- #1
Ash L
- 19
- 0
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.
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.