why are you thinking about taking it? did someone recommend it? could you ask them why? you need to talk to the people who are aware of yiour needs for your program.i know people in economics doctoral programs who used some elementary concepts from functional analysis. but the subject is basically infinite dimensional differential and integral calculus.
since differential calculus is about approximating non linear functions by linear ones, a necessary preliminary part of functional calculus is infinite dimensional linear algebra.
it also involves integral operators with functional "kernels". i.e. it is calculus on spaces whose "points" are functions. e.g. a basic problem is to examine curves on a given surface and determine the shortest ones.
i do not know if infinite dimensionsl analysis is really used in derivatives trading. but if you can handle func analysis, you might be good at derivatives trading. isn't that a rather speculative and unpredictable pursuit?
'