To introduce the basic equations of mathematical physics and the main tools for their solution. The basic knowledge of the theory will be provided as well as the applications of developed techniques to different problems. Only analytical methods will be considered, not numerical methods.
|Partial differential equation of mathematical physics and an introduction to their study. Classification of second order PDE's in two independent variables. Derivation of the wave, Laplace and Poisson equations. Change of variables in differential expressions, method of separation of variables, method of characteristics.||6|
|Orthogonal series of functions. Introduction to Fourier series theory. Half-range Fourier series. Fourier series on an arbitrary interval. Periodic continuation. Problem of convergence. Dirichlet theorem. Minimal property of partial sums. Parseval's identity. Fourier series in complex form. Fourier series of several variables. Integration and differentiation of Fourier series. Application of Fourier series to boundary value problems.||12|
|The Fourier transform and its inverse. The Fourier transform properties. The convolution theorem. Applications to boundary value problems, and to integral equations. The Laplace transform, its properties and applications.||6|