Ordinary Differential Equations

In this course, we study existence and uniqueness theorems for first order differential equations, as well as stability analysis for linear and nonlinear systems.

Existence and Uniqueness Results

We look at Picard-Lindelof local existence and uniqueness result, Cauchy-Lipschitz global existence and uniqueness result, and Peano’s existence result.

Stability and Asymptotic Behaviour

Here, we look at conditions for stablity of the trivial equilibrium state for linear systems and the Lyapunov linearization principle for nonlinear systems.

Boundary Value Problems

Here, we provide a necessary and sufficient condition so that a given boundary value problem has a unique solution. We also study Green’s functions and how to use them to write the solutions of BVPs.