Student Body:
Math majors and students in the sciences and engineering.
Background and Goals:
Provides a rigorous introduction to ordinary differential equations and dynamical systems. Enroll Info: Intended for math majors and advanced (or graduate) students in other disciplines.
Alternatives:
Math 319 for a lower level introduction to Differential Equations
Subsequent Courses:
N/A
Course Content:
- 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.
credits:
3. (N-A)
semester:
Spring
prereqs:
(MATH 320, 340, 341 or 375) and (MATH 322, 376, 421 or 521) or graduate or professional standing or member of the Pre-Masters Mathematics (Visiting International) Program