Dynamical Systems

2019-2020

Course Objective

At the end of this course students ...
... know the existence an uniqueness theorem for initial value
problems;
... are able to solve constant coefficient linear (matrix) differential
equations and know the elementary linear algebra needed for that;
... can analyze one- and two-dimensional dynamics and are able to draw
phase space / phase plane pictures;
... know elementary bifurcation theory and in particular the saddle-node
bifurcations;
... can recognize and analyze gradient, conservative and Hamiltonian
dynamical systems;
... know and understand the stable and unstable manifold theorem and the
principle of linearization;
... know what limit sets are;
... are able to apply the Poincaré-Bendixson theorem;
... understand the concept of compactification and know the Poincaré
sphere.

Course Content

This course entails the theory of ordinary differential equations from
the modern point of view of dynamical systems.
Subjects are:
1. Existence an uniqueness of initial value problems;
2. Linear systems and elementary linear algebra;
3. One-dimensional dynamics and two-dimensional phase plane pictures;
4. Elementary bifurcation theory and saddle-node bifurcations;
5. Gradient dynamics;
6. Conservative systems and Hamiltonian dynamics;
7. Stable and unstable manifolds and linearization;
8. Limiting behavior;
9. The Poincaré-Bendixson theorem;
10. Compactification and the Poincaré sphere.

Teaching Methods

Regular instruction class in combination with tutorial classes.

Method of Assessment

Hand-in exercises, a midterm and a final exam. The hand-ins count for
10% each. The first midterm counts for 30% and the second midterm counts
for 50%.

The resit exam counts for 100% (hand-ins don't count anymore).

Literature

Lawrence Perko, "Differential Equations and Dynamical Systems", third
edition, Springer-Verlag 2001,
ISBN-10: 0387951164.

In addition there are notes that will be communicated to the students
via Canvas.

Target Audience

Bachelor Mathematics Year two

Additional Information

Additional information on Canvas

Recommended background knowledge

First year courses Calculus and Analysis.

General Information

Course Code X_400637
Credits 6 EC
Period P4+5
Course Level 300
Language of Tuition English
Faculty Faculty of Science
Course Coordinator prof. dr. R.C.A.M. van der Vorst
Examiner prof. dr. B.W. Rink
Teaching Staff prof. dr. R.C.A.M. van der Vorst

Practical Information

You need to register for this course yourself

Last-minute registration is available for this course.

Teaching Methods Seminar, Lecture
Target audiences

This course is also available as: