MATA321 Calculus of Variations (5 cr)

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

Description

Examples of main problems of the Calculus of Variations; variational integrals; externals; Euler-Lagrange equation; first integrals; isoperimetric problems; geodetic curves.

Learning outcomes

After passing the course the student

  • has basic knowledge of mains problems in the Calculus of Variations
  • can form the Euler-Lagrange equation of a variational integral and solve it in simple cases
  • has acquired knowledge and skill for typical applications.

Description of prerequisites

Introduction to mathematical analysis 3 and 4, Differential equations, Vector calculus 1 and 2.

Study materials

Bruce van Brunt: The Calculus of Variations. Springer, 2004.
Ernst Lindelöf: Differentiali- ja integralilasku ja sen sovellutukset IV. Johdatus variatiolaskuun. Mercatorin Kirjapaino Osakeyhtiö, 1946.

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 (5 cr)

Type:
Participation in teaching
Grading scale:
0-5
Language:
Finnish
Study methods:
Lectures and homework exercises
No published teaching
x

Exam (5 cr)

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

Independent study and final exam

No published teaching