Partial differential equations represented as "operators" 1. The problem statement, all variables and given/known data Partial differential equations (PDEs) can be represented in the form Lu=f(x,y) where L is an operator. Example: Input: u(x,y) Operator: L=∂xy + cos(x) + (∂y)2 => Output: Lu = uxy+cos(x) u + (uy)2 2. Relevant equations N/A 3. The attempt at a solution I don't understand the parts in red. What does (∂y)2 mean? Shouldn't it mean (∂y)(∂y) which (I believe) means taking the second partial derivative with respect to y. But the above example seems to imply that (∂y)2 means take the partial derivative with respect to y and then square the result. But I just can't possibly understand how (∂y)2u would be equal to (∂yu)2 I don't have a lot of experience working with operators, so I am feeling really confused. Could someone please kindly explain? Thank you very much!