| Course Name | Introduction to Spectral Analysis I |
| Code | Semester | Theory (hour/week) | Application/Lab (hour/week) | Local Credits | ECTS |
|---|---|---|---|---|---|
| MATH 407 | 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 | This course aims to provide basic and some further concepts of spectral theory of differential equations such as Sturm Liouville differential equation in regular case and in singular case. |
| Learning Outcomes | The students who succeeded in this course;
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| Course Description | This course aims to cover basic theory and applications of spectral analysis. |
| Related Sustainable Development Goals | |
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| Core Courses | |
| Major Area Courses | ||
| Supportive Courses | X | |
| Media and Managment Skills Courses | ||
| Transferable Skill Courses |
| Week | Subjects | Required Materials |
| 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 | Differential expressions | "Linear Differential Operators: Two Volumes Bound as One" by M. A. Naimark, Dover Publications, 2014. ISBN-13: 978-0486468976 |
| 3 | Boundary conditions | "Linear Differential Operators: Two Volumes Bound as One" by M. A. Naimark, Dover Publications, 2014. ISBN-13: 978-0486468976 |
| 4 | Selfadjoint Sturm Liouville operator | "Linear Differential Operators: Two Volumes Bound as One" by M. A. Naimark, Dover Publications, 2014. ISBN-13: 978-0486468976 |
| 5 | Lagrange formula and its applications | "Linear Differential Operators: Two Volumes Bound as One" by M. A. Naimark, Dover Publications, 2014. ISBN-13: 978-0486468976 |
| 6 | Spectral analysis in regular case | "Linear Differential Operators: Two Volumes Bound as One" by M. A. Naimark, Dover Publications, 2014. ISBN-13: 978-0486468976 |
| 7 | Eigenvalues and eigenvectors | "Linear Differential Operators: Two Volumes Bound as One" by M. A. Naimark, Dover Publications, 2014. ISBN-13: 978-0486468976 |
| 8 | Solutions and their asymptotic behaviours | "Linear Differential Operators: Two Volumes Bound as One" by M. A. Naimark, Dover Publications, 2014. ISBN-13: 978-0486468976 |
| 9 | Integral equations | "Linear Differential Operators: Two Volumes Bound as One" by M. A. Naimark, Dover Publications, 2014. ISBN-13: 978-0486468976 |
| 10 | Asymptotic behaviour of eigenvalues and eigenvectors | "Linear Differential Operators: Two Volumes Bound as One" by M. A. Naimark, Dover Publications, 2014. ISBN-13: 978-0486468976 |
| 11 | The resolvent operator | "Linear Differential Operators: Two Volumes Bound as One" by M. A. Naimark, Dover Publications, 2014. ISBN-13: 978-0486468976 |
| 12 | 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 |
| 13 | A spectral expansion for resolvent | "Linear Differential Operators: Two Volumes Bound as One" by M. A. Naimark, Dover Publications, 2014. ISBN-13: 978-0486468976 |
| 14 | The spectral expansion in eigenvectors, spectral analysis in singular case | "Linear Differential Operators: Two Volumes Bound as One" by M. A. Naimark, Dover Publications, 2014. ISBN-13: 978-0486468976 |
| 15 | Semester Review | |
| 16 | Final Examl |
| 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 |
| Semester Activities | Number | Weigthing |
| Participation | ||
| Laboratory / Application | ||
| Field Work | ||
| Quizzes / Studio Critiques | ||
| Portfolio | ||
| Homework / Assignments | 5 | 20 |
| Presentation / Jury | ||
| Project | ||
| Seminar / Workshop | ||
| Oral Exam | ||
| 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 |
| Semester Activities | Number | Duration (Hours) | Workload |
|---|---|---|---|
| Course Hours (Including exam week: 16 x total hours) | 16 | 3 | 48 |
| Laboratory / Application Hours (Including exam week: 16 x total hours) | 16 | ||
| Study Hours Out of Class | 14 | 3 | 42 |
| Field Work | |||
| Quizzes / Studio Critiques | |||
| Portfolio | |||
| Homework / Assignments | 5 | 6 | |
| Presentation / Jury | |||
| Project | |||
| Seminar / Workshop | |||
| Oral Exam | |||
| Midterms | 1 | 25 | |
| Final Exams | 1 | 35 | |
| Total | 180 |
| # | 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. | |||||
| 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. | |||||
| 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. | |||||
| 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. | |||||
| 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. | |||||
*1 Lowest, 2 Low, 3 Average, 4 High, 5 Highest
