Math majors and students in the sciences and engineering.

Math 519 is a rigorous self contained introduction to ordinary differential equations intended for undergraduate math majors and advanced or graduate students from economics, engineering and physics. Topics will include theory of linear systems \[ \frac{dx}{dt} = Ax(t) + f(t) \] based on linear algebra, proofs of basic existence theorems for nonlinear systems of differential equations

\[ \frac{dx}{dt} = F(t, x(t)) \] as well as stability theory, bifurcations and applications to mechanical and biological systems.

Math 319 for a lower level introduction to Differential Equations

N/A

- Systems of differential equations
- Stability for linear systems. Fundamental matrix, periodic systems and Floquet theory.
- Continuity and differentiability of solutions in initial conditions.
- Flow of differential equations.
- Qualitative behavior of nonlinear systems. Stability and Liapunov functions.
- Periodic orbits, Poincare maps, attractors and Poincare-Bendixon Theorem.
- Bifurcation for equilibria and periodic orbits (time permits).
- Applications to Classical Mechanics and biological systems.