Theory of ODE

[theFuture]

So there's a new class being taught in our department next semester on the theory of ODEs. I took an intro class to ODEs and I think it would be interesting to go into more depth on the subject. Thing is I'm worried that if I take it I'll be doing uniqueness and existence theorems all semester; something I don't want to do. My question to you is: what is there to study in the theory of ODEs?

[ReyChiquito]

Stability of solutions, autonomous systems, conservative systems, etc. Perturbation method, qualitative solutions, bifurcations, etc.

[NeutronStar]

With all due respect I don't know why you are asking us? Why not contact the professor of that course and ask for a sylalbus? Then you would know precisely what that particular instructor intends to cover. Or better yet, visit with the instructor in person, or over the phone if at all possible.

[Mk]

What are ODEs?

[gazzo]

... Ordinary Differential Equation.

unlike PDE (Partial Differential Equation)