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| MATL7120 | Optimization and Stabilization in Numerical Methods | 3+0+0 | ECTS:7.5 | | Year / Semester | Fall Semester | | Level of Course | Third Cycle | | Status | Elective | | Department | DEPARTMENT of MATHEMATICS | | Prerequisites and co-requisites | None | | Mode of Delivery | | | Contact Hours | 14 weeks - 3 hours of lectures per week | | Lecturer | Prof. Dr. Selçuk Han AYDIN | | Co-Lecturer | | | Language of instruction | | | Professional practise ( internship ) | None | | | | The aim of the course: | | In order to gain to basic information about the optimization and stabilization methods |
| Programme Outcomes | CTPO | TOA | | Upon successful completion of the course, the students will be able to : | | | | PO - 1 : | Learns the basic optimization methods | 5,7 | 1,3, | | PO - 2 : | Learns the basic stabilization methods | 5,7 | 1,3, | | PO - 3 : | Improves the computer programming experience | 5,7 | 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 | | |
| Optimization and Stabilization methods |
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| Course Syllabus | | Week | Subject | Related Notes / Files | | Week 1 | Introduction | | | Week 2 | Approximation and convex functions | | | Week 3 | Optimization methods and conditions | | | Week 4 | Golden-Section and Newton methods | | | Week 5 | Trust-Region methods | | | Week 6 | Line search methods | | | Week 7 | Quasi-Newton methods | | | Week 8 | Cojugate-Gradient methods | | | Week 9 | Mid Tearm | | | Week 10 | Basics of the finite difference method | | | Week 11 | Upwind methods | | | Week 12 | Shishkin and Bakhvalov methods | | | Week 13 | Short Exam | | | Week 14 | Basics of the finite element method | | | Week 15 | SUPG and SSM methods | | | Week 16 | Final | | | |
| 1 | Igor Griva, Stephen G. Nash, Ariela Sofer, 2009; Linear and Nonlinear Optimization, Second Edition, SIAM, Society for Industrial and Applied Mathematics, Philadelphia | | | |
| 1 | Jorge Nocedal Stephen J. Wright, 2006; Numerical Optimization, Second Edition, Springer, USA. | | | |
| Method of Assessment | | Type of assessment | Week No | Date | Duration (hours) | Weight (%) | | Mid-term exam | 9 | 09/11/2023 | 120 | 30 | | Homework/Assignment/Term-paper | 5
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15 | 15/10/2023 | 120 | 20 | | End-of-term exam | 16 | 10/01/2024 | | 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 | 13 | 39 | | Sınıf dışı çalışma | 4 | 16 | 64 | | Arasınav için hazırlık | 6 | 1 | 6 | | Arasınav | 2 | 1 | 2 | | Kısa sınav | 1 | 1 | 1 | | Dönem sonu sınavı için hazırlık | 6 | 1 | 6 | | Dönem sonu sınavı | 2 | 1 | 2 | | Total work load | | | 120 |
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