MATHEMATICAL PHYSICS
cod. 00421

Academic year 2010/11
1° year of course - Second semester
Professor
Gian Luca CARAFFINI
Academic discipline
Fisica matematica (MAT/07)
Field
Formazione modellistico-applicativa
Type of training activity
Characterising
72 hours
of face-to-face activities
9 credits
hub:
course unit
in - - -

Learning objectives

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.

Prerequisites

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Course unit content

Advanced classical analytical mechanics. Application of Lie group theory to the solution of problems of physical-mathematical interest.

Full programme

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.

Bibliography

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.

Teaching methods

Frontal lectures.

Assessment methods and criteria

Oral examination.

Other information

In 2010-11 the course has been carried out in the first half-year

2030 agenda goals for sustainable development

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