Ordinary Differential Equations

12 units · Graduate

Intermittent: 12 units Basic concepts covered are existence and uniqueness of solutions, continuation of solutions, continuous dependence, and stability. For autonomous systems, topics included are: orbits, limit sets, Liapunov's direct method, and Poincar-Bendixson theory. For linear systems, topics included are: fundamental solutions, variation of constants, stability, matrix exponential solutions, and saddle points. Time permitting, one or more of the following topics will be covered: differential inequalities, boundary-value problems and Sturm-Liouville theory, Floquet theory. (Three 50 minute lectures) Prerequisites: ( 21-455 Min. grade B or 21-235 Min. grade B or 21-355 Min. grade B) and ( 21-373 Min. grade B or 21-237 Min. grade B)