Topic outline

  • General

    Please note that the TA position for spring 2025 has been filled and so is no longer available. Thank you for all who applied!

    The exam will be on April 15, 9 am (check for the place in Sisu). The next chance will be on June 5 (again, details in Sisu). Take a function calculator with you. (A function calculator is one that cannot be programmed. Also, it has no graphics, meaning you cannot plot functions with it.) There's some instructions under 'Exam Stuff' on the left sidebar.

    Lectures: Wednesdays 2.15 - 3.45 pm, starting January 10. In the classroom T3 in the Computer Science building, the 2nd floor: One fly of stairs up on the right of the main entrance, turn left and cross the bridge to the other side of the centre hall. T3 is on the left there.

    Exercise sessions: Thursdays 2.15 - 4.00 pm, starting January 18. In the classroom T6.

    Slack: There's a Slack  workspace for discussion, questions etc. It's voluntary, join if you feel like it. The link for joining: 

    Slack link

     Links in Slack get stale in time, so if you decide to join later, you'll have to ask for a new link.

    Overview

    Nonlinear dynamics is relevant in the fields of brain dynamics, 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. Some numerical exercises (in python) will be distributed to aid those interested in getting started with numerical solutions of nonlinear systems. However, numerical problems will not be part of requirements in assignments or the exam.

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

    Solutions to the weekly returned exercises will be uploaded after exercise sessions.

    About the exam: The problems in the exam will be pen & paper: the type of analysis problems done in the exercises and possibly an essay.

    Lecturer: Riku Linna

    Teaching Assistants: Anna Kosklin (Anna.kosklin@aalto.fi) and Juho Tuomaala (juho.tuomaala@aalto.fi)

    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. Basic understanding of programming.

    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.

    Note

    Solutions to assignments are to be returned in exercise sessions or uploaded in MyCourses. Uploaded solutions must be in pdf format.  If a scanner is not available to you, a good alternative is Adobe Scan app available for mobile phones. Numerical solutions are to be uploaded as Jupyter notebooks.