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 Phisics (potential equation, heat equation, wave equation, etc.).
Course contents summary
Advanced Analytical Mechanics.
Boundary problems for 2-nd order linear ODE.
PDE "of Mathematical Physics"
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.
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.
Assessment methods and criteria
The course is held in the first semester