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
MAT40220121310	FUNCTIONAL ANALYSIS	Compulsory	4	8	5

Level of Course Unit

First Cycle

Objectives of the Course

To introduce the basics of functional analysis .

Name of Lecturer(s)

Yrd. Doç. Dr. Erdal ÜNLÜYOL

Learning Outcomes

1	will develop the right thinking and the ability to comment and students will gain basic knowledge about mathematics.

Mode of Delivery

Formal Education

Prerequisites and co-requisities

None

Recommended Optional Programme Components

None

Course Contents

Metric Spaces, Normed Linear Spaces, Bounded Linear Maps,, Inner Product Spaces, Hilbert Spaces, Fourier Series in Hilbert Spaces, Applications of Fourier Series, Compact and Hermit Operators in Hilbert Spaces

Weekly Detailed Course Contents

Week	Theoretical	Practice	Laboratory
1	Metric spaces, complete metric spaces
2	Compactness of metric spaces
3	Normed linear spaces
4	Banach spaces
5	inner product spaces
6	Hilbert spaces
7	Fourier series in Hilber spaces
8	Midterm exam
9	Applications of Fourier series
10	Topological vector spaces
11	Norm of continuous linear operators on normed spaces
12	Theorem of Banach-Stayhaus
13	Conjugate spaces, conjugate operators and the concept of strong convergence
14	Kompat and Hermitian operators in Hilbert spaces
15	L_p spaces and the space L_{\infty}
16	Final exam

Recommended or Required Reading

1 Hüsnü KIZMAZ, Fonksiyonel ANALYSIS, Karadeniz Teknik Üniversitesi Yayınları 2098. Other Textbook and /or References 2 Yosida K. Functional Analysis, Berlin, 1971 3 Danford N., Schwartz J.T. Lineer operators, New York, 1971 4 Kreyszig E. Introductory functional analysis with application, New York, 1978

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	10	4	40
Self Study	10	3	30
Individual Study for Mid term Examination	10	4	40
Individual Study for Final Examination	10	4	40
TOTAL WORKLOAD (hours)			156

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