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| MAT3003 | Riemann Integrals Dependent on Parameters | 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. Zameddin İSMAİLOV | | Co-Lecturer | As. Prof. Pembe İpek Al | | Language of instruction | Turkish | | Professional practise ( internship ) | None | | | | The aim of the course: | | It is aimed to explain the limit, continuity, differentiation and integrability of definite Riemann integrals depending on the parameter. |
| 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. | 5,6 | 1, | | LO - 2 : | see some problems that arise as a result of mathematical modeling in life sciences. | 5,6 | 1, | | LO - 3 : | solve some mathematical problems in life sciences. | 5,6 | 1, | | LO - 4 : | understand what analysis information is useful for in our daily life. | 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 | | |
| Limit, contunuity, derivation and integral of Riemann inregrals depending of parameter; Gamma and Beta functions.
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| Course Syllabus | | Week | Subject | Related Notes / Files | | Week 1 | Basic Concept and Preliminaries | | | Week 2 | Basic Concept and Preliminaries | | | Week 3 | Limit of definite integrals depending of a parameter | | | Week 4 | Continiuty of definite integrals depending of a parameter a parameter | | | Week 5 | Applications | | | Week 6 | Derivation of definite integrals depending of a parameter | | | Week 7 | Integral of definite integrals depending of a parameter | | | Week 8 | Applications | | | Week 9 | Midterm | | | Week 10 | Uniformly convergence of generalized integrals depending of a parameter | | | Week 11 | Euler Gamma Functions | | | Week 12 | Applications | | | Week 13 | Euler Beta Functions | | | Week 14 | Applications | | | Week 15 | General Applications | | | Week 16 | Final | | | |
| 1 | B. Musayev, K.Koca, N.Mustafayev, 2006; Analiz IV, Seçkin Yayınevi, Ankara. | | | |
| 1 | Murray R.Spiegel,1978; İleri analiz, Ankara . | | | 2 | V.A.Zorich, 2004; Mathematical Analysis 2, Springer . | | | |
| Method of Assessment | | Type of assessment | Week No | Date | Duration (hours) | Weight (%) | | Mid-term exam | 9 | 27.11.2024 | 2 | 50 | | End-of-term exam | 16 | 15.01.2025 | 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 | 5 | 14 | 70 | | Arasınav için hazırlık | 6 | 3 | 18 | | Arasınav | 2 | 1 | 2 | | Dönem sonu sınavı için hazırlık | 12 | 4 | 48 | | Dönem sonu sınavı | 2 | 1 | 2 | | Diğer 1 | 12 | 1 | 12 | | Diğer 2 | 17 | 1 | 17 | | Total work load | | | 225 |
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