Ideally, a theory based on which engineers built something, but not the other way around, i.e. when something exists and some theorists are trying to build a de facto model of it. Edit: a theory that involves infinities.
Spot the contradiction in this sentence. Even if I would like to argue with you on unedefined problem you have, I can't satisfy your requirements when they're contradictory.
I see PDE's in TCP papers, I don't know what's your problem.
Of course I expect you will dismiss that as too "astral" of an example, but ask Vint Cerf if he did not need any calculus. And then ask him (or Lloyd Wood) again about his new suite of protocols designed for guaranteed connectivity in spite of enormous latencies in orbital and interplanetary internet (with cisco routers with PDE-optimized buffer sizes orbiting already on several satellites).