# MATA174 Introduction to mathematical analysis 4 (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

## Tweet text

The main topics of the study module are improper integral, number series, function series and sequences.

## Description

Improper integrals. Number series. Sequences and series of functions and their convergence. Power series. Taylor polynomials and Taylor series.

## Learning outcomes

The student
• knows the definition(s) of improper integral and knows how to study their convergence
• knows the definition for the convergence of a number series and is able to recognize the most common series
• is able to use the most common convergence tests
• knows the definitions for point wise and uniform convergence for function sequences and series, and is able to use them
• knows which properties are stable under uniform convergence
• knows how to apply Weierstrass' test to study uniform convergence
• is familiar with the definitions of power series and its radius convergence, and knows how to study the convergence of a power series
• knows what are Taylor polynomials and how they can be used to study limits
• is able to recognize the most common power series representations

## Description of prerequisites

Introduction to mathematical analysis 1-3

## Study materials

Lecture notes (in Finnish)

Fitzpatrick: Advanced Calculus, chap. 8-9. or Brannan: A first course in Mathematical Analysis, chap. 3 and 8.

## Literature

• P.M Fitzpatrick: Advanced Calculus (2nd ed); ISBN: 978-0-8218-4791-6
• D. Brannan: A first course in Mathematical Analysis; ISBN: 13 978-0-521-6842-8

## 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 4
Select all marked parts

### Method 2

Description:
Lopputentti. Luento-opetukseen osallistuneiden harjoitustehtäväpisteitä ei huomioida.
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 (in Finnish) 48 h, exercises

x

Type:
Exam