Math Help - How deep is the rabbit hole: Calculus, DEQ, Linear Algebra?

I've taken calculus (Differential, Antiderivative, Multivar), DEQ, and Linear Algebra at the intro level as a requirement for my electrical engineering BS. I was wondering if there are math concepts that underlie the theorems found in these courses. Do these concepts draw from other branches of mathematics or are these concepts as complete as they can be?

I'm not sure what you are asking. Obviously they "draw" on arithmetic and algebra.

Sorry, I'm having a difficult time phrasing my question so that it is specific and allow for a non-exhaustive reply.

According to wikipedia, mathematics studies quantity, structure, space, and change. Do these categories overlap (i.e., are there theorems in a category that might reference a theorem from another category)? Are there such theorems in calculus?