Syllabus - Part I - Weeks 1 to 6

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. Partial Differential Equations.

5) Qualitative Theory of Differential Equations
(Poincaré-Bendixson Theorem on the plane, Hartman-Grobman Theorem, Fenichel Theory)

Calculus of Variations and Optimal Control. 

6) Test 1.

Syllabus - Part II - Weeks 7 to 12
 
7) Review on stochastic processes

8) The Wiener process

9) Diffusion processes and Stochastic integrals

10) Stochastic differential equations