Differential equations

A detailed summary of the compulsory course of ordinary differential equations, which has been read by the author for many years for students of the Faculty of Mechanics and Mathematics of Lomonosov Moscow State University, is presented. The textbook introduces readers to the geometric interpretation of the first-order equation, with the first integrals, special points and limit cycles of autonomous systems, with the theory of linear equations and systems, including constant and periodic coefficients, with the questions of the existence, uniqueness and continuability of solutions, their continuity and differentiability by parameter, Lyapunov stability, as well as with questions of the existence and uniqueness of the solution of the Cauchy problem for a partial differential equation of the first order.

Precise definitions are given, statements are carefully formulated and proved, the most important methods of solving problems are strictly justified. All the necessary theoretical information, related concepts and facts from related branches of mathematics are given. The tasks for independent solution are proposed, allowing to penetrate deeper into the read material. For students and postgraduates studying the classical theory of ordinary differential equations.