Università Roma Tre

1. General theory:
- Existence and uniqueness theorems (Gronwall's lemmas; Picard's theorem, Peano's theorem).
- Existence intervals and maximal solutions.
- Dependence on initial data and parameters.

2. Qualitative analysis of some simple EDO classes. Phase space.

3. Linear systems with constant coefficients. Exponential of matrices and Jordan's normal form theorem.

4. Linear systems with variable coefficients. Solution spaces. The Wronskian.

6. Periodic solutions and Fourier series.

7. Hamiltonian systems and celestial mechanics (introduction)

Gerald Teschl: Ordinary Differential Equations and Dynamical Systems , Graduate Studies in Mathematics Volume 140, American Mathematical Society, 2011

Shair Ahmad and Antonio Ambrosetti, Differential Equations. A first course on ODE and a brief introduction to PDE
Series: De Gruyter Textbook De Gruyter | 2019 DOI: https://doi.org/10.1515/9783110652864