Dynamical Systems and Conservation Laws


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Module Overview - Dynamical Systems and Conservation Laws

The goal of the first part of this module is to present some basic concepts about the
geometry of dynamics and bifurcations of ordinary differential equations. A large part of this is devoted to scalar equations where, despite their simplicity, many modern concepts of dynamical systems can be explained. The second part introduces partial differential equations describing conservation laws. Again we focus on scalar equations but conclude the module with systems of hyperbolic PDEs, shock waves, and entropy conditions.

  • Dynamical systems and bifurcation
  • Scalar conservation laws
  • Systems of hyperbolic PDEs and shock waves

The module is examined in two assignments.
Assignment 1 due end of November, Assignment 2 due at the end of the module.


This module assumes knowledge of undergraduate level ordinary differential equations, single- and multivariable real analysis, and linear algebra.