# MATA181 Vector calculus 1 (5 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

## 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.

## 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
0-5
Evaluation criteria:
Course exam, weekly tests and exercises
Language:
Finnish
Study methods:

28 h lectures, 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 (5 cr)

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

Final exam

Study materials: