Are there typos?

[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]

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.

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/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).

[Shentao YANG]

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.

[Victor Ivrii]

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).

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 $y$.

Indeed