Dynamical Systems and Conservation Laws

Content

Please log in to view module content:

log in

Description

Time: Tuesdays, 15.30-17.30

Location for Maxwell Institute students: Bayes Centre (room 5.46)

Module Leader: Lucia Scardia (Heriot-Watt University)

Module Summary

The content of this module is split into five chapters.

Chapter 1 starts with a review of the basic theory of ODEs (Existence, Uniqueness, Maximal solutions). Then it focuses on autonomous systems, and discusses phase portraits and stability of equilibria for linear and nonlinear systems.

Chapter 2 deals with the stability analysis more in depth, in terms of stable, unstable and centre manifolds.

Chapter 3 presents the basics of the Bifurcation Theory for nonlinear systems.

Chapter 4 is an intermezzo on PDEs.

The final Chapter 5  lays the foundations of the theory for Conservation Laws. 

Assessment

A take-home test at the end of the course.