Topic outline

  • General

    Overview

    Nonlinear dynamics is relevant in the fields of population and social dynamics, mathematical biology, physics, electrical engineering, and many more. Recently, machine learning methods have been applied to nonlinear dynamics. 

    The course covers the fundamental concepts and tools  for solving systems involving  nonlinear dynamics. Emphasis is on the qualitative graphical outlining of the solutions for the problems whose detailed analytical solutions are typically overwhelming or downright impossible. Still, even this level of solving requires some familiarity with differential equations and linear algebra. We will cover the material and do the exercises at a pace that gives everyone the chance to brush up the required pieces of mathematics. 

    The Course book is Steven Strogatz: Nonlinear Dynamics and Chaos can be found under Materials. 

    Solutions to the weekly returned exercises will be uploaded after exercise sessions. They can can also be found under Materials.

    Lecturer: Riku Linna

    Assistant: Tarmo Nurmi

    Learning Outcomes

    After completing the course the student will have an understanding of  the basic  classes  of nonlinear systems and will be able to analyse them using analytic and diagrammatic methods. Based on these skills he/she will be able to solve these systems also numerically (although numerical methods will be in minor role in this course). The student will have an understanding of how and why a dynamical system becomes chaotic. He/she will understand fundamental characteristics of chaotic systems and how they are modelled.

    Prerequisites

    Roughly first-year mathematics.

    Grading

    The grade (1-5) will be determined by an exam. Doing the assignments is voluntary but highly recommendable. 20% of lost exam points can be compensated by points gathered from assignments. See further details under Assignments. There will be 10 lectures and 10 rounds of assignments.

    Credits

    5 ECT.

    Information for the exam:

    A basic scientific calculator (funktiolaskin) is allowed in the exam. Graphing calculators / programmable calculators / symbolic math solving calculators are NOT allowed. In addition to a calculator, writing utensils are allowed. Remember to also bring your student card.