# MATA172 Introduction to mathematical analysis 2 (5 cr)

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## 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

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### Method 2

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### Teaching (5 cr)

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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).

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Lecture notes (in Finnish)

#### Teaching

##### 10/25–12/17/2021 Lectures

##### 12/17–12/17/2021 Exam

##### 1/12–1/12/2022 Exam, remote

### Exam (5 cr)

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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.