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Description of Individual Course Units| Course Unit Code | Course Unit Title | Type of Course Unit | Year of Study | Semester | Number of ECTS Credits | | MT304B | Differential Equations | Compulsory | 3 | 6 | 4 |
| | Level of Course Unit | | First Cycle | | Objectives of the Course | | To supply the candidate teachers knowledge about contemporary teaching methods and techniques in science and technology teaching courses. To provide opportunity of using teaching materials or activities which are prepared suitable for these methods and techniques with sample course presentations. | | Name of Lecturer(s) | | Prof. Dr. Rabil AYAZOĞLU | | Learning Outcomes | | 1 | Explain the concept of differential equation | | 2 | Categorise differential equatons | | 3 | Solve initial value problems, first degree linear differential equations | | 4 | Solve homogeneous and complete differential equations. | | 5 | Solve differential equations which are in the type of Bernoulli | | 6 | Solve Riccati and high grade differential equations. |
| | Mode of Delivery | | Normal Education | | Prerequisites and co-requisities | | None | | Recommended Optional Programme Components | | None | | Course Contents | | The concept of differential equation, the classification of the differential equations, Initial value problems, general solutions, Separable differential equations, homogeneous equations, the equations that can be turned into the homogeneous state, total differential equations, the equations that can be turned into the integration multipliers and the total differential equations, primary linear differential equations, Bernoulli and Riccati-type differential equations. Primary high-level equations, secondary level equations not including any one of the variables, the applications of the secondary level differential equations. High-level differential equations and linear differential equations and their solutions. | | Weekly Detailed Course Contents | |
| 1 | The concept of differential equation, the classification of the differential equations | | | | 2 | First order differential equations,existance and uniquieness of solutions,slope fields and solution curves | | | | 3 | Initial value problems, general solutions, Separable Differential equations | | | | 4 | Seperable equations and applications, linear First order equations,Bernoulli equations | | | | 5 | Solution of some nonlinear differential equations,clairaut equations | | | | 6 | Solution of some nonlinear differential equations,clairaut equations | | | | 7 | Mathematical models,population models,equlibrium solutions and stability | | | | 8 | Reduction of order,linear equations of higher order,introduction to second order linear equations | | | | 9 | Midterm exam | | | | 10 | Reduction of order,linear equations of higher order,introduction to second order linear equations | | | | 11 | General solutions of linear equations,homogeneous equations with constant coefficients,some applications,nonhomogeneous equations | | | | 12 | General solutions of linear equations,homogeneous equations with constant coefficients,some applications,nonhomogeneous equations | | | | 13 | Undetermined coefficient and variation of parameters methods,Cauchy Euler equations | | | | 14 | Undetermined coefficient and variation of parameters methods,Cauchy Euler equations | | | | 15 | Application of higher order equations,end point problems and eigenvalues | | | | 16 | Final Exam | | |
| | Recommended or Required Reading | | 1. Doç. Dr. İrfan Baki YAŞAR, Diferensiyel Denklemler ve uygulamaları
2. Prof. Dr. H. Hilmi HACISALİHOĞLU, Diferensiyel Denklemler(Çeviri)
| | Planned Learning Activities and Teaching Methods | | | 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 | | Turkish | | Work Placement(s) | | None |
| | Workload Calculation | |
| Midterm Examination | 1 | 1 | 1 | | Final Examination | 1 | 1 | 1 | | Attending Lectures | 14 | 3 | 42 | | Self Study | 4 | 1 | 4 | | Individual Study for Mid term Examination | 6 | 6 | 36 | | Individual Study for Final Examination | 6 | 6 | 36 | |
| Contribution of Learning Outcomes to Programme Outcomes | | | * Contribution Level : 1 Very low 2 Low 3 Medium 4 High 5 Very High |
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