### General Information

Course Code | X_400647 |
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Credits | 6 EC |

Period | P4+5 |

Course Level | 200 |

Language of Tuition | English |

Faculty | Faculty of Science |

Course Coordinator | dr. R. Planque |

Examiner | dr. R. Planque |

Teaching Staff |
dr. R. Planque |

### Practical Information

You need to register for this course yourself

Last-minute registration is available for this course.

Teaching Methods | Seminar, Lecture, Practical |
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Target audiences

This course is also available as:

### Course Objective

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.

### Course Content

In this course you will be given an overview of the theory of discreteand 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

### Teaching Methods

lectures, tutorials, computer labs### Method of Assessment

Written exam (part 1) and computer programming exercises (part 2). Bothform 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.