| MATHEMATICS (TURKISH, PHD) | |||||
| PhD | TR-NQF-HE: Level 8 | QF-EHEA: Third Cycle | EQF-LLL: Level 8 | ||
| Course Code | Course Name | Semester | Theoretical | Practical | Credit | ECTS |
| MAT4060 | Mathematical Biology | Fall | 3 | 0 | 3 | 6 |
| The course opens with the approval of the Department at the beginning of each semester |
| Language of instruction: | En |
| Type of course: | Departmental Elective |
| Course Level: | |
| Mode of Delivery: | Face to face |
| Course Coordinator : | Dr. Öğr. Üyesi TUĞCAN DEMİR |
| Course Objectives: | This course introduces many mathematical models in biology. To use the mathematical tools like difference equations, differential equations, probability theory to model various biological phenomena, and also understand the basic analytical method based on calculus and algebra, qualitative analysis based on elementary geometry and computer aid numerical method to completely analize some basic models. These mathematical tools will be useful for life sciences major students in any quantitative and qualitative analysis in the future. Biological applications include various population growth models. |
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The students who have succeeded in this course; The students who succeeded in this course; will be able to understand conceptual and visual representation of biological models. will be able to understand population models and analyze them. will be able to analyze data in biological applications. will be able to understand dynamic systems in biology. will be able to linearize biological nonlinear models and determine the stability. |
| Biological applications of difference and differantial equations. Biological applications of nonlinear differantial equations. Stability and applications. Bifurcation and applications. |
| Week | Subject | Related Preparation | |
| 1) | Basic definitions and notations | ||
| 2) | Mathematical models | ||
| 3) | Difference equations : Lineer, nonlinear | ||
| 4) | Biological Applications of Difference Equations | ||
| 5) | Discrete time dynamic equations: Cobwebbing method, equilibrium, and stability. | ||
| 6) | Discrete exponential and logistic growth. | ||
| 7) | Nonlinear difference equations. | ||
| 8) | Bifrucation theory | ||
| 9) | Review | ||
| 10) | Biological applications of differentail equations. | ||
| 11) | Predator-Prey models | ||
| 12) | Routh-Hurwitz criteria and applications. | ||
| 13) | Epidemic models, Genetics models. | ||
| 14) | Nonlinear differential equations and biologic models, periodic solution, Poincare-Bendixon Theorem. | ||
| Course Notes: | 1-An Introduction to Mathematical Biology, Linda J.S.Allen, Pearson, 2007. 2-Mathematical Biology, J. d. Murray, Springer-Verlag, Second, corrected edition, 1993. |
| References: |
| Semester Requirements | Number of Activities | Level of Contribution |
| Attendance | % 0 | |
| Laboratory | % 0 | |
| Application | % 0 | |
| Field Work | % 0 | |
| Special Course Internship (Work Placement) | % 0 | |
| Quizzes | % 0 | |
| Homework Assignments | % 0 | |
| Presentation | % 0 | |
| Project | 1 | % 20 |
| Seminar | % 0 | |
| Midterms | 1 | % 30 |
| Preliminary Jury | % 0 | |
| Final | 1 | % 50 |
| Paper Submission | % 0 | |
| Jury | % 0 | |
| Bütünleme | % 0 | |
| Total | % 100 | |
| PERCENTAGE OF SEMESTER WORK | % 30 | |
| PERCENTAGE OF FINAL WORK | % 70 | |
| Total | % 100 | |
| Activities | Number of Activities | Duration (Hours) | Workload |
| Course Hours | 14 | 3 | 42 |
| Laboratory | 0 | 0 | 0 |
| Application | 0 | 0 | 0 |
| Special Course Internship (Work Placement) | 0 | 0 | 0 |
| Field Work | 0 | 0 | 0 |
| Study Hours Out of Class | 3 | 10 | 30 |
| Presentations / Seminar | 0 | 0 | 0 |
| Project | 1 | 10 | 10 |
| Homework Assignments | 0 | 0 | 0 |
| Quizzes | 0 | 0 | 0 |
| Preliminary Jury | 0 | ||
| Midterms | 1 | 5 | 5 |
| Paper Submission | 0 | ||
| Jury | 0 | ||
| Final | 1 | 13 | 13 |
| Total Workload | 100 | ||
| No Effect | 1 Lowest | 2 Low | 3 Average | 4 High | 5 Highest |
| Program Outcomes | Level of Contribution |