# MATA255 Vector Analysis 1 (4 cr)

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## Description

The structure of Euclidean space: norm, inner product, convergence, Bolzano-Weierstrass, completeness. Functions of several real variables, continuity, level sets. Open and closed sets, boundary, closure. Differentiability, partial and directional derivatives, gradient, chain rule, approximation with linear mappings, mean value theorems

## Learning outcomes

The aim of the course is to strengthen the conceptual understanding of multidimensional analysis and to become more accustomed to more abstract reasoning than Vector calculus courses. After completing the course the student:

- knows how to use and define the basic metric and topological concepts of the Euclidean space (norm, dot product, open and closed sets, boundary set, convergence) and how to prove problems related to them
- understands the definition of continuity and limit of a vector-valued function, and is familiar with the connections between them and the basic concept of topology
- understands differentiability, derivative and directional derivatives and their geometrical interpretation

## Description of prerequisites

Introduction to mathematical analysis 1-4, Linear algebra and geometry 1, Vector calculus 1-2

## Study materials

Lecture notes (in Finnish)

## Literature

- P.M Fitzpatrick: Advanced Calculus (2nd ed); ISBN: 978-0-8218-4791-6

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### Method 2

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### Teaching (4 cr)

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Lectures 28 h (in Finnish), homework exercises

#### Teaching

##### 1/12–3/19/2023 Lectures

### Exam (4 cr)

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Independent study and final exam