Vak nog zonder naam

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;
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.

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

Overige informatie

Additional information on Canvas

Aanbevolen voorkennis

First year courses Calculus and Analysis.

Algemene informatie

Vakcode X_400637
Studiepunten 6 EC
Periode P4+5
Vakniveau 300
Onderwijstaal Engels
Faculteit Faculteit der Bètawetenschappen
Vakcoördinator prof. dr. R.C.A.M. van der Vorst
Examinator prof. dr. R.C.A.M. van der Vorst
Docenten prof. dr. R.C.A.M. van der Vorst

Praktische informatie

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