Toronto Math Forum
APM3462015F => APM346Misc => Textbook errors => Topic started by: Yunheng Chen on October 18, 2015, 02:00:18 PM

For equation 2 we have (âˆ‚^2tâˆ’c^2âˆ‚^2x)=(âˆ‚tâˆ’câˆ‚x)(âˆ‚t+câˆ‚x)u=0 (2)
Shouldn't we have a u on the left side?

Also in the following line for equation2
We have "w=(âˆ‚tâˆ’câˆ‚x)u=utâˆ’cux"
Shouldn't it be "w=(âˆ‚tâˆ’câˆ‚x)u=wt  wux"
I just found out that I was wrong about it.
Thanks for Emily's explanation

Also in the following line for equation2
We have "w=(âˆ‚tâˆ’câˆ‚x)u=utâˆ’cux"
Shouldn't it be "w=(âˆ‚tâˆ’câˆ‚x)u=wt  wux"
But why would the w come into the equation here? I think we are saying that \begin{equation}
w = (\partial_t  c\partial_x)u = \partial_tu  c\partial_xu \end{equation}
As in, we are expanding what is in the brackets so that it acts on u, and thus this is what w is equal to. Maybe I am misunderstanding?
Edit: I agree with the original post though, I think a u is missing.

Indeed, $u$ was missing