MATH 587 Ordinary Differential
Equations I (Fall 2012)
Schedule: Monday 13:40-15:30 | Wednesday 10:40-12:30 (M-215)
(4 weeks) Initial Value
Problems: Existence and Uniqueness of Solutions; Continuation of
Solutions; Continuous and Differential Dependence of Solutions.
(1
week) Systems: Restating the theorems from scalar case
(3
weeks) Linear Systems: Linear Homogeneous and Non-homogeneous Systems
with Constant and Variable Coefficients; Structure of Solutions of
Systems with Constant and Periodic Coefficients; Higher Order Linear
Differential Equations.
(2 weeks) Sturmian Theory.
(3
weeks) Stability: Lyapunov Stability and Instability. Lyapunov
Functions; Lyapunov's Second Method; Linearization; Quasilinear
Systems.
(1 week) Stable Manifold Theorem for Non-autonomous
Systems.
R. K. Miller:
Ordinary Differential Equations.
J. Cronin: Differential
Equations: Introduction and Qualitative Theory.
J.K. Hale:
Ordinary Differential Equations.
C. Corduneanu: Introduction to
Differential Equations and Integral Equations.
E.
A. Coddington,
N. Levinson:
Theory
of differential equations.
Examinations
(50-70%)
Assignments (50-30%)