course-details-portlet

TMA4165

Dynamical Systems

Choose study year
Credits 7.5
Level Third-year courses, level III
Course start Spring 2025
Duration 1 semester
Language of instruction English
Location Trondheim
Examination arrangement School exam

About

About the course

Course content

The course gives an introduction to dynamical systems with an emphasis on analytical and qualitative methods for linear and nonlinear ordinary differential equations. Topics covered: Linear and nonlinear systems, existence and uniqueness, continuous dependence, phase plane analysis, equilibria, limit cycles, stability, Lyapunov's direct method, index theory, the Poincaré-Bendixson theorem, and examples of applications. Additional topics that may change from year to year may include bifurcations, discrete dynamical systems and chaos, topics from calculus of variations and classical mechanics.

Learning outcome

1. Knowledge. The student knows basic concepts and methods from the theory of dynamical systems, including analytical and geometrical techniques for the study of qualitative properties of solutions. In particular, the student is familiar with linear and nonlinear systems, existence and uniqueness, continuous dependence, phase plane analysis, equilibria, limit cycles, stability, Lyapunov's direct method, index theory, the Poincaré-Bendixson theorem, the additional topics and examples of applications.

2. Skills. The student is able to apply his or her knowledge to the study of concrete examples. The student masters central techniques of proof and is able to apply these to related problems.

Learning methods and activities

Lectures and exercises.

Further on evaluation

Retake of examination may be given as an oral examination. The retake exam is in August. Students are free to choose Norwegian or English for written assessments.

Course materials

Will be announced at the start of the course.

Credit reductions

Course code Reduction From
SIF5025 7.5 sp
This course has academic overlap with the course in the table above. If you take overlapping courses, you will receive a credit reduction in the course where you have the lowest grade. If the grades are the same, the reduction will be applied to the course completed most recently.

Subject areas

  • Mathematics
  • Technological subjects

Contact information

Course coordinator

Department with academic responsibility

Department of Mathematical Sciences