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.
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
x
Exam (5 cr)
Type:
Exam
Grading scale:
0-5
Language:
English, Finnish
Study methods:
Independent study and final exam