محاضرات في مقياس Stability of Solutions of Ordinary Differential Equations

Abstract

This document presents a module on stability of ODE solutions, intended for first-year master's students in mathematics. It is organized as follows:

∙ Chapter 1: Fundamentals of ODEs, including the Cauchy problem, linear systems (with variable/constant coefficients), and Floquet theory for periodic systems. ∙ Chapter 2: Notion of Lyapunov stability, with a focus on linear and nonlinear systems. ∙ Chapter 3: In-depth study of stability, particularly the stability of the zero solution for both linear and nonlinear systems. ∙ Chapter 4: In this chapter, you will find Directed Work problems reinforcing concepts from earlier chapters along with actual exam questions from previous years.

The objective is to provide both theoretical foundations and practical applications.