OPTICIANRY (TURKISH) | |||||
Associate | TR-NQF-HE: Level 5 | QF-EHEA: Short Cycle | EQF-LLL: Level 5 |
Course Code: | MAT2062 | ||||||||
Ders İsmi: | Differential Equations | ||||||||
Ders Yarıyılı: | Spring | ||||||||
Ders Kredileri: |
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Language of instruction: | English | ||||||||
Ders Koşulu: | |||||||||
Ders İş Deneyimini Gerektiriyor mu?: | No | ||||||||
Type of course: | Non-Departmental Elective | ||||||||
Course Level: |
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Mode of Delivery: | Face to face | ||||||||
Course Coordinator : | Dr. Öğr. Üyesi GÜLSEMAY YİĞİT | ||||||||
Course Lecturer(s): | |||||||||
Course Assistants: |
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. |
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. |
The students who have succeeded in this course;
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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. |
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. |
Ders Öğrenme Kazanımları | ||||||||
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Program Outcomes | ||||||||
1) The student acquires theoretical and practical knowledge related to his field at a basic level. | ||||||||
2) The student owns information about moral discipline and ethical rules related to his field. | ||||||||
3) The student uses theoretical and practical knowledge related to his field at a basic level; basic fundamental computer programs and related technologies. | ||||||||
4) The student manages a duty independently by using the knowledge about his field at a basic level. | ||||||||
5) The student evaluates the knowledge about his field at a basic level with a critical approach, he designates his learning needs and directs his learning. | ||||||||
6) The student uses information and communication technologies with at least at basic level of European Computer Using Licence basic level of computer software which his field of study requires. | ||||||||
7) The student complies with and contributes to quality management and processes. | ||||||||
8) The student has sufficient consciousness about individual and public health, environmental protection and work safety issues. | ||||||||
9) The student acts in accordance with laws, regulations, legislations and professional ethics related to individual duties, rights and responsibilities. |
No Effect | 1 Lowest | 2 Low | 3 Average | 4 High | 5 Highest |
Program Outcomes | Level of Contribution | |
1) | The student acquires theoretical and practical knowledge related to his field at a basic level. | |
2) | The student owns information about moral discipline and ethical rules related to his field. | |
3) | The student uses theoretical and practical knowledge related to his field at a basic level; basic fundamental computer programs and related technologies. | |
4) | The student manages a duty independently by using the knowledge about his field at a basic level. | |
5) | The student evaluates the knowledge about his field at a basic level with a critical approach, he designates his learning needs and directs his learning. | |
6) | The student uses information and communication technologies with at least at basic level of European Computer Using Licence basic level of computer software which his field of study requires. | |
7) | The student complies with and contributes to quality management and processes. | |
8) | The student has sufficient consciousness about individual and public health, environmental protection and work safety issues. | |
9) | The student acts in accordance with laws, regulations, legislations and professional ethics related to individual duties, rights and responsibilities. |
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 |