DEs in general are something that I find very interesting. Though my knowledge of DEs are very rudimentary to say the least, I find them fascinating. In particular, I want to learn about PDEs and obtain a deeper understanding for ODEs. My question is, then, what kind of math preparation would I need before attempting to tackle PDEs? Currently, I'm trying to at least obtain a basic understanding Analysis (reading some Spivak as well as other things to get my proof skills up). I've also got a basic understanding of Linear Algebra. How far in advanced mathematics must I be to truly be ready for PDEs? Must I have completed most of the Math 'staples' (Abstract algebra, Topology, analysis) before tackling PDEs?