The theory of computation doesn't really have anything to do with math. It's based on logic, machines, automata, etc. You can use it for math but, in principal it has nothing to do with math. For example, the automata may not be calculating anything. It may be describing a process of doing something more abstract.

Solving DE in computation is an interesting point to make tho. I've seen analysis style arguments, like real analysis or calculus, in symbolic languages like lisp.

Actually, there's a really interesting set of papers very much related to this topic. Link below.

http://strictlypositive.org/calculus/