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| MATI5170 | Applied Partial Differential Equations | 3+0+0 | ECTS:7.5 | | Year / Semester | Spring Semester | | Level of Course | Second Cycle | | Status | Elective | | Department | DEPARTMENT of MATHEMATICS | | Prerequisites and co-requisites | None | | Mode of Delivery | Face to face | | Contact Hours | 14 weeks - 3 hours of lectures per week | | Lecturer | Prof. Dr. Erhan COŞKUN | | Co-Lecturer | | | Language of instruction | | | Professional practise ( internship ) | None | | | | The aim of the course: | | The course aims to provide general background on mathematical models arising from physics, chemistry, biology and engineering that can be formulated in the form of partial differential equations and introduce basic analytical methods for obtaining solutions with appropriate initial and boundary conditions. |
| Programme Outcomes | CTPO | TOA | | Upon successful completion of the course, the students will be able to : | | | | PO - 1 : | analyse mathematical models in the form of partial differential equations that arise in science and engineering | 1,2,3,4 | 1,3, | | CTPO : Contribution to programme outcomes, TOA :Type of assessment (1: written exam, 2: Oral exam, 3: Homework assignment, 4: Laboratory exercise/exam, 5: Seminar / presentation, 6: Term paper), PO : Learning Outcome | | |
| Transition from ODE's to PDE's. Linearity vs nonlinearity, Classification of second-order linear equations, reduction to canonical form and general solutions, D'Alembert solution of wave equation, Advection equation on infinite and semi-infinite domain, A review from Sturm-Liouville Theory, A review of Fourier series, Separation of variables, Diffusion equation on a finite problem, Wave equation on a finite domain, Laplace equation on a finite domain. |
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| Course Syllabus | | Week | Subject | Related Notes / Files | | Week 1 | Basic concepts, ODE vs PDE, order, linearity,equations that can be solved using ODE techniques | | | Week 2 | Classification of second-order differential equations and reduction to canonical forms. | | | Week 3 | General solution of some equations, D'Alembert solution of wave equation | | | Week 4 | Advection equation on a finite and infinite domains | | | Week 5 | A review of Sturm-Liouville theory | | | Week 6 | Fourier series | | | Week 7 | Convergence of Fourier series | | | Week 8 | Method of separation of variables and initial-baundary value problems for heat equations | | | Week 9 | Midterm | | | Week 10 | Nonhomogeneous boundary value problems form heat equations | | | Week 11 | Method of separation of variables and initial-baundary value problems for wave equations | | | Week 12 | Nonhomogeneous boundary value problems form wave equations | | | Week 13 | Applications with maxima | | | Week 14 | Nonhomogeneous boundary value problems form laplace equations | | | Week 15 | Applications with maxima | | | Week 16 | Review | | | |
| 1 | Paul DuChateau and David Zachmann, Applied Partial Differential Equations, Dover Publications, Inc., New York, 1989. | | | |
| 1 | Erhan Coşkun, Lineer Kısmi Diferensiyel Denklemlere Giriş, Ders notları, URL:erhancoskun.com.tr | | | |
| Method of Assessment | | Type of assessment | Week No | Date | Duration (hours) | Weight (%) | | Mid-term exam | 9 | 20/04/2022 | 2 | 50 | | End-of-term exam | 16 | 10/06/2022 | | 50 | | |
| Student Work Load and its Distribution | | Type of work | Duration (hours pw) | No of weeks / Number of activity | Hours in total per term | | Yüz yüze eğitim | 3 | 14 | 42 | | Sınıf dışı çalışma | 4 | 14 | 56 | | Arasınav için hazırlık | 10 | 1 | 10 | | Ödev | 2 | 14 | 28 | | Dönem sonu sınavı için hazırlık | 10 | 1 | 10 | | Dönem sonu sınavı | 2 | 1 | 2 | | Total work load | | | 148 |
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