How useful is nonlinear ODE (stability, periodic solutions, etc)?

[PieceOfPi]

Hi,

I have a choice of taking this advanced ODE course, and I am wondering if this is worth studying. The course will cover mainly chapter 9 of Boyce/DiPrima textbook after we cover existence and uniqueness theorem. Chapter 9 is called "Nonlinear Differential Equations", and covers topics like stability and phase plane, autonomous systems and stability, almost linear systems, Liapunov's second method, periodic solutions and limit cycles, and a little bit on chaos theory. I wonder where I see these kind of topics (physics? engineering?). The course does sound fairly interesting, though.

Thanks

 

[PieceOfPi]

Any help on this would be appreciated.

 

[f95toli]

It would probably not be very useful (although it might still be interesting) for "practical" problems; mainly because most real world problems need to be solved using numerical methods.
"Paper and pen" methods for ODE/PDEs are not nearly as important today as they used to be, mainly because there are only a few "real" problems can actually be solved or even analyzed using analytical problems.
Hence, given a choice between this course and e.g. a course in FEM I would choose the latter; at least if "usefulness" was the most important criteria.

 

[PieceOfPi]

Thanks for your reply,

I'm currently a sophomore math major, and I'm planning to take a fair amount of both applied and pure math courses. While this course is one of my options, there are a few draw backs for this course:

1) This is a stand alone course, so I can take this course later if I wanted to.
2) As far as I know, there is no course that list this course as a pre-requisite, even in physics department.
3) The chaos part was something that interested to me the most, but there's actually another course that deals with that topic called "Discrete Dynamical Systems".

So I was hoping this course to have more applications, and potentially useful in area outside of mathematics, but it may not be. Of course, usefulness is not the only criteria, but I think there are other course that I should consider taking.

Any other advice would be appreciated.