(example below):
Modeling planetary motion, wave propagation, and quantum mechanics. differential equation course
This is often considered the "magic bullet" of the course. The Laplace Transform is a technique that converts a difficult calculus problem (differential equation) into a simpler algebra problem. It is the standard tool used in control systems engineering and signal processing. It allows students to handle discontinuous "forcing functions" (like a switch turning on and off) with ease. (example below): Modeling planetary motion