MATA174 Introduction to mathematical analysis 4 (5 cr)

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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

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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
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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
Grading scale:
0-5
Language:
Finnish
Study methods:

Lectures (in Finnish) 48 h, exercises

Teaching

x

Exam (5 cr)

Type:
Exam
Grading scale:
0-5
Language:
English, Finnish
Study materials:

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

Teaching