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
FMA605	FUNCTIONAL ANALYSIS I	Compulsory	1	1	6

Level of Course Unit

Second Cycle

Objectives of the Course

• to gain the basic information necessary in the field of functional analysis

Name of Lecturer(s)

Yrd. Doç. Dr. Erdal ÜNLÜYOL

Learning Outcomes

1	Alanı ile ilgili ileri düzeyde alan bilgisine, becerisine sahip olmak ve bunu gerçek öğretim ortamlarında kullanmak

Mode of Delivery

Formal Education

Prerequisites and co-requisities

None

Recommended Optional Programme Components

None

Course Contents

• Basic Concepts of normed spaces • Hahn-Banach theorem • Uniform Boundedness Theorem • Open Conversion Theorem • Closed Graph Theorem • Banach Fixed Point Theorem and application of this theorem to linear, Differential and Integral Equations • Spectral Theory of Linear Operators in Normed Spaces • Resolvent and Spectrum Properties • Banach Algebras and Properties

Weekly Detailed Course Contents

Week	Theoretical	Practice	Laboratory
1	Basic Concepts of normed spaces
2	Hahn-Banach theorem
3	Uniform Boundedness Theorem
4	Open Conversion Theorem
5	Closed Graph Theorem
6	Banach Fixed Point Theorem and application of this theorem to linear, Differential and Integral Equations
7	Banach Fixed Point Theorem and bu Application of this theorem to linear, Differential and Integral Equations
8	Midterm exam
9	Spectral Theory of Linear Operators in Normed Spaces
10	Spectral Theory of Linear Operators in Normed Spaces
11	Paracompactness of Metric Spaces
12	Resolvent and Spectrum Properties
13	Resolvent and Spectrum Properties
14	Banach Algebras and Properties
15	Banach Algebras and Properties
16	Final exam

Recommended or Required Reading

1 Yuli Eidelman, Vitali D.Milman, Antonis Tsolomitis; Functional Analysis: An introduction, American Mathematical Society Other References 1 Reed, M. and Simon, Nad B. 1972;Methods of Modern Mathematical Physics. 1. Functional Analysis, Academic Press, New York

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
Makeup Examination	1	2	2
Attending Lectures	15	3	45
Problem Solving	8	5	40
Discussion	8	5	40
Self Study	10	4	40
Individual Study for Mid term Examination	8	5	40
Individual Study for Final Examination	8	5	40
TOTAL WORKLOAD (hours)			251

Contribution of Learning Outcomes to Programme Outcomes

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

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