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| MATL7980 | Green' s Functions | 3+0+0 | ECTS:7.5 | | Year / Semester | Spring 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 | Dr. Öğr. Üyesi Elif BAŞKAYA | | Co-Lecturer | Assistant Professor Ayşe KABATAŞ | | Language of instruction | Turkish | | Professional practise ( internship ) | None | | | | The aim of the course: | | Constructing Green's Function for Initial Value Problems, Constructing Green's Function for Boundary Value Problems, Constructing Green's Function for Laplace's Equation, Constructing Green's Function for Klein-Gordon Equation |
| Programme Outcomes | CTPO | TOA | | Upon successful completion of the course, the students will be able to : | | | | PO - 1 : | Determine the initial and boundary value problems from the second order and use their properties. | 1 | 1,3, | | PO - 2 : | Can perform the construction of Green's function with the standard method. | 1 | 1,3, | | PO - 3 : | Can perform the construction of Green's function with the image method and the conformal mapping method. | 1 | 1,3, | | PO - 4 : | Can perform the construction of Green's function by eigenfunction expansion method. | 1 | 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 | | |
| One-sided Green's Functions for Initial Value Problems; Standard Method for Construction of Green's Function in Boundary Value Problems; Symmetry of Green's Function; Alternative Construction Method for Green's Function; Construction of Green's Function for Laplace's Equation-Image Method; Construction of Green's Function for Laplace's Equation-Compatible Mapping Method; Construction of Green's Function for Laplace's Equation-Eigenfunction Expansion Method; Construction of Green's Function for Klein-Gordon Equation-Image Method; Construction of Green's Function for Klein-Gordon Equation-Eigenfunction Expansion Method |
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| Course Syllabus | | Week | Subject | Related Notes / Files | | Week 1 | Main Definitions and Theorems | | | Week 2 | One-sided Green's Functions for Initial Value Problems | | | Week 3 | Standard Method for Construction of Green's Function in Boundary Value Problems | | | Week 4 | Symmetry of Green's Function | | | Week 5 | Alternative Construction Method for Green's Function | | | Week 6 | Alternative Construction Method for Green's Function | | | Week 7 | Construction of Green's Function for Laplace's Equation-Image Method | | | Week 8 | Construction of Green's Function for Laplace's Equation-Image Method | | | Week 9 | Quiz | | | Week 10 | Construction of Green's Function for Laplace's Equation-Compatible Mapping Method | | | Week 11 | Construction of Green's Function for Laplace's Equation-Compatible Mapping Method | | | Week 12 | Construction of Green's Function for Laplace's Equation-Eigenfunction Expansion Method | | | Week 13 | Definition of Green's Function for the Klein-Gordon Equation | | | Week 14 | Construction of Green's Function for Klein-Gordon Equation-Image Method | | | Week 15 | Construction of Green's Function for Klein-Gordon Equation-Eigenfunction Expansion Method | | | Week 16 | Final | | | |
| 1 | Melnikon, Yuri A., Melnikov Max Y. 2012; Green's Function Construction and Applications, Walter de Gruyter GmbH & Co. KG, Berlin/Boston | | | |
| 1 | Andrews, Larry C. 1986; Elementary Partial Differential Equations with Boundary Value Problems, Academic Press College Division, Berkeley | | | |
| Method of Assessment | | Type of assessment | Week No | Date | Duration (hours) | Weight (%) | | Mid-term exam | 9 | 18.04.2024 | 3 | 20 | | Quiz | 12 | 09.05.2024 | 3 | 10 | | Homework/Assignment/Term-paper | 4 | 14.03.2024 | 144 | 20 | | End-of-term exam | 16 | 06.06.2024 | 3 | 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 | 5 | 14 | 70 | | Arasınav için hazırlık | 3 | 1 | 3 | | Arasınav | 3 | 1 | 3 | | Ödev | 144 | 1 | 144 | | Kısa sınav | 3 | 1 | 3 | | Dönem sonu sınavı için hazırlık | 3 | 1 | 3 | | Dönem sonu sınavı | 3 | 1 | 3 | | Total work load | | | 271 |
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