Math 588

Ordinary Differential Equations II

Schedule: Monday 9:00-11:00, Wednesday 9:00-10:00  Friday 14:00-15:00 (Place: M231)  

Content: Boundary Value Problems: Linear Differential Operators; Boundary Conditions; Existence of Solutions; Adjoint Problems; Eigenvalues and Eigenfunctions for Linear Differential Operators; Green’s Function of Linear Differential Operators. Nonlinear Periodic Systems: Poincare-Bendixon Theorem. Linearization Along Periodic Solutions;  Orbital Stability. Bifurcation: Bifurcation Fixed Points; The Saddle-Node Bifurcation; The Transcritical Bifurcation ; The Pitchfork Bifurcation; Hopf Bifurcation; Branching of Periodic Solutions for Non-autonomous Systems.

References:

1.   R. K. Miller, Ordinary Differential Equations.
2.   M. A. Naimark, Linear Differential Operators.
3.   S. Wiggins, Introduction to Applied Nonlinear Systems and Chaos.
4.   J.K. Hale, Ordinary Differential Equations.
5.   M. W. Hirsh and S. Smale, Differential Equations, Dynamical Systems, and Linear Algebra.