INTRODUCTION TO MATHEMATICAL PHYSICS
LEARNING OUTCOMES OF THE COURSE UNIT
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 CONTENTS SUMMARY
Advanced Analytical Mechanics.
Expansion in orthogonal functions.
Boundary problems for second order linear ODE.
Second order partial differential equations "of Mathematical Physics".
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.
ASSESSMENT METHODS AND CRITERIA
The course is held in the first semester.
The sector is MAT/07 and not MAT/05.
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.
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.