Mathematics | University of Parma

Professor
Academic discipline: Fisica matematica (MAT/07)
Field: Formazione modellistico-applicativa
Type of training activity: Characterising

73 hours
of face-to-face activities

9 credits

hub: PARMA

course unit
in - - -

lectures timetable unavailable

exam calls

Learning objectives

The course is dedicated to an advanced study of classical analytical mechanics and, through the so called "group analysis", to the research of solutions to differential equations, mainly arising from Mathematical Physics.

Prerequisites

Knowledge of topics of mathematical courses of class L-35 (first degree)

Course unit content

Advanced Analytical Mechanics.
Lie transformation groups.
Similarity solution of partial differential systems.
Invariant Lagrangians and conserved vectors.
Elements of dimensional analysis.

Full programme

Elements of calculus of variations.
Variational principles of classical Mechanics.
Recall on differential geometry. Lie groups and Lie algebras. Symplectic matrices and Hamiltonian matrices.
Canonical transformations.
Poincaré-Cartan differential form. Lie condition. Poisson brackets.
Lie transformation groups.
Similarity solutions for ODE and PDE systems.
Lie-Bäcklund transformations. Equivalent transformations. Canonical form.
Conservation laws. Invariant Lagrangians. Noether's theorem.
Elements of dimensional analysis.

Bibliography

A.FASANO - S.MARMI, Meccanica Analitica, Bollati-Boringhieri.
P.J.OLVER, Applications of Lie groups to partial differential equations, Springer.
N.H.IBRAGIMOV, CRC handbook of Lie group analysis of differential equations, CRC Press.

Teaching methods

Hall lectures

Assessment methods and criteria

Oral examination

Other information

The course is held in the first semester.

MATHEMATICAL PHYSICS cod. 00421