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| MAT3000 | Special functions classes | 4+0+0 | ECTS:6 | | Year / Semester | Spring 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. Zameddin İSMAİLOV | | Co-Lecturer | As.Prof. Dr. Pembe İpek Al | | Language of instruction | Turkish | | Professional practise ( internship ) | None | | | | The aim of the course: | | To present of special functions classes arising in theoretical and applicable sciences |
| Learning Outcomes | CTPO | TOA | | Upon successful completion of the course, the students will be able to : | | | | LO - 1 : | establish a relationship with the problems encountered in physics and mechanics. | | | | LO - 2 : | see some problems that arise as a result of mathematical modeling in life sciences. | | | | LO - 3 : | solve some mathematical problems in life sciences. | | | | LO - 4 : | understand what analysis information is useful for in our daily life. | | | | 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 | | |
| Metric and lineer normed spaces; continuous and continuously differentiable functions; absolutely continuous functions; monotone functions and functions of bounded variation ; classes of Lipschitz and Hölder functions; Riemann- Stieltjes integral. |
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| Course Syllabus | | Week | Subject | Related Notes / Files | | Week 1 | Metric and lineer normed spaces | | | Week 2 | Metric and lineer normed spaces | | | Week 3 | Class of continuous and continuously differentiable functions | | | Week 4 | Class of absolutely continuous functions | | | Week 5 | Monotone functions | | | Week 6 | Functions of bounded variation | | | Week 7 | Functions of bounded variation | | | Week 8 | Applications | | | Week 9 | Midterm exam | | | Week 10 | Functions of bounded variation and monotonicity | | | Week 11 | Class of Lipschitz functions | | | Week 12 | Lineer normed space of Lipschitz functions | | | Week 13 | Lineer normed space of Hölder functions | | | Week 14 | Riemann-Stieljes integral | | | Week 15 | Applications | | | Week 16 | End-of-term exam | | | |
| 1 | Kolmogorov, A.N.,Fomin, F.S. Elements of Theory of functions and Functional Analysis, Courier Dover Publications, 1999, 288p. | | | |
| 1 | Natanson, I.P., Theory of Functions of Real Variables, New York, Ungar, 1955, 277p. | | | 2 | B.Musayev, M.Alp, Fonksiyonel analiz, Kutahya, 2008 | | | |
| Method of Assessment | | Type of assessment | Week No | Date | Duration (hours) | Weight (%) | | Mid-term exam | 9 | 16/04/2022 | 120 | 50 | | End-of-term exam | 16 | 06/06/2022 | 120 | 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 | 8 | 1 | 8 | | Arasınav | 2 | 1 | 2 | | Uygulama | 2 | 14 | 28 | | Dönem sonu sınavı için hazırlık | 10 | 1 | 10 | | Dönem sonu sınavı | 2 | 1 | 2 | | Total work load | | | 190 |
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