Text

Course syllabus - Fourier Analysis

Scope

7.5 credits

Course code

MAA323

Valid from

Autumn semester 2026

Education level

First cycle

Progressive Specialisation

G2F (First cycle, has at least 60 credits in first-cycle course/s as entry requirements)

Main area(s)

Mathematics/Applied Mathematics

Organisation

Department of Business and Mathematics

Ratified

2019-12-09

Revised

2025-11-03

Literature lists

Course literature is preliminary up to 8 weeks before course start. Course literature can be valid over several semesters.

    • Ratified date: 2025-05-21
    • Latest update: 2025-05-27

    Books

    Riley, Kenneth Franklin; Hobson, Michael Paul; Bence, Stephen John

    Mathematical methods for physics and engineering

    ISBN: 978-0-511-16842-0

    LIBRIS-ID: 11708818

    3. ed., Cambridge, Cambridge Univ. Press, PDF (xxvii, 1333 s.

    Mandatory

    Works of reference

    Stein, Elias M.; Shakarchi, Rami

    Fourier analysis: an introduction

    ISBN: 069111384X

    LIBRIS-ID: 8925098

    Princeton, N.J., Princeton University Press, xvi, 311 p.

Objectives

The objective of the course is to give the student opportunity to acquire basic understanding of the theory of orthogonal series and transforms, with applications in engineering and physics.

Learning outcomes

Upon completion of the course, the student is expected to be able to

  1. apply the Laplace transform to find solutions to linear differential and integral equations with given initial conditions
  2. determine pointwise convergence of Fourier series, and explain the Gibbs phenomenon
  3. determine orthogonality and completeness of systems of functions in L2, and find optimal approximations of L2 functions with respect to linear subspaces spanned by orthogonal systems
  4. calculate eigenvalues and eigenvectors/eigenfunctions, with and without a computer
  5. solve boundary value and initial value problems, including the one-dimensional heat equation, the one-dimensional wave equation, and the Laplace equation in two dimensions
  6. apply the Fourier transform to functions on unbounded intervals, including the application of the inversion theorem and Plancherel's formula

Course content

  • Laplace transform, Fourier transform
  • Fourier series, eigenfunctions and eigenvalues
  • Fourier methods and separation of variables
  • Sturm-Liouville problems, L2-theory, orthogonal systems
  • Basic distributions, the Heaviside function, Dirac's delta
  • Examples of applications of Fourier analysis in e.g. physics and signal processing

Specific requirements

45 credits in Mathematics/Applied Mathematics which includes Single Variable Calculus, 7,5 credits, Calculus of Several Variables, 7,5 credits, and Vector Algebra, 7,5 credits, or equivalent.

Examination

LAB1, Laboratory work, 1.5 credits, computer lab with written and oral report concerning learning outcome 4, grades Fail (U) or Pass (G).
INL1, Assignment, 3 credits, written assignment concerning learning outcomes 1-6, grades Fail (U), 3, 4 or 5.
TEN1, Written examination, 3 credits, individual written exam concerning learning outcomes 1-6, grades Fail (U), 3, 4 or 5.

There may also be optional assignments that give bonus points for the examinations above. See more information in the study guide.

For grade 4 on the course as a whole, the student must have earned a grade average of 4 for INL1 and TEN1. For grade 5 on the course as a whole, the student must have earned that grade for INL1 and TEN1.

A student who has a certificate from MDU regarding disability study support, can request adaptions for the examination. It is the examiner who takes decisions on any adaptions, based on the certificate and other conditions.

Grade

Grading scale: 5, 4, 3