# MATA181 Vector calculus 1 (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

Coordinates and vectors in 3-dimensional space, dot product, cross product. Equations of lines and planes, quadratic surfaces. Curves, differentiation and integration of vector valued functions of one variable. Limits and continuity for functions of two and three variables. Partial derivatives, tangent planes and approximation. Chain rule, gradient vector, directional derivatives. Extreme values, Lagrange multipliers.

## Learning outcomes

After the course the student

- can use coordinates, vectors, dot products and cross products in geometric applications
- can express lines and planes using equations
- understands the concept of derivative for vector functions and its geometric interpretation
- can solve extreme value problems for vector functions

## Description of prerequisites

Calculus 1-2 (or Introduction to mathematical analysis 1-2). Calculus 3.

## Study materials

Adams: Calculus, Chapters 10-13.

## 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 1

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

**Evaluation criteria:**

Course exam, weekly tests and exercises

**Language:**

Finnish

**Study methods:**

28 h lectures, 7 exercise sessions

**Study materials:**

Adams: Calculus, Chapters 10-13.

**Literature:**

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

#### Teaching

##### 9/7–10/29/2023 Lectures

##### 11/8–11/8/2023 Exam

##### 11/22–11/22/2023 Exam

x

### Exam (5 cr)

**Type:**

Exam

**Grading scale:**

0-5

**Evaluation criteria:**

Final exam

**Language:**

English, Finnish

**Study methods:**

Final exam

**Study materials:**

Adams: Calculus, Chapters 10-13.

**Literature:**

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