Toronto Math Forum
APM346-2015F => APM346--Misc => Textbook errors => Topic started by: Yunheng Chen on October 18, 2015, 02:00:18 PM
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For equation 2 we have (∂^2t−c^2∂^2x)=(∂t−c∂x)(∂t+c∂x)u=0 (2)
Shouldn't we have a u on the left side?
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Also in the following line for equation2
We have "w=(∂t−c∂x)u=ut−cux"
Shouldn't it be "w=(∂t−c∂x)u=wt - wux"
I just found out that I was wrong about it.
Thanks for Emily's explanation
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Also in the following line for equation2
We have "w=(∂t−c∂x)u=ut−cux"
Shouldn't it be "w=(∂t−c∂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.
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Indeed, $u$ was missing