# MATA256 Vector Analysis 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

## Description

Vector analysis: Higher order derivatives, extreme values, inverse mapping theorem, implicit function theorem, surfaces, paths and path integrals, path connected set, sequential compactness.

## 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 on earlier courses. After completing the course the student:

- is familiar with compact and path connected subsets of the Euclidean space and knows how to prove problems related to them
- understands differentiability, derivative and directional derivatives and their geometrical interpretation
- knows how to analyze extreme values using the Hessian matrix and Lagrange multipliers
- is familiar with the inverse mapping theorem and implicit function theorem and knows how to apply them
- knows the concepts of curve and arc length

## Description of prerequisites

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

## Literature

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

## Completion methods

### Method 1

**Evaluation criteria:**

Grading is based on points from exam and weekly exercises

**Time of teaching:**

Period 4

Select all marked parts

### Method 2

**Evaluation criteria:**

Grading is based on points from the 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:**

Grading is based on points from exam and weekly exercises

**Language:**

Finnish

**Study methods:**

28 h lectures (in Finnish) and 7 exercise sets.

#### Teaching

##### 3/23–5/28/2023 Lectures

x

### Exam (4 cr)

**Type:**

Exam

**Grading scale:**

0-5

**Language:**

English, Finnish

**Study methods:**

Independent study and final exam