I'm writing a university essay on the wave equation, and I'm just looking for ideas as to what I could include. So far I have:
-Introduced the wave equation as a second-order, hyperbolic PDE, giving examples of it's physical applications.
-Derived the wave equation
-Solved the wave equation over a finite interval using seperation of variables and solved the equation over an infinite spectrum according to d'Alembert
-Talked about some properties of these solutions, including the domain of influence, the domain of dependece, and the conservation of energy.
I've also briefly mentioned d'Alembert, Daniel Bernoulli, Leonhard Euler and Joseph-Louis Lagrange, though I couldn't find much to write about. I'm almost at my word count now and could probably stretch what I've already written to be sufficient, I just wondered if anyone has any tips as to anything else I could include. Any help would be appreciated =D