MATHEMATICAL PHYSICS 2
Learning outcomes of the course unit
The course, of an interdisciplinary nature within a mathematical context, aims among other things to deal with elements of Analytical Mechanics from an advanced point of view, and to provide methods useful to the search for exact solutions of differential equation systems, often related to problems of physical-mathematical interest.
Course contents summary
Advanced classical analytical mechanics. Application of Lie group theory to the solution of problems of physical-mathematical interest.
Elements of calculus of variations. Variational principles of classical mechanics. Review of differential geometry. Lie groups. Lie algebras. Lie algebra of a Lie group. Symplectic matrices and Hamiltonian matrices. Canonical transformations. Hamilton-Jacobi theory. Lie groups of transformations. Similarity solutions for a system of partial differential equations (PDE). Invariant manifolds. Extension theory. The main symmetry group of a PDE system. Elements of dimensional analysis; the "pi" theorem. Application to problems of physical-mathematical interest.
A.Fasano-S.Marmi, Meccanica analitica, Bollati-Boringhieri.
P.J.Olver, Applications of Lie groups to partial differential equations, Springer.
N.H.Ibragimov (ed.), CRC handbook of Lie group analysis of differential equations, CRC Press.
Assessment methods and criteria
In 2010-11 the course has been carried out in the first half-year