Academic Catalog

MATH588 ORDINARY DIFFERENTIAL EQUATIONS II

Course Code: 2360588
METU Credit (Theoretical-Laboratory hours/week): 3(3-0)
ECTS Credit: 8.0
Department: Mathematics
Language of Instruction: English
Level of Study: Graduate
Course Coordinator: Prof.Dr. AACIK ZAFER
Offered Semester: Fall Semesters.

Course Content

Nonlinear Periodic Systems: Limit Sets; Poincare-Bendixon Theorem. Linearization Near Periodic Orbits; Method of Small Parameters in Noncritical Case; Orbital stability. Bifurcation: Bifurcation of Fixed Points; The Saddle-Node Bifurcation; The Transcritical Bifurcation; The Pitchfork Bifurcation; Hopf Bifurcation; Branching of Periodic Solutions for Nonautonomous Systems. Boundary Value Problems: Linear Differential Operators; Boundary Conditions; Existence of Solutions of BVPs; Adjoint Problems; Eigenvalues and Eigenfunctions for Linear Differential Operators; Green's Function of a Linear Differential Operator.