Osion kuvaus

  • Yleinen

    According to 'Upcoming events/KT' on the right sidebar, the exam on April 17, 9-12 am, will be in T1 (aka C202) in the Computer Science building.

    Note on exams: Please make sure to take a simple function calculator with you to the exam. Function (non-programmable) calculator is allowed. If the student only has a programmable calculator, they must show that its memory is empty.  Graphical calculators that show plots of functions are not allowed.

    Lectures: Wednesdays 2.15 - 3.45 pm, starting January 11. In the classroom T3.

    Exercise sessions: Thursdays 2.15 - 4.00 pm, starting January 19. In the classroom T6.

    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. We will also have some numerical exercises (in python).

    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. There will not be numerical problems in the exam.

    Lecturer: Riku Linna

    Teaching Assistants: Pauliina Kärkkäinen (pauliina.karkkainen@aalto.fi) and Susanna Holmström (susanna.holmstrom@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.