Selected topics on mathematical analysis ES3A100002

Course content:
Systems of ordinary differential equations
Existence and uniqueness of solutions
Systems of linear equations
Stability of linear systems
Vector fields on R^n
Lie bracket of vector fields
Involutive and integrable distributions
Banach and Hilbert spaces
Problems of calculus of variations
Euler-Lagrange equations
Examples of problems of calculus of variations

Learning outcomes:
Ability to solve linear systems and to check its stability. Ability to check involutivity of distributions. Knowledge of notions of Banach space and Hilbert space. Ability to create Euler-Lagrange equations.