


--- Quote ---By the way, I cannot understand why there is a $k$ in this equation, can any one explain it to me?

--- End quote ---
Factor $k$ comes from the same factor in $ku_{xx}$ term in the heat equation.


--- Quote ---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 ${(2\sqrt {\pi kt} )^{{{ - n} \over 2}}}$

--- End quote ---
Fixed. There was another misprint in the same formula (also fixed).

Shentao YANG:

--- Quote ---
--- Quote ---By the way, I cannot understand why there is a $k$ in this equation, can any one explain it to me?

--- End quote ---
Factor $k$ comes from the same factor in $ku_{xx}$ term in the heat equation.

--- End quote ---
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.

Victor Ivrii:

--- Quote ---I am curious where / when this $k$ is introduced in the derivation of the final formula
--- End quote ---
It was present in   non-numbered equation before (13) but missing in (13).

--- Quote ---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 $y$.
--- End quote ---
Indeed

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