Course ObjectiveAt the end of this course students ...
... know the existence an uniqueness theorem for initial value
... 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
... can recognize and analyze gradient, conservative and Hamiltonian
... 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
Course ContentThis course entails the theory of ordinary differential equations from
the modern point of view of dynamical systems.
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 MethodsRegular instruction class in combination with tutorial classes.
Method of AssessmentHand-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
The resit exam counts for 100% (hand-ins don't count anymore).
LiteratureLawrence Perko, "Differential Equations and Dynamical Systems", third
edition, Springer-Verlag 2001,
In addition there are notes that will be communicated to the students
Target AudienceBachelor Mathematics Year two
Additional InformationAdditional information on Canvas
Recommended background knowledgeFirst year courses Calculus and Analysis.
|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|
prof. dr. R.C.A.M. van der Vorst
You need to register for this course yourself
Last-minute registration is available for this course.
|Teaching Methods||Seminar, Lecture|
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