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| MAT3026 | Difference Equations | 4+0+0 | ECTS:6 | | Year / Semester | Spring Semester | | Level of Course | First Cycle | | Status | Elective | | Department | DEPARTMENT of MATHEMATICS | | Prerequisites and co-requisites | None | | Mode of Delivery | Face to face | | Contact Hours | 14 weeks - 4 hours of lectures per week | | Lecturer | Prof. Dr. Haskız COŞKUN | | Co-Lecturer | | | Language of instruction | Turkish | | Professional practise ( internship ) | None | | | | The aim of the course: | | This course aims to provide students learning the basic concepts related to difference equations, understanding the difference between the differential eequations and difference equations, describing the discrete problems as difference equations. |
| Learning Outcomes | CTPO | TOA | | Upon successful completion of the course, the students will be able to : | | | | LO - 1 : | Learns that the difference between the differential equations and difference equations | 4,5,6,7 | 1,3, | | LO - 2 : | Learns that the difference equations are a numerical methods approach to getting approximate solutions to differential equations | 4,5,6,7 | 1,3, | | LO - 3 : | learns that the difference equations can be used to model discrete problems. | 4,5,6,7 | 1,3, | | 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), LO : Learning Outcome | | |
| First order linear dfference equations. Second order linear difference equations; constant coefficient homogeneous difference equations, constant coefficient non-homogeneous difference equations, variable coefficient homogeneous difference equations,variable coefficient non-homogeneous difference equations. Applications of difference equations.Higher order linear difference equations.Systems of first order difference equations |
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| Course Syllabus | | Week | Subject | Related Notes / Files | | Week 1 | introduction; Notation and basic concepts | | | Week 2 | First order difference equations | | | Week 3 | Second order linear difference equations, the constant coefficient homogeneous difference equations | | | Week 4 | The constant coefficient non-homogeneous difference equations,undetermined coefficient method | | | Week 5 | The variable coefficient homogeneous difference equations,reduction of order | | | Week 6 | The variable coefficient non-homogeneous difference equations | | | Week 7 | Second order difference equations,linear algebra | | | Week 8 | Overview | | | Week 9 | Midterm | | | Week 10 | Higher order linear difference equations | | | Week 11 | Systems of difference equations,basic theory | | | Week 12 | Second order difference equations as a system | | | Week 13 | Further results on matrix powers, Putzer's Algorithm | | | Week 14 | Stability | | | Week 15 | Overview | | | Week 16 | Final exam | | | |
| 1 | Elaydi, Saber.1999;An introduction to difference equations,Springer,USA | | | |
| Method of Assessment | | Type of assessment | Week No | Date | Duration (hours) | Weight (%) | | Mid-term exam | 9 | 10/11/2023 | 2 | 50 | | End-of-term exam | 16 | 17/01/2024 | 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 | 4 | 14 | 56 | | Sınıf dışı çalışma | 6 | 14 | 84 | | Arasınav için hazırlık | 10 | 1 | 10 | | Arasınav | 2 | 1 | 2 | | Ödev | 2 | 4 | 8 | | Dönem sonu sınavı için hazırlık | 15 | 1 | 15 | | Dönem sonu sınavı | 2 | 1 | 2 | | Total work load | | | 177 |
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