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.).
Prerequisites
- - -
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.
Bibliography
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
