# MATA182 Vector calculus 2 (4 cr)

Study level:
Intermediate studies
0-5
Language:
English, Finnish
Responsible organisation:
Department of Mathematics and Statistics
Curriculum periods:
2020-2021, 2021-2022, 2022-2023, 2023-2024

## Description

Two and three dimensional integration, iterated integrals. Polar, cylindrical and spherical coordinates. Vector fields, line integrals, the fundamental theorem for line integrals, Green's theorem. Parametric surfaces and surface integrals. Stokes' theorem and the divergence theorem.

## Learning outcomes

After the course the student

• knows the basic integration techniques for functions of two and three variables
• understands the concept of vector field and their geometric interpretation
• can find and use parametrizations for surfaces
• can apply the most important integration by parts formulas for vector fields

## Description of prerequisites

Calculus 1-3. (or Introduction to mathematical analysis 1-3 and Calculus 3). Vector calculus 1.

## Literature

• Adams, Robert A. Calculus: a complete course, 8. painos, Pearson 2013.; ISBN: 978-0-321-78107-9

## Completion methods

### Method 1

Evaluation criteria:
Course exam, weekly tests and exercises
Time of teaching:
Period 2
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
0-5
Evaluation criteria:
Course exam, weekly tests and exercises
Language:
Finnish
Study methods:

28 h lectures (in Finnish), 7 exercise sessions

Study materials:

Literature:
• Adams, Robert A. Calculus: a complete course, 8. painos, Pearson 2013.; ISBN: 978-0-321-78107-9

x

### Exam (4 cr)

Type:
Exam
0-5
Evaluation criteria:
Final exam
Language:
English, Finnish
Study methods:

Final exam

Study materials: