Take any serious book on modeling bus and routing infrastructure (and not vocational guide on using protocols designed by someone else) and you will see plenty of partial differential equations.
Edit: a theory that involves infinities.
Edit: I'd like to warn you though, that because I'm more or less familiar with the subject, I think it will be very difficult to find what I'm asking for.
Cool. Rather than posted challenges, how about educating us to why we are wrong. If you know this area well I'd be interested to learn more.
The engineers who designed these systems all made frequent use of the notion of infinity
and I'm yet to see the proof.
The engineers who designed these systems all made frequent use of the notion of infinity, particularly in their use of limits and calculus.
Do you disbelieve that engineers make frequent use of limits and calculus?
Do you disbelieve that notions of limit, derivative, and integral are contingent on the idea of infinity?
Why should anyone answer your questions while you continue to ignore mine?
Although in some narrow areas I've seen non-trivial calculus, but I barely remember anything that involves infinities and is significant for the solution.
Now you seem to be saying: "I have never, myself, seen the concept of infinity used to solve a problem in a way I deem significant. Therefore, infinity does not exist and is not useful to anybody."
If I said the same thing about the number 65536, would it force you to program only 8-bit processors for the rest of your life?
Based on some of your earlier statements, I'm going to guess that we're using different definitions of the word "infinity." I'd guess that to you, the word "infinity" means something like "the largest possible number, denoted ∞." I'd also guess that, in your claim about calculus above, you mean something like "I have never seen a calculus problem whose solution required you to write down an ∞." Am I right?
Since the MRI machine only samples the signal coming in it uses a DFT, but that doesn't negate the fact that the theory of Fourier Transforms involves the notion of infinity and that engineers used that body of mathematics to build a real machine.
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).
Why didn't he just ask about discrete mathematics, then?
Asymptotic analysis of the computational complexity of algorithms.