Ordinary Differential Equations I

Department: 
MATH
Course Number: 
6307
Hours - Lecture: 
3
Hours - Lab: 
0
Hours - Recitation: 
0
Hours - Total Credit: 
3
Typical Scheduling: 
Every fall semester

This sequence develops the qualitative theory for systems of ordinary differential equations. Topics include stability, Lyapunov functions, Floquet theory, attractors, invariant manifolds, bifurcation theory, normal forms. (1st of two courses)

Prerequisites: 

MATH 4541 and MATH 4542 or permission of the instructor

Course Text: 

No text

Topic Outline: 
  • General Properties Existence, uniqueness, continuous dependence, Liapunov functions, attractors, chain recurrence, Morse decomposition, Poincaré-Bendixson theorem
  • Linear Systems Stability and perturbations, periodic systems, nonhomogeneous systems, Fredholm alternative, Hamiltonian systems, mappings
  • Local Theory of Equilibria Hartman-Grobman theorem, stable and unstable manifolds, foliations, center manifolds, elementary bifurcations
  • Bifurcations Poincare-Andronov-Hopf bifurcation, behavior near a homoclinic