# SUPPLEMENT TO MATHEMATICAL PHYSICS

## Learning outcomes of the course unit

The course, of an interdisciplinary nature within a mathematics context, aims among other things to provide methods useful to the search for exact solutions of differential and integrodifferential equation systems, often related to problems of physical-mathematical interest.

## Course contents summary

Review of differential geometry. Lie groups. Lie algebras. Lie algebra of a Lie group. Lie group acting on a variety. Lie groups of transformations. Similarity solutions for a system of partial differential equations (PDE). Invariant varieties. Extension theory. The main symmetry group of a PDE system. Elements of dimensional analysis. The "pi" theorem. Applications to problems of physical-mathematical interest. Lie-Backlund transformations. The symmetry group of the Boltzmann equation.

## Recommended readings

G.W.BLUMAN - J.D.COLE, Similarity methods for differential equations, Springer.

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.