Application or Theoretical Differential Equations?

[PhotonSSBM]

There are two courses I can take for a Differential Equations class at my school. One is for Engineering students and is described this way (I'm a physics major fyi):

This course presents an introduction to the theory of differential equations from an applied perspective. Topics include linear and nonlinear ordinary differential equations, Laplace transform, and introduction to partial differential equations.

The theoretical version is for math majors and is described this way:

This course covers methods of solving ordinary differential equations which are frequently encountered in applications. General methods will be taught for single n-th order equations, and systems of first order linear equations. An introduction will be given to the qualitative theory of first-order nonlinear systems. This will include phase plane methods and stability analysis. Computer experimentation may be used to illustrate the behavior of solutions of various equations.

Which would you say is more ideal for a Physics major? Note I plan on taking a course on PDE's or a Mathematical Methods course.

 

[S.G. Janssens]

The two descriptions have some overlap. Of course I'm biased, but I think I would go for the theoretical version, because it seems actually quite application driven and, very important in my opinion, spends some time on introducing students to the modern, qualitative study of nonlinear systems. This is useful and can be very motivating.

I would not care too much about whether or not an ODE course contains an introduction to PDE. It is better to just take a proper PDE course afterwards, which you already seem to be considering.