Syllabus and course schedule
MATH 511, Spring 2008

The syllabus will consist of the material covered in class.
The list below describes what has been covered.

WEEK           TOPICS                   


Week 1: 
	Basic definitions, notation, examples, relevant issues, (history).
	Applications, phase space, flow. 
     	Examples.
	
Week 2:
	Fundamental existence and uniqueness result. Contraction mapping theorem.
	(Note that [Perko] does this, without much loss of generality, for a autonomous 
	systems only). 
	Maximal interval of existence. 
 
Week 3: 
	Dependence on initial data and parameters. (I used mostly notes from 
	Coddington & Levinson ``Theory of Ordinary Differential Equation"
	for this part). 
 
Week 4: 
	Linear systems: Linear algebra. Case of real diagonalizable systems. Examples.
	
Week 5:
	Linear systems: General theory. Case of complex eigenvalues. Examples.
	
Week 6: 
	Linear systems: Case of repeated eigenvalues. Normal forms. Stability. Examples.
	
Week 7:
	Nonhomogeneous linear systems. Fundamental matrix. 
	
Week 8:
	Linearization. 
	Exam 1.

Week 9:
	Spring break.
	
Week 10:
	 Invariant manifolds. Stability.
	
Week 11: 
	Stability and Lyapunov functions. 
	
Week 12: 
	Stable Manifold Theorem. Center manifold theory. 
	
Week 13: 
	Center manifold theory. Hartman-Grobman theorem.  

Week 14: 
	Introduction to dynamical systems. Limit sets, attractors.

Week 15: 
	Periodic orbits, and Cycles.

Week 16: 
	Poincare-Bendixson theory on the plane.