Università Roma Tre

1. Phenomenology, models. Examples.

2. Some exactly solvable ODE (Ordinary Differential Equations) classes (equations with separable variables, homogeneous equations, Bernoulli equation, Clairaut equation, exact differential equations, equations with constant coefficients, Hamiltonian equations with one degree of freedom)

3. 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.

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

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

6. Linear systems with variable coefficients. Solution spaces. The Wronskian. The periodic cae (Floquet Theory).

7. Periodic solutions and Fourier series.

8. Power series.

9. Stability.

10. Boundary problems for second order equations.

[AA] 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

[S] Schaum's Outline of Differential Equations, 4th Edition 4th Edition 0071824855 · 9780071824859