Mathematical Physics Sector

This page is obsolete. The former Sector of Mathematical Physics is now part of the Mathematics Area.

SISSA — International School for Advanced Studies Phonebook Webmail Library catalogue

Via Bonomea 265 — 34136 Trieste — Italy 45.679538°N, 13.774999°E

Introduction to Mathematical Physics

Prof. Boris Dubrovin

Contents:

1. Fundamental equations in Mathematical Physics. Oscillator, Helmholtz, heat, Laplace and Poisson equations. Classification of second order partial differential equations
2. Boundary problems for linear second order partial differential equations. The Cauchy problem. Cauchy-Kowalevskaya theorem. Boundary problem for elliptic equations. Well-posed problems.
3. Banach and Hilbert spaces. L2 and C spaces. Selfadjoint operators.
4. Separation of variables for wave, Laplace and Poisson equations
5. The spectrum of the Sturm-Liouville operator. Particular cases and classic orthogonal polynomials (connection with random matrices). Spherical functions.
6. Elements of nonlinear equations theory. Hopf and Kortweg-de Vries equations.

Bibliography:

• A. Tikhonov, A. Samarskij, Equazioni della fisica matematica (Edizioni MIR, 1977)
• R. Courant, D. Hilbert, Methods of Mathematical Physics (New York Intersci. Publ., 1989)