Optimization methods in economics (MASTER)

Introduction to mathematical concepts and methods needed to pursue economic analysis, in particular, to optimization methods.

1. Dynamic programming
2. Functions of several variables, continuity, limit, partial derivatives
3. Differential, Taylor's formula
4. Implicit functions, linearization, log-linearization
5. Gradient, extrema, convexity, quadratic forms
6. Constrained extrema, Lagrange method, envelope theorem, Kuhn-Tucker conditions
7. Vector spaces, linear mappings, eigenvectors, matrix decompositions
8. Differential equations, systems of linear differential equations, stability
9. Difference equations, systems of linear difference equations, stability
10. Probability, random variables, moments, limit theorems, random vectors