Is differential equation required to study real analysis?

[woundedtiger4]

Hi all,
Is differential equation a prerequisite to study real analysis (in context of baby Rudin)? And does it have any use in measure theory or Stochastic Calculus?
Thanks in advance.

 

[xaos]

i'm not sure, but i suppose you can connect these by way of distributions in functional analysis as solutions to stochastic dynamical systems especially diffusions. the idea of a distribution comes out of lebesgue integration in real analysis and depends on the idea that you can integrate up to sets of measure zero removed from the domain. this makes it a little easier to solve dynamical systems where continuity becomes an issue.

 

[HallsofIvy]

But "distributions" and "stochastic dynamical systems" are not likely to show up in a first semester class in analysis! No, I would not consider differential equations a prerequisite for real analysis.

 

[AlephZero]

Arguably it is the other way round, if the ODE course is focused on the math (existence and uniqueness of solutions, etc) rather than being a cookbook of recipes for solving particular types of ODEs.