I'm a PhD student in biology, and I'm trying to teach myself the necessary math to get into mathematical modeling of the phenomenon we study, because this is an area of inquiry that 1) I'd like to get into and 2) the lab I work for may like to get into, and it'd be on my shoulders to do it.
The phenomenon we study, among other things, has been modeled using delay differential equations and stochastic differential equations.
I have courses under my belt in differential/integral calculus and am teaching myself differential equations, and possess the requisite computational background. Multivariable calculus is next on my list. What else do I need to know to get to a level where I can adequately make use of DDEs and SDEs?