MATH 640 and MATH 641. Ordinary Differential Equations I and II. (3), (3) This two-semester course is taken by many engineering, mathematics, and science majors. Topics include a brief review of the material from the introductory ODE course, first and second order equations and applications, existence and uniqueness theorems, oscillation theorems, series solutions, Sturm-Liouville problems, special function, Laplace transformations, linear and non-linear systems, stability via first and second Liapunov's method, and asymptotoic methods. Applications are made to many areas, including biology, populations dynamics, electric circuits, physics, and engineering. Elements of Hamiltonian mechanics including the Hamilton-Jacobi method are studied.