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
FMA716	INTRODUCTION TO LINEAR OPERATOR THEORY	Compulsory	1	2	6

Level of Course Unit

Third Cycle

Objectives of the Course

Teaching the properties of some classes of linear operators. Teaching the bases of the spectral theory of linear operators.

Name of Lecturer(s)

Learning Outcomes

1	Explain the properties of linear operators (bounded, unbounded, compact, closed, self-adjoint, symmetric etc.)
2	Constructing the adjoint operators of bounded and unbounded operators.
3	Explain the extension of a linear operator.
4	Explain the bases of the spectral theory of linear operators.

Mode of Delivery

Formal Education

Prerequisites and co-requisities

None

Recommended Optional Programme Components

None

Course Contents

Linear bounded operator and its spectrum. Compact operator. Closed operator. The closed graph theorem. Symmetric operator. The extension of a symmetric operator. The principle of minimax for self adjoint operators.

Weekly Detailed Course Contents

Week	Theoretical	Practice	Laboratory
1	Linear bounded operator
2	Bounded self-adjoint operator
3	The spectrum of a bounded operator
4	Compact operator. The spectrum of a compact operator
5	Unbounded operator
6	Closed operator. The closed graph theorem
7	Adjoint operator. The adjoint of an unbounded operator
8	Midterm Exam
9	The spectrum of an unbounded operator
10	Criterions for self-adjointness
11	The classification of spectrum of a self-adjoint operator
12	An extension of a symmetric operator
13	Self-adjoint operator and quadratic form
14	The principle of minimax for self adjoint operators
15	Limit spectrum. Wale’s theorem
16	Final exam

Recommended or Required Reading

1) Akhiezer N.I., Glazman I.M., “Theory of linear operators in Hilbert space”, Moskova, 1966 2) Birman M.S., Solomyak M.Z., “Spectral Theory of Self-Adjoint Operators in Hilbert Space”, Leningrad, 1980

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
Question-Answer	14	1	14
Individual Study for Homework Problems	14	4	56
Individual Study for Mid term Examination	1	30	30
Individual Study for Final Examination	1	30	30
TOTAL WORKLOAD (hours)			176

Contribution of Learning Outcomes to Programme Outcomes

	PO 1	PO 2	PO 3	PO 4	PO 5	PO 6	PO 7
LO1
LO2
LO3
LO4

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