Differential equations and dynamical systems

Course Code :1000WETDDS
Study domain:Mathematics
Academic year:2019-2020
Semester:1st semester
Contact hours:60
Study load (hours):168
Contract restrictions: No contract restriction
Language of instruction:Dutch
Exam period:exam in the 1st semester
Lecturer(s)Sonja Hohloch
Yannick Gullentops

3. Course contents *

Chapter 1: Basic definitions

  1. Ordinary differential equations.
  2. Systems of ordinary differential equations.
  3. Ordinary differential equations of higher order.

Chapter 2: Explicit techniques

  1. Autonomous ordinary differential equations.
  2. Separation of variables.
  3. Change of variables
  4. Homogeneous differential equations.
  5. Fractions.

Chapter 3: Existence and uniqueness

  1. Fixed point theorem of Banach
  2. Theorem of Picard-Lindelöf and the Theorem of Peano.
  3. Continuous/smooth dependence on initial conditions.

Chapter 4: Linear systems

  1. Homogeneous and inhomogeneous systems.
  2. Systems with constant coefficients.
  3. Classification in 2 dimensions.

Chapter 5: Boundary value problems

  1. Boundary value problem of Sturm-Liouville.
  2. Uniqueness.
  3. Construction of solutions.

Hoofdstuk 6: Basic properties of dynamical systems

  1. Discrete and continuous dynamical systems.
  2. Vector fields and flows.
  3. Fixed points, periodic and non-periodic orbits.
  4. Commuting flows.

Chapter 7: Local and global behaviour of dynamical systems

  1. Stability and invariant sets.
  2. Local behaviour close to hyperbolic fixed points: the theorem of Hartman-Grobman.
  3. Limit sets.
  4. Dynamics in 2 dimensions: the theorem of Poincaré-Bendixon.

Chapter 8: Chaos: Strange attractors

  1. What is chaos?
  2. The Lorenz system.
  3. Strange attractors.