Fourier Analysis

5 credits

Syllabus, Bachelor's level, 1MA211

A revised version of the syllabus is available.
Education cycle
First cycle
Main field(s) of study and in-depth level
Mathematics G1F
Grading system
Fail (U), Pass (3), Pass with credit (4), Pass with distinction (5)
Finalised by
The Faculty Board of Science and Technology, 30 August 2018
Responsible department
Department of Mathematics

Entry requirements

Several Variable Analysis or Geometry and Analysis III, and Linear Algebra II.

Learning outcomes

On completion of the course, the student should be able to

  • account for basic concepts and theorems within the Fourier analysis;
  • demonstrate basic numeracy skill concerning the concepts in the previous point;
  • use the numeracy skill at the solution of mathematical and physical problems formulated as ordinary or partial differential equations.


Fourier series in complex and trigonometric form. Pointwise and uniform convergence. The Dirichlet kernel. The Cesàro summability and the Fejér kernel. L2-theory: Orthogonality, completeness, ON systems. Applications to partial differential equations. Separation of variables. Something about Sturm-Liouville theory and eigenfunction expansions.

The Fourier transform and its properties. Convolution. The inversion formula. The Plancherel theorem.

The Laplace transform and its properties. Convolution. Applications to initial value problems and

integral equations.


Lessons in large and small groups.


Written examination at the end of the course.

If there are special reasons for doing so, an examiner may make an exception from the method of assessment indicated and allow a student to be assessed by another method. An example of special reasons might be a certificate regarding special pedagogical support from the disability coordinator of the university.

Other directives

The course may not be included in higher education qualification together with Fourier Analysis (1MA035), 5 credits.