cod. 14758

Academic year 2012/13
3° year of course - Second semester
Academic discipline
Analisi matematica (MAT/05)
Attività formative affini o integrative
Type of training activity
48 hours
of face-to-face activities
6 credits
hub: PARMA
course unit
in - - -

Learning objectives

The aim of the course is, on one hand, to provide wide supplements to subjects of Analytical Mechanics and, on the other, to tackle some problems connected with the classical equations commonly indicated as "Differential equations of Mathematical Physics" (potential equation, heat equation, wave equation, etc.)


Knowledge of classical Physics

Course unit content

Advanced Analytical Mechanics.
Expansion in orthogonal functions.
Boundary problems for second order linear ODE.
Sturm-Liouville problems.
Second order partial differential equations "of Mathematical Physics".

Full programme

Elements of calculus of variations,
Variational principles of classical Mechanics.
Canonical and completely canonical transformations.
Poincaré-Cartan differential form. Lie condition. Poisson brackets.
Infinitesimal canonical transformations.
Hamilton-Jacobi theory.
Expansion in series of orthogonal functions.
Boundary value problems for 2nd order ODE.
Sturm-Liouville problems, eigenvalues and eigenfunctions.
Non-homogeneous boundary value problems and Green's function.
Laplace and Poisson equations. Dirichlet and Neumann problems.
The heat equation.
The wave equation.
Cauchy problems.


A.Fasano - S.Marmi, Meccanica Analitica, Bollati-Boringhieri.
E.Persico, Introduzione alla Fisica Matematica, Zanichelli.
G.Spiga, Problemi matematici della Fisica e dell'Ingegneria, Pitagora.
A.N.Tichonov - A.A.Samarskii, Equazioni della Fisica Matematica, MIR.
F.G.Tricomi, Equazioni differenziali, Boringhieri.

Teaching methods

Hall lectures.

Assessment methods and criteria

Oral examination.

Other information

The course is held in the first semester.
The sector is MAT/07 and not MAT/05.