| Course Unit Code | Course Unit Title | Type of Course Unit | Year of Study | Semester | Number of ECTS Credits | | MAT30520121310 | PARTIAL DIFFERENTIAL EQUATIONS | Compulsory | 3 | 5 | 5 |
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| Level of Course Unit |
| First Cycle |
| Objectives of the Course |
| Explain the properties of mathematical models related to PDE and give solution method for PDE. |
| Name of Lecturer(s) |
| Yrd. Doç. Dr. Erdal ÜNLÜYOL |
| Learning Outcomes |
| 1 | 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 |
| Basic concepts, classification and creation of partial differential equations. First order linear and quasi - linear partial differential equations, Lagrange's method, the surface families to perpendicular intersecting, the Cauchy problem. Non-linear first order partial differential equations, Compatible Systems, Charpit method, contrary to the solutions and the surfaces of the envelope. High order linear partial differential equations with constant coefficients, nonhomogeneous equations, operator method, the Euler-type equations. |
| Weekly Detailed Course Contents |
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| 1 | Basic concepts, classification and creation of partial differential equations
| | | | 2 | First order linear and quasi - linear partial differential equations
| | | | 3 | Lagrange's method
| | | | 4 | The surface families to perpendicular intersecting
| | | | 5 | The Cauchy problem
| | | | 6 | Non-linear first order partial differential equations
| | | | 7 | Compatible Systems
| | | | 8 | Midterm exam
| | | | 9 | Charpit method
| | | | 10 | Contrary to the solutions and the surfaces of the envelope
| | | | 11 | High order linear partial differential equations with constant coefficients
| | | | 12 | Nonhomogeneous equations, operator method
| | | | 13 | The Euler-type equations
| | | | 14 | D'Alambert formula and interpretation. D'Alambert formula for non-homogeneous equation
| | | | 15 | Finite interval of separation of variables (Fourier) method
| | | | 16 | Final exam | | |
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| Recommended or Required Reading |
| 1 Kısmi Diferansiyel Denklemler, Kerim KOCA, Nobel Yayıncılık, 2002.
Other Textbook and /or References
2 A. N. Tychonov and A. A. Samarski, Partial Differential Equations of Mathematical Physics, Pergamon, 1964.
3 S. L. Sobolev, Equations of Mahtematical Physics, Moscow, Mir, 1982.
4 S. Lipschutz, Partial differential Equations, Schaum’s Outline Series, McGraw-Hill Pub. Com
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| 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 | 2 | 2 |
| Final Examination | 1 | 2 | 2 |
| Makeup Examination | 1 | 2 | 2 |
| Attending Lectures | 12 | 5 | 60 |
| Problem Solving | 10 | 2 | 20 |
| Self Study | 8 | 5 | 40 |
| Individual Study for Mid term Examination | 8 | 2 | 16 |
| Individual Study for Final Examination | 6 | 2 | 12 |
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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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