# MATA173 Introduction to mathematical analysis 3 (5 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, 2023-2024

## Description

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

## Learning outcomes

The student
• 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

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 exercises.
Time of teaching:
Period 3
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
Grading scale:
0-5
Evaluation criteria:
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).
Language:
Finnish
Study methods:

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

x

### Exam (5 cr)

Type:
Exam
Grading scale:
0-5
Evaluation criteria:
Lopputentin maksimipistemäärästä saatava vähintään 50%.
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. 6-7,

or

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