Introduction to Mathematical Physics

Prof. Boris Dubrovin


  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.