The course aim to provide some introductory notions on ordinary differential equations.

In particular, after a review on prerequisites concerning linear ordinary differential equations with constant coefficients, some further complements are provided.

The course is organised in five two hours lectures:

Part 1: 

• Linear Ordinary differential equations with constant coefficients;
• Solution  via series expansion method 
• Frobenius method to solve linear ordinary differential equations with continuous coefficients.
• Bessel Equation and other well known ordinary differential equations of mathematical physics

Part 2:

• Perturbation methods to solve differential equations in which a small perimeter appear (small means positive and much smaller than 1)
• Qualitative analysis: Conservative versus dissipative systems
• Straightforward perturbation method
• Multiple scale method
• Boundary value problems and boundary layers

Part 3:

• linear partial differential equations: equazione delle onde del I ordine
• equazione del calore
• equazione delle onde del II ordine
• Equazione di Laplace
• Metodo di soluzione per "separazione delle variabili".