The role of the theory differential equations in modern mathematics and its applications

Abstract

The article describes the role of the theory of differential equations in modern mathematics and its application. To describe its place in modern mathematical science, first of all, the main features of the theory of differential equations, consisting of two broad areas of mathematics: the theory of ordinary differential equations and the theory of partial differential equations, are highlighted. The first feature of this theory is its close connection with applications. It is noted that the theory of differential equations is primarily based on the formulation and understanding of quantitative and qualitative laws that make up the content of the natural sciences as an integral part of natural science. The article also emphasizes the second feature of the theory of differential equations, its connection with other areas of mathematics, such as functional analysis, algebra and probability theory. The purpose of this article is to identify modern problems in the theory of differential equations and to construct a system of corresponding problems.