Course content

The course gives an introduction to differential equations and dynamical systems with an emphasis on analytical and qualitative methods for linear and nonlinear 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 has knowledge of basic concepts and methods from the theory of differential equations and dynamical systems, including analytical and geometrical techniques for the study of qualitative properties of solutions. In particular, the student is familiar 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. Retake of examination may be given as an oral examination. If the course is taught in English, the exam will be given only in English. Students are free to choose Norwegian or English for written assessments.

Recommended previous knowledge

The course is based on TMA4100/05/10/15/20 Calculus 1/2/3/4K, or equivalent.

Course materials

Will be announced at the start of the course.

Credit reductions