Question

a

Answer 1

Yes, these two notations are the same.
\( \dfrac{\partial^2 u}{\partial x^2} = u_{xx} \)

Answer 2

Just to make sure, I was checking some resources online as well
http://www.acad.polyu.edu.hk/~mackchan/Teaching0405/ama202/PDE.pdf
"For convenience, we denote... (the above notation, and also one for d^2 u/dxdy)"

Answer 3

Glad to help! :)