GAZI UNIVERSITY INFORMATION PACKAGE - 2019 ACADEMIC YEAR

COURSE DESCRIPTION
SPECTRAL ANALYSİS OF NON-SELFADJOİNT DİFFERENTİAL OPERATORS/6091305
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 operator
To comprehend the difference between singular and regular differential operators
To define selfadjoint, non-selfadjoint differential operators
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
NO
 PROGRAM LEARNING OUTCOMES
1
2
3
4
5
1To be able to develop their knowledge of theory and applications at master degree depending on the competencies acquired in undergraduate level.X
2To be able to recognize different problems encountered in mathematics and to be able to make studies for their solutions.X
3To be able to formulate new solutions with scientific methods mostly based on analysis and synthesis.X
4To be able to carry out his/her works either independently or in groups within a project considering his/her knowledge on the field he/she works in a critical approach.X
5To be able to continue his/her works considering social, scientific and ethical values.X
6To be able to follow scientific and social developments related to his/her field.X
7To be able to carry out his/her works within the framework of quality management, workplace safety and environmental awareness and to be able to present systematically his/her works using various methods like written, oral or visual.X
8To be able to use methods of accessing knowledge effectively in accordance with ethical values.X
9To be able to use knowledge in other disciplines by combining it with mathematical information.X
10To be able to make activities in the awareness of need for lifelong learning.X
11To be able to make connections between mathematical and social concepts and produce solutions with scientific methods.X
12To be able to use his/her mathematical knowledge in technology.X