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| MAT7173 | Mathematical Modelling | 3+0+0 | ECTS:7.5 | | Year / Semester | Spring 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 | Doç. Dr. Muhammet YAZICI | | Co-Lecturer | None | | Language of instruction | Turkish | | Professional practise ( internship ) | None | | | | The aim of the course: | | The course aims to provide students the basic knowledge and skills required to model various phenomenon of interest and analyse the resulting models with theoretical and numerical tools. |
| Programme Outcomes | CTPO | TOA | | Upon successful completion of the course, the students will be able to : | | | | PO - 1 : | analyse simple models | 1 - 3 | 1 | | PO - 2 : | remove some assumptions of the simple models and thus obtain relatively generalized models | 1 - 3 | 1 | | PO - 3 : | Model and analyse various problems of interest | 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 | | |
| Simple dynamical systems, Stability of dynamical systems, Models based on conservation of mass(Population models, Pollution in Rivers, Highway traffic),
Models with multiple scales(Zeeman pumping Heart model, Insects and trees, The erath's magnetic field), Chaos |
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| Course Syllabus | | Week | Subject | Related Notes / Files | | Week 1 | Simple Dynamic Models | | | Week 2 | Stability of Dynamic Models | | | Week 3 | Models based on conservation of mass-I(Population models) | | | Week 4 | Models based on conservation of mass-I(Pollution in rivers, Highway traffic) | | | Week 5 | Models based on conservation of momentum(Tidal dynamics) | | | Week 6 | Travelling wave solutions | | | Week 7 | A review | | | Week 8 | Mid-term exam | | | Week 9 | Limit cycles | | | Week 10 | Bifurcation analysis | | | Week 11 | Models with multiscales | | | Week 12 | Models with boundary layers and asymptotic expansions | | | Week 13 | Matched asymptotic expansions | | | Week 14 | Perturbation methods(regular perturbation) | | | Week 15 | Perturbation methods(singular perturbation) | | | Week 16 | End-of-term exam | | | |
| 1 | Beltrami, Edward, 1997, Mathematics for Dynamic Modelling, Academic Press | | | |
| 1 | Sam Howison, 2005, Practical Applied Mathmatics(Modelling, Analysis and approximation), Cambridge University Press. | | | |
| Method of Assessment | | Type of assessment | Week No | Date | Duration (hours) | Weight (%) | | Mid-term exam | 9 | 7/04/2020 | 2 | 30 | | Quiz | 4
6
12
14 | | | 20 | | End-of-term exam | 16 | 04/06/2020 | 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 | 5 | 14 | 70 | | Arasınav için hazırlık | 40 | 1 | 40 | | Arasınav | 2 | 1 | 2 | | Kısa sınav | 2 | 1 | 2 | | Dönem sonu sınavı için hazırlık | 40 | 1 | 40 | | Dönem sonu sınavı | 2 | 1 | 2 | | Total work load | | | 198 |
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