Ordinary Differential Equations
The course will start with the theory of linear systems with constant coefficients, and then it will move on to nonlinear systems, including existence and uniqueness theorems, continuity of solutions with respect to parameters, stability of equilibria, Poincare-Bendixson theory, and periodic attractors. Applications to classical mechanics, circuit theory, and ecology will be examined.
Other topics covered will depend on the interests of the class and the instructor. Possibilities include the Sturm Liouville theory, and nonlinear dynamics, including the Stable Manifold Theorem.
Since numerical methods are covered in CAAM 452, they will not be
taught in this course. However students will be required to compute
and analyze solutions in order to gain a visual and geometric
understanding of the concepts. For this purpose they will have to use
ODE45 and PPLANE
in MATLAB, or other comparable routines.
Students who are unfamiliar with the computation of solutions of ODEs should read Ordinary Differential Equations using MATLAB, by John C. Polking
PPLANE. Look here for a
description of the newest features.
Homework 50%
Final exam 50%
The final exam will be a takehome exam.
All homework is due in class on the date announced. Each student will be allowed to have at most one late homework assignment during the semester. The one late homework will be accepted up to seven days after the due date, with or without excuse, and without penalty. No other late homeworks will be accepted even with an excuse. There will be absolutely no exceptions to these rules.
The homework is not pledged. You are encouraged to discuss the homework, and to work together on the problems. However each student is responsible for the final preparation of his or her own homework papers.