1) Differential Equations of first order

(linear, separable, exact, applications)

2) Theorem of Existence and Uniqueness of solution: Picard Theorem

3) Linear systems of differential equations and Phase portraits;

(general solution, equilibria, Lyapunov stability).

4) Differential equations of second order. General Methods.

Qualitative Theory of Differential Equations

(Poincaré-Bendixson Theorem on the plane, Hartman-Grobman Theorem, Fenichel Theory)

5)  Calculus of Variations and Dynamical Optimization

 (Euler Lagrange equation, Pontryagin maximum principle).

6) Test 1. 

Syllabus - Part II - Weeks 7 to 12