MATHEMATICAL PHYSICS
Learning outcomes of the course unit
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.
Course contents summary
Advanced Analytical Mechanics.
Lie transformation groups.
Similarity solution of partial differential systems.
Invariant Lagrangians and conserved vectors.
Elements of dimensional analysis.
Course contents
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.
Recommended readings
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 informations
The course is held in the first semester.
