Answer by user for Help with explanation of change of variables (wave equation)
Because now we are considering the $u$ as a funcion of the two new variables then$$u(x,t)=u\bigg(\frac{\xi+\eta}{2}, \frac{\xi-\eta}{2c}\bigg)=f(\xi)+g(\eta)=u(\xi,\eta)$$The confusion arises because...
View ArticleHelp with explanation of change of variables (wave equation)
I have the wave equation, $u:\mathbb{R}^2\rightarrow\mathbb{R}, c\in\mathbb{R}_{\neq 0}$, \begin{gather}\frac{\partial^2 u(x,t)}{\partial x^2}=\frac{1}{c^2}\frac{\partial^2 u(x,t)}{\partial t^2}...
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