Information Package / Course Catalogue
Introduction to Infinite Series
Course Code: MAT443
Course Type: Area Elective
Couse Group: First Cycle (Bachelor's Degree)
Education Language: Turkish
Work Placement: N/A
Theory: 3
Prt.: 0
Credit: 3
Lab: 0
ECTS: 6
Objectives of the Course

The aim of the course is to give some basic concepts of the infinite series and its idea

Course Content

Series and convergence tests for series, types of series, divergent series and summability methods, Cesàro convergence, Abel convergence, Hölder means, relation between the convergence and summability methods, relation between summability methods, the basic Tauberian theorems for Cesàro and Abel methods.

Name of Lecturer(s)
Lec. Muhammet Ali OKUR
Learning Outcomes
1.Ability to comprehend the basic topics of series
2.Ability to clasify the series by convergence tests
3.Ability to comprehend some series types
4.Ability to understand the classification of infinite series
5.Ability to comprehend the Tauberian theorems
Recommended or Required Reading
1.Konrad Knopp, “Infinite Sequences and Series”, Dover Publications, 1956
2.Godfrey H. Hardy, “Divergent Series”, AMS Chelsea Publishing, (Second Edition 1991)
Weekly Detailed Course Contents
Week 1 - Theoretical
Series and general properties of series
Week 2 - Theoretical
Numerical Series
Week 3 - Theoretical
Convergence tests
Week 4 - Theoretical
Function Series
Week 5 - Theoretical
Divergent series, some computes related with divergent series
Week 6 - Theoretical
Cesàro convergence
Week 7 - Theoretical
Abel convergence
Week 8 - Theoretical
Hölder means (MIDTERM EXAM)
Week 9 - Theoretical
Relation between the methods and convergence
Week 10 - Theoretical
Relation between the methods
Week 11 - Theoretical
Examples
Week 12 - Theoretical
The basic Tauberian theorem for Cesàro method
Week 13 - Theoretical
The basic Tauberian theorem for Abel method
Week 14 - Theoretical
The basic Tauberian theorem for Hölder method
Assessment Methods and Criteria
Type of AssessmentCountPercent
Midterm Examination1%40
Final Examination1%60
Workload Calculation
ActivitiesCountPreparationTimeTotal Work Load (hours)
Lecture - Theory140342
Individual Work140342
Midterm Examination128230
Final Examination134236
TOTAL WORKLOAD (hours)150
Contribution of Learning Outcomes to Programme Outcomes
PÇ-1
PÇ-2
PÇ-3
PÇ-4
PÇ-5
PÇ-6
PÇ-7
PÇ-8
PÇ-9
PÇ-10
PÇ-11
PÇ-12
PÇ-13
PÇ-14
PÇ-15
PÇ-16
PÇ-17
PÇ-18
OÇ-1
3
4
3
4
3
2
OÇ-2
3
4
3
4
3
2
OÇ-3
3
2
4
3
4
3
2
OÇ-4
1
3
2
4
1
OÇ-5
5
1
1
4
3
4
Adnan Menderes University - Information Package / Course Catalogue
2026