# MATA172 Introduction to mathematical analysis 2 (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

Continuity and limit for functions of one real variable. Basic properties of continuous functions. Uniform continuity.

In this study-module, students practice reading and writing mathematics. They learn the basics of logic and practice proving mathematical statements.

## Learning outcomes

The student

• knows the epsilon-delta definition for continuity, and is able to apply the definition in simple situations
• knows the characterization of continuity in terms of limits of sequences
• is familiar with the most important consequences of continuity
• knows the definition of limit of a function
• understands the connection between continuity and limit, and knows how they differ
• is able to formulate and prove mathematical claims
• has improved her/his ability to read and write mathematics

## Description of prerequisites

Introduction to mathematical analysis 1

## Study materials

Lecture notes (in Finnish)

The contents of the study-module correspond to

D. Brannan: A first course in mathematical analysis, chap. 4-5,

or

P. Fitzpatrick: Advanced Calculus, chap. 3.

## Completion methods

### Method 1

Description:
Final exam and exercises. The weekly exercises are handed in and graded. To attend the final exam, the students must receive enough bonus-points from the exercises (the exact amount is mentioned in the teaching schedule).
Evaluation criteria:
Final exam and weekly exercises.
Time of teaching:
Period 2
Select all marked parts

### Method 2

Description:
Final exam.
Evaluation criteria:
Final exam.
Select all marked parts
Parts of the completion methods
x

### Teaching (5 cr)

Type:
Participation in teaching
0-5
Language:
Finnish
Study methods:

Lectures 42 h and exercises. The weekly exercises are handed in and graded. To attend the final exam, the students must receive enough bonus-points from the exercises (the exact amount is mentioned in the teaching schedule).

Study materials:

Lecture notes (in Finnish)

x

### Exam (5 cr)

Type:
Exam
0-5
Language:
English, Finnish
Study methods:

Final exam.

Study materials:

The contents of the study-module correspond to

D. Brannan: A first course in mathematical analysis, chap. 4-5,

or

P. Fitzpatrick: Advanced Calculus, chap. 3.