MOLECULAR BIOLOGY AND GENETICS
Bachelor	TR-NQF-HE: Level 6	QF-EHEA: First Cycle	EQF-LLL: Level 6

Course Introduction and Application Information

Course Code	Course Name	Semester	Theoretical	Practical	Credit	ECTS
MAT2062	Differential Equations	Spring	3	0	3	6

This catalog is for information purposes. Course status is determined by the relevant department at the beginning of semester.

Basic information

Language of instruction:	English
Type of course:	Non-Departmental Elective
Course Level:	Bachelor’s Degree (First Cycle)
Mode of Delivery:	Face to face
Course Coordinator :	Dr. Öğr. Üyesi GÜLSEMAY YİĞİT
Course Lecturer(s):	Prof. Dr. NAFİZ ARICA
Recommended Optional Program Components:	None
Course Objectives:	This course covers the fundamental concepts of an introductory level of elementary differential equations with basic concepts, theory, solution methods and applications. Main goal is to develop the basics of modeling at an introductory level and connect this step to the theoretical and methodological resource of mathematics.

Learning Outcomes

The students who have succeeded in this course;
1. Classify differential equations and determine the existence and uniqueness of solutions of Initial Value Problems
2. Solve first order separable and linear differential equations
3. Use substitution methods to solve homogeneous and Bernoulli equations
4. Solve exact differential equations
5. Solve the higher order linear homogeneous and nonhomogeneous differential equations
6. Solve the systems of linear differential equations
7. Solve differential equations by using Laplace transform method

Course Content

In this course basic concepts of elementary differential equations will be covered. The solution techniques for the different types of first order differential equations will be given and the solution methods will be taught. The higher order linear differential equations and solution methods will be discussed. The systems of linear equations will be covered with different techniques. Finally, the Laplace Transform method will be taught to solve linear differential equations.

Weekly Detailed Course Contents

Week	Subject	Related Preparation
1)	Classification of differential equations, Explicit solution, implicit solution, Initial Value Problems, Integrals as General and Particular Solutions.
2)	Existence and Uniqueness of Solution. Separable Differential Equations.
3)	First Order Linear Differential Equations.
4)	Substitutions methods. Homogeneous Differential Equations. Bernoulli Differential Equations.
5)	Exact Differential Equations.
6)	Population models. Reducible second order equations.
7)	Theory of Higher Order Linear Differential Equations, Existence and Uniqueness Theorem, Linear Dependence and Independence, Representation of Solutions for Homogeneous and Nonhomogeneous Cases.
8)	Homogeneous Linear Equations with Constant Coefficients. Euler Equations.
9)	Solution of Nonhomogeneous Linear Differential Equations. Method of Undetermined Coefficients.
10)	Solution of Nonhomogeneous Linear Differential Equations. Method of Variation of Parameters.
11)	Theory of Systems of Linear Differential Equations.
12)	The Eigenvalue Method for Systems of Linear Differential Equations.
13)	Laplace Transforms: Definition of the Laplace Transform, Properties of the Laplace Transform. Inverse Laplace Transform.
14)	Solution of Differential Equations by using Laplace Transform.

Sources

Course Notes / Textbooks:	Differential Equations with Boundary Value Problems by C. Henry Edwards & D. E.Penney, sixth edition
References:	Introduction to Ordinary Differential Equations” by Shepley L. Ross. Fourth Edition, John Wiley and Sons.

Evaluation System

Semester Requirements	Number of Activities	Level of Contribution
Quizzes	2	% 20
Midterms	1	% 35
Final	1	% 45
Total		% 100
PERCENTAGE OF SEMESTER WORK		% 55
PERCENTAGE OF FINAL WORK		% 45
Total		% 100

Contribution of Learning Outcomes to Programme Outcomes

No Effect	1 Lowest	2 Low	3 Average	4 High	5 Highest

	Program Outcomes	Level of Contribution
1)	Utilize the wealth of information stored in computer databases to answer basic biological questions and solve problems such as diagnosis and treatment of diseases.	3
2)	Acquire an ability to compile and analyze biological information, clearly present and discuss the conclusions, the inferred knowledge and the arguments behind them both in oral and written format.	4
3)	Develop critical, creative and analytical thinking skills.	5
4)	Develop effective communication skills and have competence in scientific speaking, reading and writing abilities in English and Turkish.	3
5)	Gain knowledge of different techniques and methods used in genetics and acquire the relevant laboratory skills.	4
6)	Detect biological problems, learn to make hypothesis and solve the hypothesis by using variety of experimental and observational methods.	4
7)	Gain knowledge of methods for collecting quantitative and qualitative data and obtain the related skills.	3
8)	Conduct research through paying attention to ethics, human values and rights. Pay special attention to confidentiality of information while working with human subjects.	5
9)	Obtain basic concepts used in theory and practices of molecular biology and genetics and establish associations between them.	4
10)	Search and use literature to improve himself/herself and follow recent developments in science and technology.	5
11)	Be aware of the national and international problems in the field and search for solutions.	4