MATA320 Fourier series (4 cr)

Open the course unit brochure on Sisu
Study level:
Intermediate studies
Grading scale:
0-5
Language:
English, Finnish
Responsible organisation:
Department of Mathematics and Statistics
Curriculum periods:
2020-2021, 2021-2022, 2022-2023, 2023-2024

Description

Review of the theory of series; orthogonal function series; trigonometric polynomials; basic properties of Fourier series; on the convergence of Fourier series; use of Fourier series in solving partial differential equations; the discrete Fourier transform.

Learning outcomes

After passing the course the student

  • has basic skills in Fourier series
  • can form the Fourier series of a given function
  • can justify the convergence of a given Fourier series
  • has the skills needed for ordinary applications.

Description of prerequisites

 Introduction to mathematical analysis 3 and 4.

Study materials

Tom M. Apostol: Mathematical analysis. A modern approach to advanced calculus, Addison Wesley, ensimmäinen laitos, viides painos 1971.
Ernst Lindelöf: Differentiali- ja integralilasku ja sen sovellutukset III.2. Raja-arvoista ja raja-menetelmistä, Mercatorin kirjapaino, 1940.

Completion methods

Method 1

Evaluation criteria:
Course exam and exercises
Select all marked parts

Method 2

Evaluation criteria:
Final exam
Select all marked parts
Parts of the completion methods
x

Teaching (4 cr)

Type:
Participation in teaching
Grading scale:
0-5
Language:
Finnish

Teaching

x

Exam (4 cr)

Type:
Exam
Grading scale:
0-5
Language:
English, Finnish

Teaching