I finished a bachelors in computer science a year ago and now work full-time. I completed calculus I/II, linear algebra, and numerical computing in undergrad and also wrote a brief term paper on numerical computations for PDEs (but only from the computational side). I want to apply to graduate schools for mathematical sciences in the coming year and I have an opportunity to do physics/math related research with a professor from my alma mater. The nature of the research is mathematically intensive and requires knowledge of partial differential equations. My question is this: Regarding this type of research, is it possible to proceed with my background while referring to textbooks as appropriate or is the nature of PDEs such that I would need to first take a sequence of courses such as ODE, functional analysis, and finally a course in PDE before I could even start this sort of research? I took the approach of referring to texts when I wrote my undergrad term paper but, again, that was purely from the computational perspective and not from the mathematical side of PDEs so perhaps more accessible.