ECTS - Mathematical Models in Biology
Mathematical Models in Biology (MATH670) Course Detail
| Course Name | Course Code | Season | Lecture Hours | Application Hours | Lab Hours | Credit | ECTS |
|---|---|---|---|---|---|---|---|
| Mathematical Models in Biology | MATH670 | Area Elective | 3 | 0 | 0 | 3 | 5 |
| Pre-requisite Course(s) |
|---|
| N/A |
| Course Language | English |
|---|---|
| Course Type | Elective Courses |
| Course Level | Ph.D. |
| Mode of Delivery | Face To Face |
| Learning and Teaching Strategies | Lecture, Discussion. |
| Course Lecturer(s) |
|
| Course Objectives | The aim of the course is to describe the application of mathematical theory in difference and differential equations to biological phenomena. No knowledge of biology, and only basic knowledge in calculus, differential equations and linear algebra are required. The use of mathematics in biological sciences will be analyzed by using several mathematical models of biological systems |
| Course Learning Outcomes |
The students who succeeded in this course;
|
| Course Content | Linear and nonlinear biological models via difference equations; linear and nonlinear biological models via differential equations; special topics in mathematical biology including predator-prey models, SI,SIS,SIR epidemic models, competition models of two and three species, Van Der Pol equation, Hodgkin-Huxley and FitzHugh-Nagumo models. |
Weekly Subjects and Releated Preparation Studies
| Week | Subjects | Preparation |
|---|---|---|
| 1 | Linear difference equations: Basic definitions, first order equations, second order and higher-order equations | 1-14 |
| 2 | Linear difference equations: Firs-order linear systems; Leslie’s age-structure model; properties of Leslie matrix | 14-28 |
| 3 | Nonlinear difference equations: Basic definitions; Local stability in first-order equations | 36-45 |
| 4 | Nonlinear difference equations: A discrete-time SIR epidemic model | 69-73 |
| 5 | Biological applications of difference equations: Population models, Nicholson-Bailey model, predatory-prey model | 89-96, 99-103 |
| 6 | Linear ordinary differential equations: Routh-Hurwitz criteria, phase-plane analysis, Gershgorin’s theorem, Pharmacokinetics model | 150-152, 157-165 |
| 7 | Nonlinear ordinary differential equations: Basic definitions, local stability of first-order equations, | 177-184 |
| 8 | Midterm | |
| 9 | Nonlinear ordinary differential equations: Phase-Line diagram, local stability of first-order systems, | 184-191 |
| 10 | Nonlinear ordinary differential equations: Phase plane analysis, Periodic solutions | 191-198 |
| 11 | Biological applications of differential equations: Predatory-prey model | 240-248 |
| 12 | Biological applications of differential equations: Competitions models for two and three species | 248-253 |
| 13 | Biological applications of differential equations: Epidemic models (SI,SIS,SIR models) | 271-279 |
| 14 | Biological applications of differential equations: Excitable systems (Van Der Pol equation, Hodgkin-Huxley and FitzHugh-Nagumo models) | 279-283 |
| 15 | Review | |
| 16 | Final |
Sources
| Course Book | 1. L.J.S. Allen, An Introduction to Mathematical Biology, Pearson, 2006 |
|---|---|
| 2. J. D. Murray, Mathematical Biology I. An Introduction ,Third Edition, Springer , 2001 | |
| 3. G. Vries, J. Müller, T. Hillen, B. Schönfisch, M. Lewis, A Course of Mathematical Biology: Quantitative modelling with mathematical and computational methods, SIAM, 2006 |
Evaluation System
| Requirements | Number | Percentage of Grade |
|---|---|---|
| Attendance/Participation | - | - |
| Laboratory | - | - |
| Application | - | - |
| Field Work | - | - |
| Special Course Internship | - | - |
| Quizzes/Studio Critics | - | - |
| Homework Assignments | 3 | 10 |
| Presentation | 1 | 10 |
| Project | 1 | 10 |
| Report | - | - |
| Seminar | - | - |
| Midterms Exams/Midterms Jury | 1 | 30 |
| Final Exam/Final Jury | 1 | 40 |
| Toplam | 7 | 100 |
| Percentage of Semester Work | 60 |
|---|---|
| Percentage of Final Work | 40 |
| Total | 100 |
Course Category
| Core Courses | X |
|---|---|
| Major Area Courses | |
| Supportive Courses | |
| Media and Managment Skills Courses | |
| Transferable Skill Courses |
The Relation Between Course Learning Competencies and Program Qualifications
| # | Program Qualifications / Competencies | Level of Contribution | ||||
|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | ||
| 1 | Alanında, bağımsız olarak, bir problem kurgulayabilir, çözüm yöntemi geliştirerek problemi çözebilir ve sonuçları değerlendirebilir | X | ||||
| 2 | Matematiğin temel alanlarında ve kendi uzmanlığı olarak seçtiği alanda gerekli alt yapıyı oluşturur. | X | ||||
| 3 | Matematik literatürünü ve özel olarak kendi araştırma konusu ile ilgili ulusal ve uluslararası güncel yayınları takip edebilir ve bunlardan kendi araştırma konusu ile ilgili olanları çalışmalarında kullanabilir | X | ||||
| 4 | Bilimsel etik değerleri ve kuralları dikkate alır ve mesleki ve toplumsal yaşamda kullanabilir | X | ||||
| 5 | Kendi çalışmalarının sonuçlarını veya belli bir konudaki güncel çalışmaları ve bulguları, çeşitli bilimsel toplantılarda topluluk önünde Türkçe ve İngilizce olarak sunabilir ve tartışmalara katılabilir. | X | ||||
| 6 | Gerek bireysel, gerek bir çalışma grubunun üyesi olarak çalışabilme becerisini geliştirir | X | ||||
| 7 | Yaratıcı ve eleştirel düşünme, problem çözme, özgün bir çalışma üretme becerisini geliştirir. Bilimsel gelişmeleri takip eder, özümsediği bilgilerin analiz, sentez ve değerlendirmesini yapabilir. | X | ||||
| 8 | Kazandığı bilgi, beceri ve yetkinlikleri yaşam boyu geliştirmeye açık olur. | X | ||||
| 9 | Alanında özümsediği bilgiyi ve problem çözme yeteneğini disiplinler arası çalışmalarda uygulayabilir; karşılaşılan problemleri matematiksel modellerle ifade ederek, matematiksel bakış açısı ile farklı çözüm yöntemleri önerir. | X | ||||
| 10 | Matematik temelli yazılımları, bilişim ve iletişim teknolojilerini bilimsel amaçlı kullanabilir. | X | ||||
ECTS/Workload Table
| Activities | Number | Duration (Hours) | Total Workload |
|---|---|---|---|
| Course Hours (Including Exam Week: 16 x Total Hours) | 16 | 3 | 48 |
| Laboratory | |||
| Application | |||
| Special Course Internship | |||
| Field Work | |||
| Study Hours Out of Class | 14 | 3 | 42 |
| Presentation/Seminar Prepration | 1 | 3 | 3 |
| Project | 1 | 4 | 4 |
| Report | |||
| Homework Assignments | 3 | 2 | 6 |
| Quizzes/Studio Critics | |||
| Prepration of Midterm Exams/Midterm Jury | 1 | 10 | 10 |
| Prepration of Final Exams/Final Jury | 1 | 12 | 12 |
| Total Workload | 125 | ||