| Course Unit Code | Course Unit Title | Type of Course Unit | Year of Study | Semester | Number of ECTS Credits | | MAT42720121310 | MATHEMATICAL MODELING I | Elective | 4 | 7 | 5 |
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| Level of Course Unit |
| First Cycle |
| Objectives of the Course |
| The establishment and solving of mathematical models of real world problems. |
| Name of Lecturer(s) |
| Dr. Canan Çiftçi |
| Learning Outcomes |
| 1 | Students will develop the right thinking and the ability to comment and students will gain basic knowledge about mathematics. |
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| Mode of Delivery |
| Formal Education |
| Prerequisites and co-requisities |
| None |
| Recommended Optional Programme Components |
| None |
| Course Contents |
| Mathematical Models and Boundary Value Problems, One-Dimensional Mathematical Model for Heat Transfer Equation, Weak derivative. Classical and Weak Solutions spaces of Boundary Value Problem related to second order ordinary differential equations. Variational Problem, Variational Numerical Solution, Boundary Value Problems related to Second Order Nonlinear in Ordinary Differential equations. Potential operator, Potential of nonlinear problem, Application to Boundary Value Problems related to the ordinary differential equations, application to elliptic problem, Linearization procedure and approximate solutions, Convergence Theorem and Convergence rate. |
| Weekly Detailed Course Contents |
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| 1 | Mathematical Models and Boundary Value Problems | | | | 2 | One-Dimensional Mathematical Model for Heat Transfer Equation | | | | 3 | Weak derivative | | | | 4 | Classical and Weak Solutions spaces of Boundary Value Problem related to second order ordinary differential equations | | | | 5 | Variational Problem | | | | 6 | Variational Numerical Solution | | | | 7 | Boundary Value Problems related to Second Order Nonlinear in Ordinary Differential equations. | | | | 8 | Midterm exam | | | | 9 | Potential operator | | | | 10 | Potential of nonlinear problem | | | | 11 | Application to Boundary Value Problems related to the ordinary differential equations | | | | 12 | Application to elliptic problem | | | | 13 | Linearization procedure and approximate solutions | | | | 14 | Convergence Theorem and Convergence rate. | | | | 15 | Convergence Theorem and Convergence rate. | | | | 16 | Final exam | | |
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| Recommended or Required Reading |
| DiPrima R.C., Boyce, W.E., Elementary Differential Equations, John Wiley, 1986
Smith, J.M., Models in Ecology, Cambridge Un.Press, 1973. |
| Planned Learning Activities and Teaching Methods |
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| Assessment Methods and Criteria | |
| SUM | 0 | |
| SUM | 0 | | Yarıyıl (Yıl) İçi Etkinlikleri | 40 | | Yarıyıl (Yıl) Sonu Etkinlikleri | 60 | | SUM | 100 |
| | Language of Instruction | | Turkish | | Work Placement(s) | | None |
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| Workload Calculation |
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| Midterm Examination | 1 | 6 | 6 |
| Final Examination | 1 | 6 | 6 |
| Quiz | 3 | 12 | 36 |
| Individual Study for Homework Problems | 3 | 12 | 36 |
| Individual Study for Mid term Examination | 3 | 12 | 36 |
| Individual Study for Final Examination | 3 | 12 | 36 |
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| Contribution of Learning Outcomes to Programme Outcomes |
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| * Contribution Level : 1 Very low 2 Low 3 Medium 4 High 5 Very High |
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