DIFFERENTIAL EQUATIONS
Learning outcomes of the course unit
To provide basic instruments for the qualitative study or the integration of ordinary differential equations or sistems of differential equations.
Prerequisites
Calcolo I
Calcolo II
Calcolo III
Course contents summary
Mathematical models of O.D.E.
Elementary integrations.
Qualitative theory. Lipschitz condition. Local existence and unicity theorem. Regularity of the solutions. Global existence theorems. Comparison theorem. Monotonicity theorem.
Linear systems. Exponential matrix. Systems with constant coefficients. Wronskian matrix. Equations with constant coefficients. Euler's equations.
Integration by series. Hermite's equations. Bessel's equations. Periodic solutions.
Liapunov's stability. The 2-dimensional case.
Boundary value problems. The variable separation method for P.D.E.
Numerical integration.
Recommended readings
1) Pagani-Salsa, " Analisi Matematica II" , ed. Masson
2) Salsa-Squellati, " Equazioni Differenziali Ordinarie", ed. Masson
3) Conti, "Calcolo", McGraw-Hill.
4) Appunti del docente reperibili al centro fotocopie del Dip. Fisica
