This book is intended for the students having basic knowledge of mathematical analysis, algebra and the theory of ordinary differential equations. The method used in this book for investigating the boundary value problems and, partly, the Cauchy problem is based on the notion of generalized solution which enables us to examine equations with variable coefficients with the same ease as the simplest equations: Poisson's equation, wave equation and heat equation. Apart from discussing the questions of existence and uniqueness of solutions of the basic boundary value problems, considerable space has been devoted to the approximate methods of solving these equations: Ritz's method in the case of elliptic equations and Galerkin's method for hyperbolic and parabolic equations.

Contents: 1. Introduction classification of equations formulation of some problems. 2. The Lebesgue integral and some questions of functional analysis. 3. Function spaces. 4. Elliptic equations. 5. Hyperbolic equations. 6. Parabolic equations.