<p>I'm taking an applied PDE class in the fall and my school has Differential Equations as a prerequisite. I'm taking a combined course in Linear Algebra and Differential Equations through a distant learning program which will satisfy the DE requirement, but since it must dedicate time to both LA and DE it doesn't cover as much DEs as a typical course in ODEs. I want to make sure I have all of the prerequisite knowledge before beginning the class so that I won't be completely lost, and I'm willing to self-study any gaps that I may have. </p>
<p>Intro to ODE topics: Separable equations, direction fields, first/second order equations, linear systems, laplace transforms, series solutions (power series, series solns around ordinary points, series solns around regular singular point, euler’s eqn, bessel’s eqn), existence/uniqueness theorems.</p>
<p>However, your PDE course will make use of a small fraction of that. With respect to ODE topics, I would guess that as long as you are comfortable solving equations of the form y’ + b*y = c(x) (this comes up in the PDE analog of separation of variables), you should be good to go for your intro to PDEs course.</p>
<p>@vanimelde Thanks for responding, it’s difficult to find information on university-level math classes on the internet, and those of whom are knowledgeable on the subject are few and far between 
My class covers most of those, but it doesn’t cover series solutions, although there is a chapter dedicated to those in our textbook, so I was planning on reading up on those regardless. Are series used extensively if at all for PDEs or will the knowledge only benefit me in solving ODEs? </p>