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| MATL5032 | Calculus on manifolds | 3+0+0 | ECTS:7.5 | | Year / Semester | Fall Semester | | Level of Course | Second 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 Seda ÖZTÜRK | | Co-Lecturer | | | Language of instruction | Turkish | | Professional practise ( internship ) | None | | | | The aim of the course: | | To examine functions in n-dimensional space. To learn how the concepts of derivative and integral work in n-dimensional Euclidean space.
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| Programme Outcomes | CTPO | TOA | | Upon successful completion of the course, the students will be able to : | | | | PO - 1 : | | 1,2 | 1,6, | | PO - 2 : | | 1,2 | 1,6, | | PO - 3 : | | 1,2 | 1,6, | | PO - 4 : | | 1,2 | 1,6, | | 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 | | |
| Functions on Euclidean space, Derivative, Integral, Integral on chains, Integral on manifolds. |
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| Course Syllabus | | Week | Subject | Related Notes / Files | | Week 1 | Norm and inner product | | | Week 2 | Subset of Euclidean space | | | Week 3 | Functions in Euclidean space | | | Week 4 | Limit and continuity | | | Week 5 | Derivative in Euclidean space | | | Week 6 | Theorems on derivatives | | | Week 7 | Partial derivatives | | | Week 8 | Inverse and implicit functions | | | Week 9 | Midterm Exam | | | Week 10 | Definition of integral in Euclidean space | | | Week 11 | Integrable functions and Fubini's theorem | | | Week 12 | Change of variables and the chain rule for integration | | | Week 13 | Fundamental theorem of analysis and its applications | | | Week 14 | Stokes theorem and its applications
| | | Week 15 | Integration on manifolds and Green's theorem | | | Week 16 | Final Exam | | | |
| 1 | Calculus on manifolds, Michael Spivak, Newyork, 1965. | | | |
| 1 | Calculus, Michael Spivak, Houston-Texas, 1994. | | | |
| Method of Assessment | | Type of assessment | Week No | Date | Duration (hours) | Weight (%) | | Mid-term exam | 9 | 21/11/2024 | 2 | 30 | | Quiz | 11 | 12/12/2024 | 1 | 20 | | End-of-term exam | 16 | 09/01/2025 | 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 | 3 | 14 | 42 | | Sınıf dışı çalışma | 5 | 14 | 70 | | Arasınav için hazırlık | 4 | 8 | 32 | | Arasınav | 2 | 1 | 2 | | Ödev | 4 | 9 | 36 | | Kısa sınav | 1 | 1 | 1 | | Dönem sonu sınavı için hazırlık | 5 | 8 | 40 | | Dönem sonu sınavı | 2 | 1 | 2 | | Total work load | | | 225 |
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