Ordinary Differential Equations (2023)

Dynamical systems are concerned with anything that changes. They originated from celestial mechanics and serve as the basis for the deterministic description of the universe. In this course we will study ordinary differential equations from the perspective of dynamical systems and perform qualitative analysis to grasp the geometric behavior of solutions. The main topics are as follows:

1. Wellposedness: Even if the explicit formula of a solution is unknown, it can still be determined that the solution exists and is unique.

2. Local stability: Analyze the deviation between solutions corresponding to perturbations on initial conditions.

3. Asymptotic behavior: Explore the long-term behavior of solutions.