Lectures on partial differential equations

The textbook is an expanded presentation of the course of lectures that the author has given in recent years to 3rd-year students of the Mechanics and Mathematics Faculty of Moscow University, and contains the main classical and modern sections of the theory of partial differential equations, as well as information from functional analysis, the theory of generalized functions and function spaces. In addition, it includes material devoted to the proof of Kovalevskaya's theorem, a mixed problem for the equation of oscillations of an inhomogeneous string, the Cauchy problem for the wave equation and the theory of symmetric hyperbolic systems. The book presents the main facts related to the Laplace equation, the heat equation and the wave equation.

The textbook is intended for students studying in the fields of "Mathematics", "Applied Mathematics", "Mathematics and Computer Science", "Fundamental Mathematics and Mechanics".