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| MAT7201 | Asymptotic Solution of Linear Diff. Sys. | 3+0+0 | ECTS:7.5 | | Year / Semester | Fall Semester | | Level of Course | Third Cycle | | Status | Elective | | Department | DEPARTMENT of MATHEMATICS | | Prerequisites and co-requisites | None | | Mode of Delivery | Face to face | | Contact Hours | 14 weeks - 3 hours of lectures per week | | Lecturer | Prof. Dr. Haskız COŞKUN | | Co-Lecturer | None | | Language of instruction | | | Professional practise ( internship ) | None | | | | The aim of the course: | | To study the asymptotic behaviour of some special differential equations. |
| Programme Outcomes | CTPO | TOA | | Upon successful completion of the course, the students will be able to : | | | | PO - 1 : | learn how the various transformations are used to obtain asymptotic solutions for some differential equations of interest. | 1,3 | 1 | | PO - 2 : | learn that many of the existing asymptotic results can be deduced directly from Levinson theorem | 1,3 | 1 | | CTPO : Contribution to programme outcomes, TOA :Type of assessment (1: written exam, 2: Oral exam, 3: Homework assignment, 4: Laboratory exercise/exam, 5: Seminar / presentation, 6: Term paper), PO : Learning Outcome | | |
| Notation and Fundamental theory, Levinson Theorem, the proof of Levinson's Theorem, Hartman- Wintner theorem, Asymptotically constant systems. Almost asymptotically diagonal system |
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| Course Syllabus | | Week | Subject | Related Notes / Files | | Week 1 | Asymptotically diagonal systems;introduction,notation and basic theory | | | Week 2 | The Levinson theorem,Proof of the Levinson theorem | | | Week 3 | The Hartman-Wintner theorem | | | Week 4 | A pointwise condition on the coefficients | | | Week 5 | Asymptotically constant systems | | | Week 6 | Higher order differential equations | | | Week 7 | Coefficient matrices of Jordan type | | | Week 8 | Two-term differential equations;The second order equation | | | Week 9 | Mid-term exam | | | Week 10 | The Liouville-Green asymptotic formulae,extended Liouville-Green asymptotic formulae | | | Week 11 | The Liouville-Green transformation,equations of Euler type | | | Week 12 | Application of the Hartman-Wintner theorem | | | Week 13 | Higher-order equations,higher-orderequations of Euler type | | | Week 14 | Equations of self-adjoint type; eigenvalues of the same magnitude | | | Week 15 | eigenvalues of different magnitudes | | | Week 16 | End-of-term exam | | | |
| 1 | Eastham,M.S.P.,1989,The asymptotic solution of Linear differential systems, Clarendon press,Oxford | | | |
| 1 | Eastham,M.S.P.,1970, Theory of ordinary differential equations, Van Nostrand Reinhold Comp. London | | | |
| Method of Assessment | | Type of assessment | Week No | Date | Duration (hours) | Weight (%) | | Mid-term exam | 9 | 2/04/2019 | 2 | 50 | | End-of-term exam | 16 | 09/06/2019 | 2 | 50 | | |
| Student Work Load and its Distribution | | Type of work | Duration (hours pw) | No of weeks / Number of activity | Hours in total per term | | Yüz yüze eğitim | 3 | 14 | 42 | | Sınıf dışı çalışma | 8 | 14 | 112 | | Arasınav için hazırlık | 15 | 1 | 15 | | Arasınav | 2 | 1 | 2 | | Ödev | 3 | 4 | 12 | | Kısa sınav | 2 | 1 | 2 | | Dönem sonu sınavı için hazırlık | 30 | 1 | 30 | | Dönem sonu sınavı | 2 | 1 | 2 | | Total work load | | | 217 |
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