# MATA182 Vector calculus 2 (4 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

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.

## Study materials

Adams: Calculus, chapters 14-16.

## 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

**Grading scale:**

0-5

**Evaluation criteria:**

Course exam, weekly tests and exercises

**Language:**

Finnish

**Study methods:**

28 h lectures (in Finnish), 7 exercise sessions

**Study materials:**

Adams: Calculus, chapters 14-16.

**Literature:**

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

#### Teaching

##### 10/27–12/16/2022 Lectures

##### 12/14–12/14/2022 Exam

##### 1/18–1/18/2023 Exam

x

### Exam (4 cr)

**Type:**

Exam

**Grading scale:**

0-5

**Evaluation criteria:**

Final exam

**Language:**

English, Finnish

**Study methods:**

Final exam

**Study materials:**

Adams: Calculus, chapters 14-16.

**Literature:**

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