Dynamics and Computation

Vrije Universiteit Amsterdam

Course Description

  • Course Name

    Dynamics and Computation

  • Host University

    Vrije Universiteit Amsterdam

  • Location

    Amsterdam, The Netherlands

  • Area of Study

    Computer Science, Mathematics

  • Language Level

    Taught In English

  • Course Level Recommendations

    Upper

    ISA offers course level recommendations in an effort to facilitate the determination of course levels by credential evaluators.We advice each institution to have their own credentials evaluator make the final decision regrading course levels.

    Hours & Credits

  • ECTS Credits

    6
  • Recommended U.S. Semester Credits
    3
  • Recommended U.S. Quarter Units
    4
  • Overview

    COURSE OBJECTIVE
    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.

    At the end of the course, the student is able to

    • analyse one and two-dimensional difference and differential equations systems
    • solve systems of non-linear ODEs numerically
    • linearise a non-linear system, compute corresponding eigenvalues (by hand and numerically), and draw conclusions on the stability of fixed points
    • use several numerical algorithms in concrete applications
    • make programs in Matlab

    COURSE CONTENT
    Dynamical Systems part:
    1. Discrete-time dynamical systems
    2. Ordinary Differential Equations in 1 and 2 dimensions: graphical methods, linearisation, phase plane analysis
    3. General theory of linear ODEs, solving initial value problems.
    4. If there is enough time: dependence of solutions on parameters.

    Numerical part:
    1. Finding roots of nonlinear equations
    2. Least Squares, curve fitting
    3. Eigenvalue Problems, Pagerank
    4. Fast Fourier Transforms, analysing signals
    5. Numerical methods for ODEs

    TEACHING METHODS
    Lectures, tutorials, computer labs

    TYPE OF ASSESSMENT
    Written exam (part 1) and computer programming exercises (part 2)

     

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