INTRODUCTION TO MATHEMATICAL PHYSICS
Learning outcomes of the course unit
The aim of the course is, on the one hand, to provide some supplements to the
Analytical Mechanics course 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.).
Course contents summary
Elements of calculus of variations.
Variational principles of classical Mechanics.
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.
E.PERSICO, Introduzione alla Fisica Matematica, Zanichelli, Bologna.
G.SPIGA, Problemi matematici della Fisica e dell'Ingegneria, Pitagora, Bologna.
A.N.TICHONOV - A.A.SAMARSKIJ, Equazioni della Fisica Matematica, MIR, Mosca.
F.G.TRICOMI, Equazioni differenziali, Boringhieri, Torino