Ordu University Lifelong Learning Programme

Description of Individual Course Units

Course Unit Code	Course Unit Title	Type of Course Unit	Year of Study	Semester	Number of ECTS Credits
FMA612	DIVERGENT SERIES	Compulsory	1	1	6

Level of Course Unit

Second Cycle

Objectives of the Course

To gain the necessary basic information in the field of Divergent Series and Summability Theory.

Name of Lecturer(s)

Learning Outcomes

1	To have the ability and knowledge of the advanced level of related to the field and use it in real learning environments.

Mode of Delivery

Formal Education

Prerequisites and co-requisities

None

Recommended Optional Programme Components

None

Course Contents

Some special summability methods such as Cesaro, Hölder, weighted mean, Riesz, Norlund and Hausdorff methods and relations between them, Summability methods defined by power series, Tauberian theorems, Tauberian theorems for Cesaro, Riesz and power series methods, O-Tauberian theorems for Abel and Borel methods of Hardy-Littlewood.

Weekly Detailed Course Contents

Week	Theoretical	Practice	Laboratory
1	Some special summability methods such as Cesaro, Hölder, weighted mean, Riesz, Norlund and Hausdorff methods and relations between them
2	Some special summability methods such as Cesaro, Hölder, weighted mean, Riesz, Norlund and Hausdorff methods and relations between them
3	Some special summability methods such as Cesaro, Hölder, weighted mean, Riesz, Norlund and Hausdorff methods and relations between them
4	Some special summability methods such as Cesaro, Hölder, weighted mean, Riesz, Norlund and Hausdorff methods and relations between them
5	Some fundamental problems of summability theory such as Tauberian theory, inclusion and consistency theorems
6	Some fundamental problems of summability theory such as Tauberian theory, inclusion and consistency theorems
7	Some fundamental problems of summability theory such as Tauberian theory, inclusion and consistency theorems
8	Midterm exam
9	Summability methods defined by power series. Tauberian theorems
10	Summability methods defined by power series. Tauberian theorems. Matrix methods
11	Tauberian theorems
12	Tauberian theorems for Cesaro, Riesz and power series methods
13	Tauberian theorems for Cesaro, Riesz and power series methods
14	O-Tauberian theorems for Abel and Borel methods of Hardy-Littlewood
15	O-Tauberian theorems for Abel and Borel methods of Hardy-Littlewood
16	Final exam

Recommended or Required Reading

1) G. H. Hardy, Divergent Series (AMS Chelsea Publishing) Hardcover – November 1, 1992. 2) J. Boos, P. Cass, Classical and modern methods in summability, Oxford: Oxford University Press, 2000.

Planned Learning Activities and Teaching Methods

Assessment Methods and Criteria

Term (or Year) Learning Activities	Quantity	Weight
SUM		0
End Of Term (or Year) Learning Activities	Quantity	Weight
SUM		0
Yarıyıl (Yıl) İçi Etkinlikleri		40
Yarıyıl (Yıl) Sonu Etkinlikleri		60
SUM		100

Language of Instruction

Turkish

Work Placement(s)

None

Workload Calculation

Activities	Number	Time (hours)	Total Work Load (hours)
Midterm Examination	1	2	2
Final Examination	1	2	2
Attending Lectures	14	3	42
Problem Solving	14	1	14
Self Study	14	4	56
Individual Study for Homework Problems	14	1	14
Individual Study for Mid term Examination	1	25	25
Individual Study for Final Examination	1	25	25
TOTAL WORKLOAD (hours)			180

Contribution of Learning Outcomes to Programme Outcomes

	PO 1	PO 2	PO 3	PO 4	PO 5	PO 6	PO 7
LO1

* Contribution Level : 1 Very low 2 Low 3 Medium 4 High 5 Very High