519 - Ordinary Differential Equations
Prerequisites:
Math 319 and 340
Frequency:
Spring (II).
Student Body:
Math majors and students in the sciences and engineering
Credits:
3. (N-A) Recent Texts:
"Differential equations, Dynamical systems and an introduction to Chaos" by Hirsch, Smale and Devaney
Course Coordinator:
Sergey Bolotin. Background and Goals:
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 based on linear algebra, proof of basic existence theorems, stability theory, bifurcations and applications to mechanical and biological systems.
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.