This information sheet indicates how the course will be organized at pandemic code level yellow and green.
If the colour codes change during the academic year to orange or red, modifications are possible, for example to the teaching and evaluation methods.

Differential equations and dynamical systems

Course Code :1000WETDDS
Study domain:Mathematics
Academic year:2020-2021
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.