ORDINARY DIFFERENTIAL EQUATIONS I-22M:213
FALL SEMESTER 2007
Instructor: Laurent O. Jay, 225L MLH, ljay@math.uiowa.edu
Time & Location: 2:30-3:20 MWF in 214 MLH.
Prerequisites: 22M:142 or equivalent or consent of instructor.
This course is a natural continuation of 22M:142 (nonlinear
dynamics with numerical methods).
Though the course is mostly about the theory of ordinary
differential equations (ODEs), we will consider this
theory in conjunction with some theoretical and practical
aspects of numerical methods for ODEs.
Textbook:
Introduction to Applied Nonlinear Dynamical Systems and Chaos by
Stephen Wiggins,
Springer, Series: Texts in Applied Mathematics, Vol. 2, 2nd edition,
2003, 808 pages, Hardcover, ISBN: 978-0387001777, list price: $99.00.
Table
of contents.
The book on amazon.com.
Course topics:
- Lyapunov-stability
- Differential inequalities
- Variational calculus
- Lagrange's and Hamilton's mechanics
- Noether's theorem
- Poisson systems
- Variational/symplectic integrators
- Divergence free ODEs (Poincare recurrence theorem)
- Reversible systems
- KAM (Kolmogorov-Arnold-Moser) theory
- Invariant (stable, unstable, center) manifolds
- Normal forms
- Structural stability
- Perturbations
- Averaging
- Bifurcations
- Homoclinic orbits
- Melnikov's method
- Boundary value problems (Sturm-Liouville systems)
- etc.
If you have a high interest in a specific topic related to ODEs,
please let me know. If a majority of students taking the class
is interested in the topic then I may cover it probably during
the second semester.
If you have any question about the course, please contact me.