Key differential equation topics for physics theories

[kent davidge]

Can someone list to me (and whoever is going to view this thread) what topics in differential equations should be studied so that we can have a decent knowledge of the general physical theories in which they occur? (And I believe, they appear in all theories.)

So far, I believe the two most important for physics due to their occurrences in electroagnetism and quantum physics is

- Fourier analysis/ Fourier transform to solve diff equations

- Green's functions

Am I right that they are the two most important?

 

[jedishrfu]

There’s also partial differential equations and boundary value problems Which pops up in many areas of physics

 

[Gaussian97]

Exact, and the Sturm-Liouvilles problem