322 Ordinary Differential Equations

Course Number: 322
Description: MATH 322 is a course in ordinary differential equations (ODEs) drawing on the dynamical systems theory of flows in phase space and methods in functional analysis. For general flows, we study equilibria (e.g. fixed points, periodic orbits), attractive vs. stable equilibria (e.g. limit cycles), and sensitivity to initial conditions (e.g. Lyapunov exponents). For flows generated by linear ODEs, we investigate spectral vs. linear stability of equilibria, Floquet theory, and the Duhamel principle. For flows generated by nonlinear ODEs, we investigate linear vs. nonlinear stability of equilibria, Lyapunov methods, invariant manifolds, and bifurcation theory. Throughout, we explore three cases – planar, gradient, and Hamiltonian systems of ODEs–using phase space and time series plots in Mathematica.