I'm trying to decide between taking an ODE class or a PDE class next. I have already done Calculus 1,2,3 so I already know some ODEs and PDEs and linear algebra. I'm a 3rd year mathematics major with a minor in Statistics and I'm interested in applied mathematics. ODE course coverage: Ordinary Differential Equations Existence, uniqueness, and stability; the geometry of phase space; linear systems and hyperbolicity; maps and diffeomorphisms. Chaotic Dynamics and Bifurcation Theory Hyperbolic structure and chaos; center manifolds; bifurcation theory; and the Feigenbaum and Ruelle-Takens cascades to strange attractors. Poincare-Bendixson theory. PDE course coverage: Method of characteristics, understanding derivations of canonical PDEs. Wave, heat, and potential equations. Fourier series; Solve boundary value problems for heat and wave equations; Fourier transform; Lapace's equation; generalized functions; and numerical methods for approximating solutions of 2nd order PDEs. I know that the difficulty of a course is loosely related to the course material. So I was wondering which of them would be harder? Which one of them would be more educational (i.e. I would learn more out of it)? And which one would be more fun in your opinion? Thanks.