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## Dynamics and Computation

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 the course,
1. the student is able to analyse one and two- dimensional differential
equations systems
2. the student is able to linearise a non-linear system, compute
corresponding eigenvalues (by hand and numerically), solve Ini(al Value
Problems and draw conclusions on the stability of fixed points
3. the student is able to analyse scalar difference equa(ons, their
fixed points and stability properties, find period doubling points for
simple systems, and sketch orbits
4. the student is able to write programs in Matlab for numerical
computations
5. the student is able to numerically solve systems of nonlinear
equations
6. the student is able to fit nonlinear data using least squares methods
7 the student is able to use Fast Fourier Transforms to analyse signals
8. the student is able to use sparse matrices to
compute dominant eigenvalues and eigenvectors for large matrices
9. the student is able to numerically integrate systems of ordinary
differential equations
10. the student is able to write reports documenting how the matlab
programs work and discuss their limitations.

### Inhoud vak

In this course you will be given an overview of the theory of discrete
and continuous dynamical systems (first period), as well as a foundation
in the most commonly applied numerical algorithms used to solve
algebraic and dynamic problems (second period) found in concrete
applications.

Dynamical Systems part:
1. Discrete-time dynamical systems: graphical methods to draw orbits,
calculating fixed points, stability analysis, period doubling.
2. Ordinary Differential Equations in 1 and 2 dimensions: graphical
methods, linearisation, phase plane analysis, classification of steady
states.
3. General theory of linear ODEs, solving initial value problems.

Numerical part
1. Introduction in Matlab programming
2. Finding roots of systems of nonlinear equations
3. Interpolation, Least Squares
4. Fast Fourier Transforms, analysing signals
5. Computing eigenvalues and eigenvectors, Pagerank
6. Numerical derivatives and integrals of functions.
7. Numerical methods for ODEs

### Onderwijsvorm

lectures, tutorials, computer labs

### Toetsvorm

Written exam (part 1) and computer programming exercises (part 2). Both
form 50% of the grade and both need to be passed to complete the entire
course. There is a resit for the first exam but none for the second
part. Students that have not passed the second part by a small margin
(max 1.0 pt) get the opportunity to hand in one or more additional
assignments to obtain a sufficient grade.

### Literatuur

S. H. Strogatz. Nonlinear Dynamics and Chaos. ISBN: 978-0738204536

2 BA

### Aanbevolen voorkennis

Linear Algebra, Calculus 1 and 2

### Algemene informatie

Vakcode X_400647 6 EC P4+5 200 Engels Faculteit der Bètawetenschappen dr. R. Planque prof. dr. G.J.B. van den Berg dr. R. Planque

### Praktische informatie

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Werkvormen Werkcollege, Deeltoets extra zaalcapaciteit, Hoorcollege, Practicum
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