MA 649 Intermediate Differential Equations
Theory and application of ordinary differential equations (ODEs) with an emphasis on ODEs as continuous dynamical systems on a finite-dimensional phase space. Standard topics include existence and uniqueness theorems, general theory for linear equations, the exponential of linear map, stability of equilibrium points, hyperbolicity and structural stability, Lyapunov’s method, invariant manifolds, Floquet theory for periodic orbits, and Poincare-Bendixon theorem. Corequisite: MA 547