FACULTY OF ENGINEERING

Department of Genetics and Bioengineering

MATH 400 | Course Introduction and Application Information

Course Name
Biomathematics
Code
Semester
Theory
(hour/week)
Application/Lab
(hour/week)
Local Credits
ECTS
MATH 400
Fall/Spring
3
0
3
7

Prerequisites
None
Course Language
English
Course Type
Elective
Course Level
First Cycle
Mode of Delivery -
Teaching Methods and Techniques of the Course Problem Solving
Q&A
Lecture / Presentation
Course Coordinator -
Course Lecturer(s)
Assistant(s)
Course Objectives In this course, how to use basic mathematical concepts such as some basic concepts in analysis and algebra, difference equations, probability theory in different biological cases will be given. On the other hand, qualitative analysis of geometry and numerical computation techniques will be done on computers.
Learning Outcomes The students who succeeded in this course;
  • will be able to analyze models theoretically and visually.
  • will be able to interpret population models.
  • will be able to do biology applications in data analysis.
  • will be able to solve linear or nonlinear dynamic systems.
  • will be able to solve biology problems with graph theory.
Course Description Biological applications of difference and differential equations. Biological applications of nonlinear differential equations. Biological applications of graph theaory.

 



Course Category

Core Courses
Major Area Courses
Supportive Courses
Media and Management Skills Courses
Transferable Skill Courses

 

WEEKLY SUBJECTS AND RELATED PREPARATION STUDIES

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: 978-0130352163 Section 4.1, 4.2, 4.7
2 Phase Analysis, an example: Pharmacokinetics model "An Introduction to Mathematical Biology" by Linda J.S.Allen, Pearson, 2006. ISBN-13: 978-0130352163 Section 4.8, 4.10
3 Application to population growth models, delay logistic equation "An Introduction to Mathematical Biology" by Linda J.S.Allen, Pearson, 2006. ISBN-13: 978-0130352163 Section 5.3, 5.9
4 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: 978-0130352163 Section 6.2, 6.3, 6.4
5 Chemostat model, epidemic models "An Introduction to Mathematical Biology" by Linda J.S.Allen, Pearson, 2006. ISBN-13: 978-0130352163 Section 6.7, 6.8
6 Excitable systems "An Introduction to Mathematical Biology" by Linda J.S.Allen, Pearson, 2006. ISBN-13: 978-0130352163 Section 6.9
7 Reaction-diffusion equation, spread of genes and traveling waves "An Introduction to Mathematical Biology" by Linda J.S.Allen, Pearson, 2006. ISBN-13: 978-0130352163 Section 7.3, 7.6
8 Euler method "Numerical solutions of ordinary differential equations", Kendall Atkinson, Weimin Han, David Stewart, Chapter 2
9 Systems of differential equations "Numerical solutions of ordinary differential equations", Kendall Atkinson, Weimin Han, David Stewart, Chapter 3
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 Applications to biological models
15 Semester Review
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

 

EVALUATION SYSTEM

Semester Activities Number Weigthing
Participation
Laboratory / Application
Field Work
Quizzes / Studio Critiques
Portfolio
Homework / Assignments
Presentation / Jury
1
30
Project
1
30
Seminar / Workshop
Oral Exams
Midterm
Final Exam
1
40
Total

Weighting of Semester Activities on the Final Grade
2
60
Weighting of End-of-Semester Activities on the Final Grade
1
40
Total

ECTS / WORKLOAD TABLE

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
30
30
Project
1
30
30
Seminar / Workshop
0
Oral Exam
0
Midterms
0
Final Exam
1
46
46
    Total
210

 

COURSE LEARNING OUTCOMES AND PROGRAM QUALIFICATIONS RELATIONSHIP

#
Program Competencies/Outcomes
* Contribution Level
1
2
3
4
5
1

To have adequate knowledge in Mathematics, Science and Genetics and Bioengineering; to be able to use theoretical and applied information in these areas on complex engineering problems.

2

To be able to identify, define, formulate, and solve complex Genetics and Bioengineering problems; to be able to select and apply proper analysis and modeling methods for this purpose.

3

To be able to design a complex system, process, device or product under realistic constraints and conditions, in such a way as to meet the requirements; to be able to apply modern design methods for this purpose.

4

To be able to devise, select, and use modern techniques and tools needed for analysis and solution of complex problems in Genetics and Bioengineering applications; to be able to use information technologies effectively.

5

To be able to design and conduct experiments, gather data, analyze and interpret results for investigating complex engineering problems or Genetics and Bioengineering research topics.

6

To be able to work efficiently in Genetics and Bioengineering disciplinary and multi-disciplinary teams; to be able to work individually.

7

To be able to communicate effectively in Turkish, both orally and in writing; to be able to author and comprehend written reports, to be able to prepare design and implementation reports, to present effectively, to be able to give and receive clear and comprehensible instructions.

8

To have knowledge about global and social impact of Genetics and Bioengineering practices on health, environment, and safety; to have knowledge about contemporary issues as they pertain to engineering; to be aware of the legal ramifications of Genetics and Bioengineering solutions.

9

To be aware of ethical behavior, professional and ethical responsibility; to have knowledge about standards utilized in Genetics and Bioengineering applications.

10

To have knowledge about industrial practices such as project management, risk management, and change management; to have awareness of entrepreneurship and innovation; to have knowledge about sustainable development.

11

To be able to collect data in the area of Genetics and Bioengineering, and to be able to 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 recognize the need for lifelong learning; to be able to access information, to be able to stay current with developments in science and technology; to be able to relate the knowledge accumulated throughout the human history to Genetics and Bioengineering.

*1 Lowest, 2 Low, 3 Average, 4 High, 5 Highest

 


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