GAZI UNIVERSITY INFORMATION PACKAGE - 2019 ACADEMIC YEAR

COURSE DESCRIPTION

SPECTRAL ANALYSİS OF NON-SELFADJOİNT DİFFERENTİAL OPERATORS/6371305

Course Title:	SPECTRAL ANALYSİS OF NON-SELFADJOİNT DİFFERENTİAL OPERATORS
Credits	3	ECTS	7.5
Semester	1	Compulsory/Elective	Elective

COURSE INFO

-- LANGUAGE OF INSTRUCTION

Turkish

-- NAME OF LECTURER(S)

Assoc. Prof. Esra Kır Arpat

-- WEB SITE(S) OF LECTURER(S)

websitem.gazi.edu.tr/site/esrakir

-- EMAIL(S) OF LECTURER(S)

esrakir@gazi.edu.tr

-- LEARNING OUTCOMES OF THE COURSE UNIT

To define of differential equation system
To define
To comprehend spectral analysis

-- MODE OF DELIVERY

The mode of delivery of this course is Face to face

-- PREREQUISITES AND CO-REQUISITES

There is no prerequisite or co-requisite for this course.

-- RECOMMENDED OPTIONAL PROGRAMME COMPONENTS

There is no recommended optional programme component for this course.

--COURSE CONTENT
1. Week	To define a differential operator produced by a differential equation
2. Week	To find solutions of a differential equation
3. Week	To calculate asymptotic relations provided by solutions
4. Week	To find discrete spectrum of a differential operator
5. Week	To calculate resolvent of a differential operator
6. Week	To find spectral singularities of a differential operator
7. Week	To calculate continuous spectrum of a differential operator
8. Week	Mid-Term Exam
9. Week	To prove the finiteness of eigenvalue and spectral singularities sentence
10. Week	To prove the finiteness of the multiples of eigenvalue and spectral singularities
11. Week	To prove eigen functions corresponding to eigen values belong to a known Hilbert Space
12. Week	To prove main functions corresponding to spectral singularities belong to another Hilber Space
13. Week	To prepare spectral expansion formula
14. Week	To prove spectral expansion formula
15. Week	To show convergence of spectral expansion formula
16. Week	Final Exam

-- RECOMMENDED OR REQUIRED READING

M.A.Naimark, Differential Operators I-II

-- PLANNED LEARNING ACTIVITIES AND TEACHING METHODS

Lecture, Question & Answer, Demonstration, Drill - Practise

-- WORK PLACEMENT(S)

None

-- ASSESSMENT METHODS AND CRITERIA

	Quantity	Percentage
Mid-terms	1	30
Assignment	2	10
Exercises	0	0
Projects	0	0
Practice	0	0
Quiz	0	0
Contribution of In-term Studies to Overall Grade		40
Contribution of Final Examination to Overall Grade		60

-- WORKLOAD

Efficiency	Total Week Count	Weekly Duration (in hour)	Total Workload in Semester
Theoretical Study Hours of Course Per Week	14	3	42
Practising Hours of Course Per Week			0
Reading	10	5	50
Searching in Internet and Library	10	6	60
Designing and Applying Materials			0
Preparing Reports			0
Preparing Presentation			0
Presentation			0
Mid-Term and Studying for Mid-Term	1	10	10
Final and Studying for Final	1	20	20
Other	2	5	10
TOTAL WORKLOAD:			192
TOTAL WORKLOAD / 25:			7.68
ECTS:			7.5

-- COURSE'S CONTRIBUTION TO PROGRAM

Gazi University