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| MAT3010 | Partial Differential Equations | 4+0+0 | ECTS:7 | | Year / Semester | Spring Semester | | Level of Course | First Cycle | | Status | Compulsory | | Department | DEPARTMENT of MATHEMATICS | | Prerequisites and co-requisites | None | | Mode of Delivery | | | Contact Hours | 14 weeks - 4 hours of lectures per week | | Lecturer | Prof. Dr. Erhan COŞKUN | | Co-Lecturer | PROF. Dr. Haskız Coşkun, Prof. Dr. Selçuk Han Aydın, Dr. Lecturer Pelin Şenel, Dr. Lecturer Elif Başkaya | | Language of instruction | Turkish | | Professional practise ( internship ) | None | | | | The aim of the course: | | This course aims to provide the students with the basic concepts and solution methods for linear partial differential equations with emphasis on second-order equations, in particular, diffusion, Laplace, Poisson and wave equations. The course allows for students to establish the relation between physical problems and mathematical models associated with them. |
| Learning Outcomes | CTPO | TOA | | Upon successful completion of the course, the students will be able to : | | | | LO - 1 : | learn about the basics concepts and solution techniques of Linear Partial Differential Equations. | 4,5,6,7 | 1, | | LO - 2 : | formulate well-defined mathematical models within the scope of the course. | 3,4,5,6 | 1, | | LO - 3 : | solve first and second-order linear Partial differential equations and interperate the solutions in the context of physical problems associated with them. | 3,4,5,6 | 1, | | 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), LO : Learning Outcome | | |
| Basic concepts, First order linear partial differential equations and solutions with the method of characteristics, Cauchy problems for first-order equations(existence and uniqueness). Method of characteristics for second-order linear differential equations in two variables. D'Alembert solution of the wave equation. Separation of variables. Fourier series, Boundary value problems, eigenvalues and eigenfuctions. Fourier series solution of homogeneous and nonhomogeneous Diffusion, Laplace, Poisson and Wave equations. |
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| Course Syllabus | | Week | Subject | Related Notes / Files | | Week 1 | Basic concepts(order, dimension, linearity, homogeneity), First and second-order equations, solutions by ODE methods. | | | Week 2 | Method of characteristics for first-order equations | | | Week 3 | Method of characteristics for second-order equtions and D'Alembert solution of wave equation | | | Week 4 | Solution by the method of separation of variables. | | | Week 5 | Boundary value problems, eigenvalues and eigenfunctions | | | Week 6 | Fourier series of periodic functions, cosine and sine series,convergence of the series | | | Week 7 | Convergence of series, general periods and intervals | | | Week 8 | Review | | | Week 9 | midterm exam | | | Week 10 | One dimensional difussion problem on a bounded interval with Dirichlet boundary conditions, | | | Week 11 | One dimensional difussion problem on a bounded interval with Neumann boundary conditions, | | | Week 12 | Nonhomogeneous diffusion problems and eigenfunction expansion method. | | | Week 13 | Wave equation | | | Week 14 | Laplace equation | | | Week 15 | Poisson equation | | | Week 16 | final exam | | | |
| 1 | Coşkun, E. Lineer Kısmi Diferensiyel Denklemlere giriş(Maxima Uygulamalı), erhancoskun.com.tr | | | |
| 1 | Andrews, L. Elementary Partial Differental Equations with Boundary value Problems, Academic Press, 1986. | | | |
| Method of Assessment | | Type of assessment | Week No | Date | Duration (hours) | Weight (%) | | Mid-term exam | 9 | | 2 | 30 | | Quiz | 4
7
12
14 | | | 20 | | End-of-term exam | 16 | | 2 | 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 | 4 | 14 | 56 | | Sınıf dışı çalışma | 8 | 14 | 112 | | Arasınav için hazırlık | 10 | 1 | 10 | | Arasınav | 2 | 1 | 2 | | Dönem sonu sınavı için hazırlık | 20 | 1 | 20 | | Dönem sonu sınavı | 2 | 1 | 2 | | Total work load | | | 202 |
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