I just finished up Stewart's Calculus Textbook, and the last section was on solving 2nd Order Non-Homogeneous Diff Eqs using power series. I've looked through Paul's Calculus page in the Differential Sections, and can see that there is still a lot more beyond Stewart's that I'd like to study; Fourier, Laplace, PDE's, systems of DE's, higher order DE's. I also however wanted to do the MIT opencourseware course on Linear Algebra after finishing Stewart's Calculus. From what I've perused, I get the impression that actually doing the more advanced Differential Equations stuff after completing Linear Algebra might be the best way to go anyway. It seems like the more advanced stuff in Paul's Calculus that wasn't covered in Stewart's involves many concepts from Linear Algebra anyway, and the Linear Algebra course seems to cover some Differential Equations stuff. Are my impressions correct? Or is this just some superficial overlap?