# Toronto Math Forum

## APM346-2015F => APM346--Misc => Textbook errors => Topic started by: Yunheng Chen on October 18, 2015, 02:00:18 PM

Title: Section2.3 equation 2
Post 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?
Title: Re: Section2.3 equation 2
Post by: Yunheng Chen on October 18, 2015, 02:10:17 PM
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
Title: Re: Section2.3 equation 2
Post by: Emily Deibert on October 18, 2015, 04:50:37 PM
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
w = (\partial_t - c\partial_x)u = \partial_tu - c\partial_xu
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.
Title: Re: Section2.3 equation 2
Post by: Victor Ivrii on October 19, 2015, 03:23:28 AM
Indeed, $u$  was missing