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## Dynamical Systems

2019-2020
Dit vak wordt in het Engels aangeboden. Omschrijvingen kunnen daardoor mogelijk alleen in het Engels worden weergegeven.

### Doel vak

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.

### Inhoud vak

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;
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.

### Onderwijsvorm

Regular instruction class in combination with tutorial classes.

### Toetsvorm

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).

### Literatuur

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.

### Doelgroep

Bachelor Mathematics Year two

### Aanbevolen voorkennis

First year courses Calculus and Analysis.

### Algemene informatie

Vakcode X_400637 6 EC P4+5 300 Engels Faculteit der Bètawetenschappen prof. dr. R.C.A.M. van der Vorst prof. dr. R.C.A.M. van der Vorst prof. dr. R.C.A.M. van der Vorst

### Praktische informatie

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