Section2.3 equation 2

[Yunheng Chen]

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?

[Yunheng Chen]

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

[Emily Deibert]

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.

[Victor Ivrii]

Indeed, $u$  was missing