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| MAT4021 | Numerical Solutions of Differential Equations | 4+0+0 | ECTS:6 | | Year / Semester | Fall Semester | | Level of Course | First Cycle | | Status | Elective | | 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. ERHAN COŞKUN, | | Language of instruction | Turkish | | Professional practise ( internship ) | None | | | | The aim of the course: | | The course aims to provide students with a general knowledge on numerical methods for initial and boundary value problems for ordinary and partial differential equations, and develop skills needed to choose and implement the right numerical method for a given problem. |
| Learning Outcomes | CTPO | TOA | | Upon successful completion of the course, the students will be able to : | | | | LO - 1 : | learn about the numerial methods used for initial and/or boundary value problems | | | | LO - 2 : | analyse weak and strong aspects of various mathods and choose and implement the right method for a given problem | | | | 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 | | |
| Mathematical models as initial value and/or boundary value problems; need for numerical methods, Initial value problems; single step methods (derivation, convergence analysis and implementation) (Euler, Trapezoidal, Runge-Kutta) , Multistep methods(explicit and implicit methods). Boundary-value problems: finite difference, shooting method; Difference methods and stability analysis for parabolic, ellliptic and hyperbolic equations. Implementations with MATLAB GUI |
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| Course Syllabus | | Week | Subject | Related Notes / Files | | Week 1 | Basics of MATLAB | | | Week 2 | Numerical Derivative and error | | | Week 3 | Single step methods and error analysis(Euler Methods) | | | Week 4 | Taylor and Runge-Kutta methods | | | Week 5 | Multistep methods(Explicit and Implicit Methods) | | | Week 6 | Predictor-Corrector Methods | | | Week 7 | MATLAB implementations | | | Week 8 | Finite difference methods for boundary-value problems | | | Week 9 | Mid-term exam | | | Week 10 | Shooting method and approximation methods(Galerkin's Method) | | | Week 11 | Finite difference methods for parabolic equations | | | Week 12 | Error and stability analysis, Pdepe ile uygulamalar | | | Week 13 | Finite difference methods for elliptic equations | | | Week 14 | Finite difference methods for hyperbolic equations | | | Week 15 | Stability analysis and implementations | | | Week 16 | End-of-term exam | | | |
| 1 | Coşkun, Erhan, MATLAB/Octave ile Sonlu Fark yöntemleri. URL: erhancoskun.com.tr | | | |
| Method of Assessment | | Type of assessment | Week No | Date | Duration (hours) | Weight (%) | | Mid-term exam | 9 | 20/11/2021 | 1 | 50 | | End-of-term exam | 1 | 15/01/2022 | 1 | 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 | 6 | 14 | 84 | | Arasınav için hazırlık | 5 | 1 | 5 | | Arasınav | 2 | 1 | 2 | | Kısa sınav | .15 | 4 | .6 | | Dönem sonu sınavı için hazırlık | 10 | 1 | 10 | | Dönem sonu sınavı | 2 | 1 | 2 | | Total work load | | | 159.6 |
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