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| MAT2012 | Introduction to Complex Analysis | 4+0+0 | ECTS:6 | | Year / Semester | Spring Semester | | Level of Course | First Cycle | | Status | Compulsory | | Department | DEPARTMENT of STATISTICS and COMPUTER SCIENCES | | Prerequisites and co-requisites | None | | Mode of Delivery | Face to face | | Contact Hours | 14 weeks - 4 hours of lectures per week | | Lecturer | Öğr. Gör. Dr Süleyman UZUN | | Co-Lecturer | Ass. Prof. Dr. Meltem Erol | | 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; Residue Theorem 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; | | | | LO - 2 : | use real and complex valued functions in applications | | | | LO - 3 : | calculate Taylor and Laurent expansions and use the calculus of residues to evaluate integrals | | | | 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 Theorem. Cauchy integral theorems. Residues and its applications. |
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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 | Connected Sets and Domains | | | Week 4 | Analitic Geometry in Complex Plane | | | Week 5 | Extended Complex Plane | | | Week 6 | Definition of Complex Functions | | | Week 7 | Definitions of Basic Complex Functions and Their Properties | | | Week 8 | Mid-term exam | | | Week 9 | Sequence of Complex Numbers and Convergence | | | Week 10 | Series of Complex Numbers and Convergence, Power Series and Convergence | | | Week 11 | Limit of Complex Functions and Continuity | | | Week 12 | Differentiablity and Analitcity, Conform Transformations | | | Week 13 | Integration on Curves | | | Week 14 | Cauchy Theorems and Applications | | | Week 15 | Rezidual Theorems and Applications | | | Week 16 | End-of-term exam | | | |
| 1 | Marsden, J.E.,1973; Basic Complex analysis, W.H.F. and Company | | | 2 | Başkan, T., 2005; Kompleks Fonksiyonlar Theorisi, Nobel Yayınları, Ankara | | | |
| Method of Assessment | | Type of assessment | Week No | Date | Duration (hours) | Weight (%) | | Mid-term exam | 9 | 07/04/2015 | 1,5 | 50 | | End-of-term exam | 9 | 27/05/2014 | 1,5 | 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 | 3 | 14 | 42 | | Arasınav için hazırlık | 2 | 2 | 4 | | Arasınav | 2 | 2 | 4 | | Kısa sınav | 1.5 | 1 | 1.5 | | Dönem sonu sınavı için hazırlık | 2 | 3 | 6 | | Dönem sonu sınavı | 2 | 1 | 2 | | Total work load | | | 115.5 |
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