I'm not sure what the HN crowd finds useful as a group, but I personally use a couple of different techniques in my work (geophysics). One of them is finite difference and finite element methods. I have a book called 'Introduction to Numerical Geodynamic Modeling' by Teras Gerya that teaches finite difference modeling of plate tectonic phenomena, particularly of 2nd order differential equations (Poisson equation and variants) that are useful in modeling heat flow, diffusion and so forth through space and time. It's a great book but written for a specialized audience. I've used finite element models a lot, and the occasional boundary element method, but never written any.

I also use Green's functions, which are equations that describe the response of a medium to an impulse (think the propagation of sound waves from a source, though I do different stuff), by using convolution.

But I think jofer is the only other geophysicist on HN so we're probably not representative. Nonetheless, a lot of HNers have a physics, classical engineering or chemistry background and use similar tools... just not to find out what happened tens of millions of years ago.