# MATA173 Introduction to mathematical analysis 3 (5 cr)

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## Description

The derivative and Riemann-integral for functions of one real variable: their definitions and basic results. The fundamental theorem of Calculus.

## Learning outcomes

- knows the definition and geometric interpretation of derivative, and the basic rules of differentiation
- can formulate the Mean Value Theorem and knows its most important consequences
- is familiar with the definition of Riemann-integral and integrability
- knows Riemann's criterion for integrability
- knows the basic properties of integral and the basic results about integrability
- is able to estimate the value of an integral using inequalities
- understands how the Fundamental Theorem of Calculus connects derivative and integral to each other
- knows the theoretical justifications of integration by parts, change of variables in integral, and L'Hopital's rule.

## Description of prerequisites

Introduction to mathematical analysis 1 and 2

## Study materials

Lecture notes (in Finnish)

The contents of the study-module correspond to

D. Brannan: A first course in mathematical analysis, chap. 6-7,

or

P. Fitzpatrick: Advanced Calculus, chap. 4 and 6

## Completion methods

### Method 1

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### Method 2

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### Teaching (5 cr)

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Lectures 48 h, exercises

**Study materials:**

Lecture notes (in Finnish)

The contents of the study-module correspond to

D. Brannan: A first course in mathematical analysis, chap. 6-7,

or

P. Fitzpatrick: Advanced Calculus, chap. 4 and 6

#### Teaching

##### 1/9–3/12/2023 Lectures

### 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. 6-7,

or

P. Fitzpatrick: Advanced Calculus, chap. 4 and 6