Dynamics and Computation

URL study guide

https://studiegids.vu.nl/en/courses/2025-2026/X_400647

Course Objective

At the end of the course,the student is able to analyse one and two
- dimensional differential equations systemsthe 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 pointsthe student is able to analyse scalar difference equa(ons, their fixed points and stability properties, find period doubling points for simple systems, and sketch orbitsthe student is able to write programs in Matlab for numerical computationsthe student is able to numerically solve systems of nonlinear equationsthe student is able to find a root of a nonlinear function numericallythe student is able to fit nonlinear data using least squares methodsthe student is able to numerically integrate systems of ordinary differential equationsthe 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 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:Discrete-time dynamical systems: graphical methods to draw orbits, calculating fixed points, stability analysis, period doubling.Ordinary Differential Equations in 1 and 2 dimensions: graphical methods, linearisation, phase plane analysis, classification of steady states.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. 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 entirecourse. There is a resit for the first exam but none for the secondpart. 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.

Literature

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

Target Audience

2 BA

Additional Information

We expect that you attend the tutorials well prepared! That means that you have already tried to make the exercises/or started coding an assignment at home! Some exercises will be treated on the blackboard. You can ask questions about other exercises or the aasigments to the teaching assistant.

Recommended background knowledge

Linear Algebra, Calculus 1 and 2