INTRODUCTION TO MATHEMATICAL PHYSICS
Learning outcomes of the course unit
The course aims to deal with advanced analytical mechanics, and moreover with problems connected to classical partial differential equations usually denoted as "equations of Mathematical Physics" (potential equation, heat equation, wave equation).
Course contents summary
Advanced analytical mechanics. Fourier series. Boundary problems for second order linear differential equations. Sturm-Liouville problems.
Partial differential equations "of Mathematical Physics"
Elements of calculus of variations. Variational principles of classical mechanics. Canonical transformations. Hamilton-Jacobi theory. Fourier series. Sturm-Liouville problems, eigenvalues and eigenfunctions. Non-homogeneous boundary problems and Green's function. Laplace and Poisson equations. Dirichlet and Neumann problems. Heat equation. Wave equation. Cauchy problems. Boundary problems.
E.Persico, Introduzione a alla Fisica Matematica, Zanichelli.
G.Spiga, Problemi matematici della Fisica e dell'Ingegneria, Pitagora.
A.N.Tichonov-A.A.Samarskij,Equazioni Equazioni della Fisica Matematica, MIR.
F.G.Tricomi, Equazioni differenziali, Boringhieri
Assessment methods and criteria
The course is addressed to 3rd year students, has 4 CFU and belongs to sector MAT07.