Upper-Div ODEs for Physics Majors: A Comprehensive Overview

[proton]

how much DEs do physics majors need to know to handle upper-div physics? I'm thinking of taking this upper-div ODEs class:
"Laplace transforms, existence and uniqueness theorems, Fourier series, separation of variable solutions to partial differential equations, Sturm-Liouville theory, calculus of variations, two point boundary value problems, Green's functions. "

but I already covered laplace transforms, Fourier series, and covered very slightly separation of variables in my lower-div DEs class. I just transferred to this school, so I heard this stuff is new for most people (it is trimester, my DEs class was semester system) Would this class be a waste of time for me? So the rest of the stuff like green's functions, sturm-liouville theory, etc are unnecessary for physics, right?

I would rather take a pure math class than this, unless this class proves tremendously helpful for my physics classes.

 

[marcusl]

So the rest of the stuff like green's functions, sturm-liouville theory, etc are unnecessary for physics, right?

Sorry, not at all true. Sturm-Liouville theory is intimately connected with eigenfunctions. Green's functions are analogous to the impulse response of electrical engineering, and are just as crucial to physics problems as impulse responses are to EE problems. One course in ODE and one in PDE is standard for upper level physics.

Can't advise you as to taking ODE from math vs physics departments. In theory both should prepare you well.

 

[Dr Transport]

Any course in applied DE's (applied means not theorem-proof/existance and uniquess etc...) will be helpful in advanced physics courses. You'll use green's functions in E&M, QM & many-body theory as a short list. The more exposure you have the better.

 

[leon1127]

you should take that upper level DE class because all you will learn in that class will eventually apply in physics. After all, a system of DEs (ODE, PDE, SDE) are what is behind physics. E&M, classical mechanic, quantum mechanic, etc are merely study of PDEs. Existence and uniqueness proof of linear ODE is very instructive in a sense that one can actually use it to generate a numerical method to compute the solution (not efficient).

 

[Chris Hillman]

proton, why not ask the professor who will be teaching the course you are asking about? (If you don't know who that is, ask in our Math Department office.) It's likely that this will result in accurate information tailored to your situation, rather than the kind of general comment which we can offer here.