Syllabus

LEARNING OUTCOMES

The student will learn the principles of analysing nonlinear and chaotic dynamical systems using mathematics, and diagrammatic and numerical methods. Basic understanding of fundamental concepts in chaotic systems such as strange attractors will be obtained.

Credits: 5

Schedule: 12.01.2022 - 11.04.2022

Teacher in charge (valid for whole curriculum period):

Teacher in charge (applies in this implementation): Riku Linna

Contact information for the course (applies in this implementation):

Lecturer:

Riku Linna 

e-mail: riku.linna@aalto.fi

Office: B334 (CS-building)

Assistants:

Pauliina Kärkkäinen

e-mail: pauliina.karkkainen@aalto.fi

Silja Sormunen

e-mail: silja.sormunen@aalto.fi

CEFR level (valid for whole curriculum period):

Language of instruction and studies (applies in this implementation):

Teaching language: English. Languages of study attainment: English

CONTENT, ASSESSMENT AND WORKLOAD

Content

• valid for whole curriculum period:

  Flows on the line. Bifurcations. Flows on the plane. Limit cycles. Lorenz equations. One-dimensional maps. Logistic maps. Lyapunov exponents. Fractals.

• applies in this implementation

  The student will learn the principles of analysing nonlinear and chaotic dynamical systems using mathematics and diagrammatic methods. Basic understanding of fundamental concepts in chaotic systems such as strange attractors will be obtained. (S)he will also gain basic understanding on numerically simulating nonlinear systems.
  

Assessment Methods and Criteria

• valid for whole curriculum period:

  Final examination and mathematical/computational exercises.

• applies in this implementation

  Doing and returning exercises is optional but highly recommended for those wanting to learn. No exercise points are required to take the exam but you can compensate for maximum of 20 % of exam points with completed exercises. There  is a threshold of 10 % of assignment points; total points exceeding this threshold will (after appropriate scaling) contribute to compensation points in the exam.
  

Workload

• valid for whole curriculum period:

  Studying the material, completing the assignments, and participating in the exercise sessions: 100 h. Ten lectures and exercise sessions. (Each week contact teaching: 3-4 h, individual studying and doing exercises appr. 6 h.)

  Preparing for and taking the exam: 35 h

  Total: 135 h (= 5 cr * 27 h)

DETAILS

Study Material

• applies in this implementation

  Lecture notes covering the required material will be given.
  

Substitutes for Courses

• valid for whole curriculum period:

  Substitutes for Courses

Prerequisites

• valid for whole curriculum period:

  Prerequisites

FURTHER INFORMATION

Further Information

• valid for whole curriculum period:

  The course runs for 9-10 weeks, so for the whole period III and part of period IV. 

  Teaching Language : English

  Teaching Period : 2022-2023 Spring III - IV
  2023-2024 Spring III - IV

  Enrollment :

  Registration for Courses: In the academic year 2021-2022, registration for courses will take place on Sisu (sisu.aalto.fi) instead of WebOodi. Via weboodi.

Details on the schedule

• applies in this implementation

  There will be ten lectures and exercise sessions. Each assignment will be given by the time of a weekly lecture and students wishing to have their assignment graded are to return their solutions by the next lecture. The solutions will be shown and discussed on the exercise session on the following Thursday. 
  

Description