cod. 14758

Academic year 2011/12
3° year of course - Second semester
Academic discipline
Fisica matematica (MAT/07)
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 Phisics (potential equation, heat equation, wave equation, etc.).


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Course unit content

Advanced Analytical Mechanics.
Fourier series.
Boundary problems for 2-nd order linear ODE.
PDE "of Mathematical Physics"

Full programme

Elements of calculus of variations.
Variational principles of classical Mechanics.
Symplectic matrices and Hamiltonian matrices. Canonical transformations.
Poincaré-Cartan differential form. Lie condition. Poisson brackets.
Hamilton-Jacobi theory.
Fourier series.
Boundary value problems for 2nd order linear 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. Boundary value problems.


A.FASANO - S.MARMI, Meccanica Analitica, Bollati-Boringhieri, Torino.
E.PERSICO, Introduzione alla Fisica Matematica, Zanichelli, Bologna.
G.SPIGA, Problemi matematici della Fisica e dellk'Ingegneria, Pitagora, Bologna.
A.N.TICHONOV - A.A.SAMARSKIJ, Equazioni della Fisica Matematica, MIR, Moskow.
F.G.TRICOMI, Equazioni differenziali, Boringhieri, Torino.

Teaching methods

Hall lectures

Assessment methods and criteria

Oral examination

Other information

The course is held in the first semester