EUROPEAN UNION RELATIONS
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 Fall 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) To be able to examine, interpret data and assess ideas with the scientific methods in the area of EU studies. 2
2) To be able to inform authorities and institutions in the area of EU studies, to be able to transfer ideas and proposals supported by quantitative and qualitative data about the problems. 2
3) To be introduced to and to get involved in other disciplines that EU studies are strongly related with (political science, international relations, law, economics, sociology, etc.) and to be able to conduct multi-disciplinary research and analysis on European politics. 3
4) To be able to evaluate current news on European Union and Turkey-EU relations and identify, analyze current issues relating to the EU’s politics and policies. 2
5) To be able to use English in written and oral communication in general and in the field of EU studies in particular. 1
6) To have ethical, social and scientific values throughout the processes of collecting, interpreting, disseminating and implementing data related to EU studies. 1
7) To be able to assess the historical development, functioning of the institutions and decision-making system and common policies of the European Union throughout its economic and political integration in a supranational framework. 2
8) To be able to evaluate the current legal, financial and institutional changes that the EU is going through. 2
9) To explain the dynamics of enlargement processes of the EU by identifying the main actors and institutions involved and compare previous enlargement processes and accession process of Turkey. 2
10) To be able to analyze the influence of the EU on political, social and economic system of Turkey. 2
11) To acquire insight in EU project culture and to build up project preparation skills in line with EU format and develop the ability to work in groups and cooperate with peers. 2
12) To be able to recognize theories and concepts used by the discipline of international relations and relate them to the historical development of the EU as a unique post-War political project. 3