# MATA182 Vector calculus 2 (5 cr)

**Study level:**

Intermediate studies

**Grading scale:**

0-5

**Language:**

English, Finnish

**Responsible organisation:**

Department of Mathematics and Statistics

**Curriculum periods:**

2024-2025, 2025-2026, 2026-2027, 2027-2028

## Description

Two and three dimensional integration, iterated integrals. Change of variables. Polar, cylindrical and spherical coordinates. Improper integrals. 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 successful completion, the student

- is able to calculate integrals of functions of two and three variables as iterated integrals, and change the order of integration if necessary
- knows how to use polar, cylindrical and spherical coordinates with integrals, and knows the general change of variables theorem
- is familiar with the multidimensional improper integral
- can find and use parametrizations for curves and surfaces
- can calculate curve and surface integrals of real-valued functions and vector fields (incl. calculation of curve length and surface area)
- can apply the most important integration theorems for vector fields (Green's and Stokes' theorems, divergence theorem)

## 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.

Stewart: Calculus, chapters 15-16.

## 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 and weekly 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

### Participation in teaching (5 cr)

**Type:**

Participation in teaching

**Grading scale:**

0-5

**Language:**

English, Finnish

#### Teaching

##### 10/24–12/20/2024 Lectures

##### 12/19–12/19/2024 Exam

##### 1/22–1/22/2025 Exam

x

### Exam (5 cr)

**Type:**

Exam

**Grading scale:**

0-5

**Language:**

English, Finnish