FACULTY OF ARTS AND SCIENCES
Department of Mathematics
SOCIAL MEDIA
MATH 408 | Course Introduction and Application Information
| Course Name |
Introduction to Spectral Analysis
|
|
Code
|
Semester
|
Theory
(hour/week) |
Application/Lab
(hour/week) |
Local Credits
|
ECTS
|
|
MATH 408
|
Fall/Spring
|
3
|
0
|
3
|
6
|
| Prerequisites |
None
|
|||||
| Course Language |
English
|
|||||
| Course Type |
Elective
|
|||||
| Course Level |
First Cycle
|
|||||
| Mode of Delivery | - | |||||
| Teaching Methods and Techniques of the Course | - | |||||
| Course Coordinator | - | |||||
| Course Lecturer(s) | ||||||
| Assistant(s) | ||||||
| Course Objectives | The objective of this course is to teach the spectral theory of nonselfadjoint differential equations developed by Naimark, Levitan, Lyance and others. |
| Learning Outcomes |
The students who succeeded in this course;
|
| Course Description | This course aims to cover basic theory and applications of spectral analysis. |
|
|
Core Courses | |
| Major Area Courses | ||
| Supportive Courses |
X
|
|
| Media and Management Skills Courses | ||
| Transferable Skill Courses |
WEEKLY SUBJECTS AND RELATED PREPARATION STUDIES
| Week | Subjects | Related Preparation |
| 1 | Introduction and fundamental concepts | "Linear Differential Operators: Two Volumes Bound as One" by M. A. Naimark, Dover Publications, 2014. ISBN-13: 978-0486468976 |
| 2 | Fourier transforms; properties and applications | "Linear Differential Operators: Two Volumes Bound as One" by M. A. Naimark, Dover Publications, 2014. ISBN-13: 978-0486468976 |
| 3 | NonSelfadjoint differential equations | "Linear Differential Operators: Two Volumes Bound as One" by M. A. Naimark, Dover Publications, 2014. ISBN-13: 978-0486468976 |
| 4 | Non-Self adjoint Sturm Liouville differential operator | "Linear Differential Operators: Two Volumes Bound as One" by M. A. Naimark, Dover Publications, 2014. ISBN-13: 978-0486468976 |
| 5 | Solutions and their asymptotic behaviours | "Linear Differential Operators: Two Volumes Bound as One" by M. A. Naimark, Dover Publications, 2014. ISBN-13: 978-0486468976 |
| 6 | Jost solution and Its properties. | "Linear Differential Operators: Two Volumes Bound as One" by M. A. Naimark, Dover Publications, 2014. ISBN-13: 978-0486468976 |
| 7 | A special integral representation for Jost solution | "Linear Differential Operators: Two Volumes Bound as One" by M. A. Naimark, Dover Publications, 2014. ISBN-13: 978-0486468976 |
| 8 | Integral equations | "Linear Differential Operators: Two Volumes Bound as One" by M. A. Naimark, Dover Publications, 2014. ISBN-13: 978-0486468976 |
| 9 | The resolvent operator | "Linear Differential Operators: Two Volumes Bound as One" by M. A. Naimark, Dover Publications, 2014. ISBN-13: 978-0486468976 |
| 10 | Green’s function and its properties | "Linear Differential Operators: Two Volumes Bound as One" by M. A. Naimark, Dover Publications, 2014. ISBN-13: 978-0486468976 |
| 11 | Boundary uniqueness theorems of analytic functions | "Linear Differential Operators: Two Volumes Bound as One" by M. A. Naimark, Dover Publications, 2014. ISBN-13: 978-0486468976 |
| 12 | Beurling and Pavlov theorems, and their applications | "Linear Differential Operators: Two Volumes Bound as One" by M. A. Naimark, Dover Publications, 2014. ISBN-13: 978-0486468976 |
| 13 | Carleson’s theorem, and its applications | "Linear Differential Operators: Two Volumes Bound as One" by M. A. Naimark, Dover Publications, 2014. ISBN-13: 978-0486468976 |
| 14 | Quantitative properties of the spectrum, spectral expansion | "Linear Differential Operators: Two Volumes Bound as One" by M. A. Naimark, Dover Publications, 2014. ISBN-13: 978-0486468976 |
| 15 | Semester Review | |
| 16 | Final Exam |
| Course Notes/Textbooks | "Linear Differential Operators: Two Volumes Bound as One" by M. A. Naimark, Dover Publications, 2014. ISBN-13: 978-0486468976 |
| Suggested Readings/Materials | "Sturm Liouville and Dirac Operators" by B.M. Levitan, I. S. Sargsjan, Springer Netherlands, 1991. Hard Cover ISBN: 978-0-7923-0992-5 |
