A detailed summary of the compulsory course on ordinary differential equations, taught by the author for many years to students of the Faculty of Mechanics and Mathematics of Lomonosov Moscow State University is presented. The textbook introduces readers to the geometric interpretation of first-order equations, first integrals, singular points and limit cycles of autonomous systems, the theory of linear equations and systems, including constant and periodic coefficients, questions of the existence, uniqueness and continuability of solutions, their continuity and differentiability with respect to a parameter, Lyapunov stability, as well as questions of the existence and uniqueness of a solution to the Cauchy problem for a first-order partial differential equation. Precise definitions are given, statements are carefully formulated and proven, and the most important methods for solving problems are strictly justified. All necessary theoretical information, related concepts and facts from related branches of mathematics are presented. Problems are proposed for independent solution, allowing you to penetrate deeper into the material you have read. For undergraduate and graduate students studying the classical theory of ordinary differential equations.
To cite this article
Sergeev I.N. Lectures on differential equations. - M.: Moscow University Publishing House, 2019. - 304 p.
A detailed summary of the compulsory course on ordinary differential equations, taught by the author for many years to students of the Faculty of Mechanics and Mathematics of Lomonosov Moscow State University is presented. The textbook introduces readers to the geometric interpretation of first-order equations, first integrals, singular points and limit cycles of autonomous systems, the theory of linear equations and systems, including constant and periodic coefficients, questions of the existence, uniqueness and continuability of solutions, their continuity and differentiability with respect to a parameter, Lyapunov stability, as well as questions of the existence and uniqueness of a solution to the Cauchy problem for a first-order partial differential equation. Precise definitions are given, statements are carefully formulated and proven, and the most important methods for solving problems are strictly justified. All necessary theoretical information, related concepts and facts from related branches of mathematics are presented. Problems are proposed for independent solution, allowing you to penetrate deeper into the material you have read. For undergraduate and graduate students studying the classical theory of ordinary differential equations.
For citations
Sergeev I.N. Lectures on differential equations. - M.: Moscow University Publishing House, 2019. - 304 p.
Moscow University Press
