What is the denominator $h$ in this slide? Is it the step in space?
I think if we use the grid discretization, $h$ is the grid size right?
@jerrypiglet: Yes, $h$ is the spacing between grid nodes (in this case, the distance between $i$ and $i+1$). One of course has to generalize in the case where the nodes are not uniformly space (or when we're on a more general "grid", like a triangle mesh).