Название: Qualitative Theory of ODEs: An Introduction to Dynamical Systems Theory
Автор: Henryk Żoladek, Raul Murillo
Издательство: World Scientific Publishing
Год: 2023
Страниц: 283
Язык: английский
Формат: pdf (true)
Размер: 16.4 MB

The Qualitative Theory of Ordinary Differential Equations (ODEs) occupies a rather special position both in Applied and Theoretical Mathematics. On the one hand, it is a continuation of the standard course on ODEs. On the other hand, it is an introduction to Dynamical Systems, one of the main mathematical disciplines in recent decades. Moreover, it turns out to be very useful for graduates when they encounter differential equations in their work; usually those equations are very complicated and cannot be solved by standard methods.

The main idea of the qualitative analysis of differential equations is to be able to say something about the behavior of solutions of equations without solving them explicitly. Therefore, in the first instance, such properties like the stability of solutions stand out. It is the stability with respect to changes in the initial conditions of the problem. Note that even with the numerical approach to differential equations, all calculations are subject to certain inevitable errors. Therefore, it is desirable that the asymptotic behavior of the solutions is insensitive to perturbations of the initial state. Chapter 1 of these book roughly focuses on this point.