Pade Approximation states that a power series can be written as a rational function. Which is a series divided by another series. (An easy example of this will be the geometric series with mod'r' < 1) I've read books about the abstract bit of this. But I am completely stuck when it goes onto applications. How does pade approximation help solving PDE and ODE? And sometimes, people optain a power series solution for PDE and ODE, (of polynomials of x) how did they do that? I would also very much like to understand the Navier-Stokes equations.. but this can come later.