Theory of Differential Equations (MATH562) Course Details

Course Name: Theory of Differential Equations
Code: MATH562
Pre-requisite Course(s): Consent of the Department
Objective: The course aims to introduce and present Initial Value Problem: Existence and Uniqueness of Solutions; Continuation of Solutions; Continuous and Differential Dependence of Solutions. Linear Systems: Linear Homogeneous And Nonhomogeneous Systems with Constant and Variable Coefficients; Structure of Solutions of Systems with Constant and Periodic Coefficients; Higher Order Linear Differential Equations; Sturmian Theory, Stability: Lyapunov Stability and Instability. Lyapunov Functions; Lyapunov's Second Method; Quasilinear Systems.
Content: IVP: existence and uniqueness, continuation and continuous dependence of solutions; linear systems: linear (non)homogeneous systems with constant and variable coefficients; structure of solutions of systems with periodic coefficients; higher order linear differential equations; Sturmian theory, stability: lyapunov (in)stability, Lyapunov functions; Lyapunov's second method; quasilinear systems; linearization; stability of an equilibrium and stable manifold theorem for nonautonomous differential equations. 
Term: Elective
Theory: 3
Application: 0
Laboratory: 0
Credit: 3
ECTS Course File: Course File
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