EVALUATION SYSTEM
| Semester Activities | Number | Weigthing |
| Participation | ||
| Laboratory / Application | ||
| Field Work | ||
| Quizzes / Studio Critiques | ||
| Portfolio | ||
| Homework / Assignments |
5
|
20
|
| Presentation / Jury | ||
| Project | ||
| Seminar / Workshop | ||
| Oral Exams | ||
| Midterm |
1
|
40
|
| Final Exam |
1
|
40
|
| Total |
| Weighting of Semester Activities on the Final Grade |
6
|
60
|
| Weighting of End-of-Semester Activities on the Final Grade |
1
|
40
|
| Total |
ECTS / WORKLOAD TABLE
| Semester Activities | Number | Duration (Hours) | Workload |
|---|---|---|---|
| Theoretical Course Hours (Including exam week: 16 x total hours) |
16
|
3
|
48
|
| Laboratory / Application Hours (Including exam week: '.16.' x total hours) |
16
|
0
|
|
| Study Hours Out of Class |
14
|
3
|
42
|
| Field Work |
0
|
||
| Quizzes / Studio Critiques |
0
|
||
| Portfolio |
0
|
||
| Homework / Assignments |
5
|
6
|
30
|
| Presentation / Jury |
0
|
||
| Project |
0
|
||
| Seminar / Workshop |
0
|
||
| Oral Exam |
0
|
||
| Midterms |
1
|
25
|
25
|
| Final Exam |
1
|
35
|
35
|
| Total |
180
|
COURSE LEARNING OUTCOMES AND PROGRAM QUALIFICATIONS RELATIONSHIP
|
#
|
Program Competencies/Outcomes |
* Contribution Level
|
||||
|
1
|
2
|
3
|
4
|
5
|
||
| 1 | To be able to have a grasp of basic mathematics, applied mathematics or theories and applications of statistics. |
X | ||||
| 2 | To be able to use advanced theoretical and applied knowledge, interpret and evaluate data, define and analyze problems, develop solutions based on research and proofs by using acquired advanced knowledge and skills within the fields of mathematics or statistics. |
X | ||||
| 3 | To be able to apply mathematics or statistics in real life phenomena with interdisciplinary approach and discover their potentials. |
X | ||||
| 4 | To be able to evaluate the knowledge and skills acquired at an advanced level in the field with a critical approach and develop positive attitude towards lifelong learning. |
X | ||||
| 5 | To be able to share the ideas and solution proposals to problems on issues in the field with professionals, non-professionals. |
|||||
| 6 | To be able to take responsibility both as a team member or individual in order to solve unexpected complex problems faced within the implementations in the field, planning and managing activities towards the development of subordinates in the framework of a project. |
|||||
| 7 | To be able to use informatics and communication technologies with at least a minimum level of European Computer Driving License Advanced Level software knowledge. |
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| 8 | To be able to act in accordance with social, scientific, cultural and ethical values on the stages of gathering, implementation and release of the results of data related to the field. |
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| 9 | To be able to possess sufficient consciousness about the issues of universality of social rights, social justice, quality, cultural values and also environmental protection, worker's health and security. |
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| 10 | To be able to connect concrete events and transfer solutions, collect data, analyze and interpret results using scientific methods and having a way of abstract thinking. |
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| 11 | To be able to collect data in the areas of Mathematics or Statistics and communicate with colleagues in a foreign language. |
|||||
| 12 | To be able to speak a second foreign language at a medium level of fluency efficiently. |
|||||
| 13 | To be able to relate the knowledge accumulated throughout the human history to their field of expertise. |
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*1 Lowest, 2 Low, 3 Average, 4 High, 5 Highest
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