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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 define the field of complex numbers, to introduce complex valued functions of one complex variable; to reintroduce limit; continuity and differentiability for real valued functions of two real variables and to define these for complex valued functions and illustrate the applications of these concepts in the theory of real valued functions of two real variables; to show that many ideas of reel analysis, such as convergence of series, have their most natural setting in the complex analysis and to emphasize difference; contour integration; Cauchy's Theorems; Taylor and Laurent series; ResidueTheorem and Its applications. |
| 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. Functions of complex variable. Elementary functions. Complex sequences and series. 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 | Sequence, Series of Complex Numbers and Convergence | | | 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 | | 2 | 50 | | End-of-term exam | 16 | | 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 | 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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