# 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, 2023-2024

## 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