MATH 587 Ordinary Differential Equations I

Announcements

Course Outline

(4 weeks) Initial Value Problems: Existence and Uniqueness of Solutions; Continuation of Solutions; Continuous and Differential Dependence of Solutions.

(1 weeks) 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 weeks) Stable Manifold Theorem for Non-autonomous Systems.


Textbook and References

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. 

Grading

Examinations (50-60%)
Assignments (40-50%)