Seeing as no one else is responding, I will give it a whack. I don't think many (if any) people on a maths forum know about engineering. You may have better luck asking engineers and asking specific maths questions here.

Calculus has many applications in physics that I know of. Newtons laws, Schrodinger equation etc. all involve some sort of a differential equation.

Best place to start (as with any research) is google and wikipedia. Don't ever reference wikipedia but the idea is to get a basic understanding, and to check out their references. Try to get hold of a university level engineering book of some sort and look at what they do.

Good luck.