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| MATI5030 | Theory of Differential Equations | 3+0+0 | ECTS:7.5 | | Year / Semester | Fall Semester | | Level of Course | Second 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 | | | Language of instruction | | | Professional practise ( internship ) | None | | | | The aim of the course: | | The course aims to provide general theory of differential equations, specifically existence and uniqueness theorems, Green functions for initial and bounday value problems. |
| Programme Outcomes | CTPO | TOA | | Upon successful completion of the course, the students will be able to : | | | | PO - 1 : | Learn about existence and uniqueness theorems | 1,2,7,8 | 1 | | PO - 2 : | have some information about Wronskian identity and theory of linear equations | 1,2,7,8 | 1 | | PO - 3 : | have some knowledge of Green functions for initial and bounday value problems | 1,2,7,8 | 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 | | |
| Successive approximations, existence and uniqueness theorems, first order systems, higher order equations, dependence of solutions on parameters and initial values, construction of fundamental sets, the wronskian identity, extension of the variation of constants method, Green functions for initial and boundary value problems. |
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| Course Syllabus | | Week | Subject | Related Notes / Files | | Week 1 | General theory of ode's | | | Week 2 | Successive approximations | | | Week 3 | Existence and uniqueness theorems | | | Week 4 | Continuation of solutions, some related examples | | | Week 5 | Maximal çözüm aralığı, başlangıç verilerine sürekli bağımlılık | | | Week 6 | Existence and uniqueness for linear systems | | | Week 7 | The construction of fundamental sets | | | Week 8 | The wronksian identity, nonhomogeneous systems | | | Week 9 | Mid-term exam | | | Week 10 | Extension of variation of constants method | | | Week 11 | One-sided Greens functions for initial value problems | | | Week 12 | Boundary-value problems | | | Week 13 | Green functions for bounday value problems | | | Week 14 | Physical interpretations of Green functions | | | Week 15 | Some examples related to Green functions | | | Week 16 | End of term exam | | | |
| Method of Assessment | | Type of assessment | Week No | Date | Duration (hours) | Weight (%) | | Mid-term exam | 9 | 13/11/2017 | 2 | 50 | | End-of-term exam | 16 | 2/1/2018 | | 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 | 4 | 14 | 56 | | Arasınav için hazırlık | 10 | 1 | 10 | | Arasınav | 2 | 1 | 2 | | Dönem sonu sınavı için hazırlık | 15 | 1 | 15 | | Dönem sonu sınavı | 2 | 1 | 2 | | Total work load | | | 127 |
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