MATH 443 | Course Introduction and Application Information - Department of Mathematics

Course Name

Biomathematics

Code	Semester	Theory (hour/week)	Application/Lab (hour/week)	Local Credits	ECTS
MATH 443	Fall/Spring	3	0	3	5

Prerequisites	None
Course Language	English
Course Type	Elective
Course Level	First Cycle
Mode of Delivery	face to face
Teaching Methods and Techniques of the Course	Problem Solving Q&A Lecture / Presentation
National Occupation Classification	-
Course Coordinator	Doç. Dr. Sevin GÜMGÜM
Course Lecturer(s)	Doç. Dr. Sevin GÜMGÜM
Assistant(s)	Arş.Gör. Merve KAHRAMAN ARİMAN Arş.Gör. SILA SELENAY KOÇ

Course Objectives	In this course, biological systems will be modeled using ordinary differential equations. The created biological models will be solved using numerical methods. Solutions will be simulated and interpreted using MATLAB.
Learning Outcomes	The students who succeeded in this course; Will be able to model biological phenomena using ordinary differential equations. Will be able to define and model population and disease models. Will be able to use numerical methods. Will be able to analyze biological systems using numerical methods. Will be able to write programs in MATLAB programming language.
Course Description	Applications of ordinary differential equations in biology will be introduced and their solutions will be examined using numerical methods.
Related Sustainable Development Goals

Course Category	Core Courses
	Major Area Courses	X
	Supportive Courses
	Media and Management Skills Courses
	Transferable Skill Courses

Week	Subjects	Related Preparation
1	Linear differential equations: theory and examples, introduction, basic definitions and notation, first-order linear systems	"An Introduction to Mathematical Biology" by Linda J.S.Allen, Pearson, 2006. ISBN-13: 9780130352163
2	Application to population growth models, delay logistic equation	"An Introduction to Mathematical Biology" by Linda J.S.Allen, Pearson, 2006. ISBN-13: 9780130352163
3	Biological applications of differential equations; harvesting a single population, predator-prey models, competiton models	"An Introduction to Mathematical Biology" by Linda J.S.Allen, Pearson, 2006. ISBN-13: 9780130352163
4	Biological applications of differential equations; Disease Models	"An Introduction to Mathematical Biology" by Linda J.S.Allen, Pearson, 2006. ISBN-13: 9780130352163
5	Biological applications of differential equations; Disease Models	"An Introduction to Mathematical Biology" by Linda J.S.Allen, Pearson, 2006. ISBN-13: 9780130352163
6	Biological applications of differential equations; Disease Models	"An Introduction to Mathematical Biology" by Linda J.S.Allen, Pearson, 2006. ISBN-13: 9780130352163
7	Euler method	"Numerical solutions of ordinary differential equations", Kendall Atkinson, Weimin Han, David Stewart, Chapter 2
8	Systems of differential equations	Numerical solutions of ordinary differential equations", Kendall Atkinson, Weimin Han, David Stewart, Chapter 3
9	The backward Euler method and the trapezoidal method	"Numerical solutions of ordinary differential equations", Kendall Atkinson, Weimin Han, David Stewart, Chapter 4
10	The backward Euler method and the trapezoidal method	"Numerical solutions of ordinary differential equations", Kendall Atkinson, Weimin Han, David Stewart, Chapter 4
11	Taylor and Runge–Kutta methods	"Numerical solutions of ordinary differential equations", Kendall Atkinson, Weimin Han, David Stewart, Chapter 5
12	Applications to biological models
13	Applications to biological models
14	Presentations
15	Presentations
16	Final Exam

Course Notes/Textbooks

"An Introduction to Mathematical Biology" by Linda J.S.Allen, Pearson, 2006. ISBN-13: 978-0130352163

Suggested Readings/Materials

"An Invitation to Biomathematics" by Raina Stefanova Robeva, James R. Kirkwood, Robin Lee Davies, Leon Farhy, Boris P. Kovatchev, Academic Press, 1st Edition, 2007. ISBN-13: 978-0120887712

"Numerical solutions of ordinary differential equations", Kendall Atkinson, Weimin Han, David Stewart

Semester Activities	Number	Weigthing
Participation
Laboratory / Application
Field Work
Quizzes / Studio Critiques
Portfolio
Homework / Assignments
Presentation / Jury	1	25
Project	1	25
Seminar / Workshop
Oral Exams
Midterm
Final Exam	1	50
Total

Weighting of Semester Activities on the Final Grade	2	50
Weighting of End-of-Semester Activities on the Final Grade	1	50
Total

Semester Activities	Number	Duration (Hours)	Workload
Theoretical Course Hours (Including exam week: 16 x total hours)	16	3	48
Laboratory / Application Hours (Including exam week: '.16.' x total hours)	16		0
Study Hours Out of Class	14	4	56
Field Work			0
Quizzes / Studio Critiques			0
Portfolio			0
Homework / Assignments			0
Presentation / Jury	1	10	10
Project	1	10	10
Seminar / Workshop			0
Oral Exam			0
Midterms			0
Final Exam	1	26	26
		Total	150

#	Program Competencies/Outcomes	* Contribution Level
#	Program Competencies/Outcomes	1	2	3	4	5
1	To be able to have a grasp of basic mathematics, applied mathematics or theories and applications of statistics.	-	-	-	-	X
2	To be able to use advanced theoretical and applied knowledge, interpret and evaluate data, define and analyze problems, develop solutions based on research and proofs by using acquired advanced knowledge and skills within the fields of mathematics or statistics.	-	-	-	X	-
3	To be able to apply mathematics or statistics in real life phenomena with interdisciplinary approach and discover their potentials.	-	-	-	X	-
4	To be able to evaluate the knowledge and skills acquired at an advanced level in the field with a critical approach and develop positive attitude towards lifelong learning.	-	-	-	-	-
5	To be able to share the ideas and solution proposals to problems on issues in the field with professionals, non-professionals.	-	-	X	-	-
6	To be able to take responsibility both as a team member or individual in order to solve unexpected complex problems faced within the implementations in the field, planning and managing activities towards the development of subordinates in the framework of a project.	-	-	-	-	-
7	To be able to use informatics and communication technologies with at least a minimum level of European Computer Driving License Advanced Level software knowledge.	-	-	-	-	-
8	To be able to act in accordance with social, scientific, cultural and ethical values on the stages of gathering, implementation and release of the results of data related to the field.	-	-	-	-	-
9	To be able to possess sufficient consciousness about the issues of universality of social rights, social justice, quality, cultural values and also environmental protection, worker's health and security.	-	-	-	-	-
10	To be able to connect concrete events and transfer solutions, collect data, analyze and interpret results using scientific methods and having a way of abstract thinking.	-	-	-	-	-
11	To be able to collect data in the areas of Mathematics or Statistics and communicate with colleagues in a foreign language.	-	-	-	-	-
12	To be able to speak a second foreign language at a medium level of fluency efficiently.	-	-	-	-	-
13	To be able to relate the knowledge accumulated throughout the human history to their field of expertise.	-	-	-	-	-