| Course Unit Code | Course Unit Title | Type of Course Unit | Year of Study | Semester | Number of ECTS Credits | | MEY132 | Optional Topics in Differential Equations | Elective | 1 | 2 | 6 |
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| Level of Course Unit |
| Second Cycle |
| Objectives of the Course |
| The aim of this course is to comprehend ordinary differential equations from mathematical and physical aspects. |
| Name of Lecturer(s) |
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| Learning Outcomes |
| 1 | Knows the basic concepts. | | 2 | Learns First Order Differential Equations and Applications. | | 3 | Knows Higher Order Linear Differential Equations with Constant and Variable Coefficients. | | 4 | Learns Higher Order Nonlinear Differential Equations. | | 5 | Solves Systems of Linear Differential Equations. | | 6 | Finds series solutions. |
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| Mode of Delivery |
| Normal Education |
| Prerequisites and co-requisities |
| - |
| Recommended Optional Programme Components |
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| Course Contents |
| Basic Concepts, First Order Differential Equations and Applications, Higher Order Linear Differential Equations with Constant and Variable Coefficients, Higher Order Nonlinear Differential Equations, Systems of Linear Differential Equations, Series Solutions |
| Weekly Detailed Course Contents |
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| 1 | Basic Concepts: Definition of differential equation, classification, solution of a differential equation | | | | 2 | First Order Differential Equations: Separable Equations, Homogeneous Equations, Linear Equations | | | | 3 | First Order Differential Equations: Bernoulli's Equation, Exact differential equations, Integral Multiplier, Ricatti Equation | | | | 4 | Applications of First Order Differential Equations: Orthogonal trajectories, Increase and Decrease, Cooling, Applications of nonlinear equations | | | | 5 | First Order and Higher Order Differential Equations | | | | 6 | Some Higher Order Nonlinear Differential Equations | | | | 7 | Higher Order Linear Differential Equations | | | | 8 | Mıd Exam | | | | 9 | Solutions of Linear Equations, Linear Homogeneous Equations | | | | 10 | Undefined Constants Method, Changing Constants Method | | | | 11 | Cauchy-Euler Differential Equation | | | | 12 | Applications of Second Order Differential Equations | | | | 13 | Systems of Differential Equations: Examples of Systems, Operator Method, First Order Systems, First Order Linear Systems, Matrix Formulation | | | | 14 | Systems of Differential Equations: Simple Theory of First Order Linear Systems, Eigenvalue-Eigenvector Method for Solutions of First Order Linear Systems with Constant Coefficients | | | | 15 | Fınal Exam | | |
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| Recommended or Required Reading |
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| Planned Learning Activities and Teaching Methods |
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| Assessment Methods and Criteria | |
| Midterm Examination | 1 | 100 | | SUM | 100 | |
| Final Examination | 1 | 100 | | SUM | 100 | | Term (or Year) Learning Activities | 40 | | End Of Term (or Year) Learning Activities | 60 | | SUM | 100 |
| | Language of Instruction | | | Work Placement(s) | |
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| Workload Calculation |
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| Midterm Examination | 1 | 1 | 1 |
| Final Examination | 1 | 2 | 2 |
| Brain Storming | 10 | 2 | 20 |
| Self Study | 20 | 3 | 60 |
| Individual Study for Mid term Examination | 1 | 10 | 10 |
| Individual Study for Final Examination | 4 | 15 | 60 |
| Homework | 9 | 3 | 27 |
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| Contribution of Learning Outcomes to Programme Outcomes |
| LO1 | 4 | 5 | 5 | 5 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | | LO2 | 4 | 4 | 4 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | | LO3 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 4 | 4 | | LO4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 5 | 5 | 5 | 5 | 4 | 4 | | LO5 | 4 | 4 | 4 | 5 | 5 | 5 | 4 | 4 | 4 | 4 | 5 | 5 | 5 | 5 | | LO6 | 5 | 5 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 |
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| * Contribution Level : 1 Very low 2 Low 3 Medium 4 High 5 Very High |
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