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| MAT3005 | Complex Analysis | 4+0+0 | ECTS:7 | | Year / Semester | Fall Semester | | Level of Course | First Cycle | | Status | Compulsory | | Department | DEPARTMENT of MATHEMATICS | | Prerequisites and co-requisites | None | | Mode of Delivery | | | Contact Hours | 14 weeks - 4 hours of lectures per week | | Lecturer | Doç. Dr. Pembe İPEK AL | | Co-Lecturer | Associate Professor Ali Hikmet Değer | | Language of instruction | Turkish | | Professional practise ( internship ) | None | | | | The aim of the course: | | To introduce complex numbers and complex valued functions with complex variables; To give the concepts of limit, continuity and differentiability for complex valued functions with complex variables; associating them with real values ??and emphasizing their differences; to explain contour integration integrals and Cauhy's Theorems. |
| Learning Outcomes | CTPO | TOA | | Upon successful completion of the course, the students will be able to : | | | | LO - 1 : | make simple arguments concerning limits of real and complex valued functions; show continuity and differentiability in real and complex valued functions; and make simple uses of these | 1,3,5,6 | 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 | | |
| Complex numbers, Topology of the complex plane, Functions of complex variable, Elementary functions. Limit and continuity of complex functions, Analytic functions, Complex integration. Cauchy integral theorems |
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| Course Syllabus | | Week | Subject | Related Notes / Files | | Week 1 | Complex Numbers | | | Week 2 | Fundamental Concepts and Results in Complex Plane
| | | Week 3 | Analitic Geometry in Complex Plane
| | | Week 4 | Topology of the Complex Plane | | | Week 5 | Definition of Complex Functions | | | Week 6 | Definitions of Basic Complex Functions and Their Properties
| | | Week 7 | Depiction of Complex Functions | | | Week 8 | Limit of Complex Functions and Continuity | | | Week 9 | Mid-term exam | | | Week 10 | Derivative of Complex Functions | | | Week 11 | Analytical Functions | | | Week 12 | Harmonic Functions
| | | Week 13 | Integration on Curves | | | Week 14 | Cauchy Theorems and Applications
| | | Week 15 | Applications | | | Week 16 | End-of-term exam | | | |
| 1 | Zill, D. G., Shanahan, P. D. 2013; Kompleks Analiz ve Uygulamaları, Nobel Yayınevi, Ankara. | | | |
| 1 | Marsden, J.E. 1973; Basic Complex Analysis, W.H.F. and Company. | | | 2 | Başkan, T. 2005; Kompleks Fonksiyonlar Teorisi, Nobel Yayınları, Ankara. | | | |
| Method of Assessment | | Type of assessment | Week No | Date | Duration (hours) | Weight (%) | | Mid-term exam | 9 | 11.2024 | 90 dakika | 50 | | End-of-term exam | 16 | 01.2025 | 90 dakika | 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 | 7 | 14 | 98 | | Arasınav için hazırlık | 10 | 1 | 10 | | Arasınav | 2 | 1 | 2 | | Ödev | 20 | 1 | 20 | | Dönem sonu sınavı için hazırlık | 22 | 1 | 22 | | Dönem sonu sınavı | 2 | 1 | 2 | | Total work load | | | 210 |
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