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| MATL7170 | Mathematical Biology | 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 | -- | | Co-Lecturer | | | Language of instruction | | | Professional practise ( internship ) | None | | | | The aim of the course: | | The course aims to analyse population models through appropriate mathematical models that can be expressed as differential equations. |
| Programme Outcomes | CTPO | TOA | | Upon successful completion of the course, the students will be able to : | | | | PO - 1 : | learn how to model population of living species | 1,2,3,4 | 1, | | PO - 2 : | how to carry out qualitative abalysis in additon to obtaining analytical solutions, | 1,2,3,4 | 1, | | PO - 3 : | interprate results of models with respect to biological events. | 1,2,3,4 | 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 | | |
| Continuous population models, growth models,outbreak models, delay models,age distribution,
discrete population models, stability, periodic solutions and bifurcations, discrete delay models,
tumour cell growth, models for interacting populations, predator-prey models, complexity and stability,
parameter domains of stability, competition models, mutualism, general models, threshold phenomena,
reaction kinetics, basic enzyme reactions, nondimesionalisation, Michealis-Menten Kinetics, autocatalysis,
activation and inhibiton, multiple steady states.
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| Course Syllabus | | Week | Subject | Related Notes / Files | | Week 1 | basic concepts in differential equations | | | Week 2 | Continuous growth models | | | Week 3 | Models that allow hunting | | | Week 4 | Delay models | | | Week 5 | Population models with age distribution | | | Week 6 | Discrete population models for a single species | | | Week 7 | Chaos in discrete models | | | Week 8 | Discrete delay models | | | Week 9 | Mid-term | | | Week 10 | Predator-Prey Models | | | Week 11 | General models | | | Week 12 | Discrete growth models for interacting populations | | | Week 13 | Enzyme Kinetics | | | Week 14 | Michaelis-Menten analysis | | | Week 15 | Autocatalysis, activation and inhibition | | | Week 16 | Multiple steady states | | | |
| 1 | Murray, J. D., Mathematical Biology, Springer, 2001 | | | |
| Method of Assessment | | Type of assessment | Week No | Date | Duration (hours) | Weight (%) | | Mid-term exam | 9 | 4/4/2022 | 2 | 50 | | End-of-term exam | 17 | 6/6/2022 | | 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 | 2 | 1 | 2 | | Ödev | 2 | 14 | 28 | | Dönem sonu sınavı için hazırlık | 10 | 1 | 10 | | Dönem sonu sınavı | 2 | 1 | 2 | | Total work load | | | 154 |
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