Course Unit Code | Course Unit Title | Type of Course Unit | Year of Study | Semester | Number of ECTS Credits | MAT30720121310 | THEORY OF COMPLEX FUNCTIONS-I | Compulsory | 3 | 5 | 5 |
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Level of Course Unit |
First Cycle |
Objectives of the Course |
To teach the basic concepts of complex analysis. |
Name of Lecturer(s) |
Doç. Dr. Erhan SET |
Learning Outcomes |
1 | will develop the right thinking and the ability to comment and students will gain basic knowledge about mathematics. |
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Mode of Delivery |
Formal Education |
Prerequisites and co-requisities |
None |
Recommended Optional Programme Components |
None |
Course Contents |
Algebraic, geometric and topological properties of Complex numbers. Single complex variable functions, transformations, limits and continuity, derivatives, Cauchy-Riemann equations, Analytic functions, Harmonic functions. exponential functions, logarithmic functions, complex powers, trigonometric and hyperbolic functions and their inverse. Complex integrals, contour integration, Cauchy-Goursat theorem, fundamental theorems of integration.
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Weekly Detailed Course Contents |
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1 | Algebraic, geometric and topological properties of Complex numbers. | | | 2 |
Single complex variable functions | | | 3 |
Transformations, limits and continuity, derivatives | | | 4 |
Cauchy-Riemann equations
| | | 5 |
Analytic functions | | | 6 |
Harmonic functions | | | 7 |
Exponential functions, logarithmic functions | | | 8 |
Midterm exam | | | 9 |
Complex powers | | | 10 |
Trigonometric and hyperbolic functions and their inverse | | | 11 |
Complex integrals | | | 12 |
Contour integration | | | 13 |
Cauchy-Goursat theorem | | | 14 |
Fundamental theorems of integration. | | | 15 |
Curves and Curve integrals
| | | 16 | Final exam | | |
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Recommended or Required Reading |
Turgut Başkan, Kompleks fonksiyonlar Teorisi, Uludağ Üniversitesi Yayınları 2000.
R.V. Churchill, Complex Variable and Applications, McGraw-Hill , Inc.
Ali Dönmez, Karmaşık Fonksiyonlar Kuramı, Dicle Üni., 1985
Marsden, J.E., Basic Complex Analysis, W.H.F. and Conpany, 1973.
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Planned Learning Activities and Teaching Methods |
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Assessment Methods and Criteria | |
SUM | 0 | |
SUM | 0 | Yarıyıl (Yıl) İçi Etkinlikleri | 40 | Yarıyıl (Yıl) Sonu Etkinlikleri | 60 | SUM | 100 |
| Language of Instruction | Turkish | Work Placement(s) | None |
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Workload Calculation |
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Midterm Examination | 1 | 1.5 | 1.5 |
Final Examination | 1 | 1.5 | 1.5 |
Attending Lectures | 4 | 14 | 56 |
Self Study | 3 | 14 | 42 |
Individual Study for Homework Problems | 2 | 14 | 28 |
Individual Study for Mid term Examination | 1 | 12 | 12 |
Individual Study for Final Examination | 1 | 12 | 12 |
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Contribution of Learning Outcomes to Programme Outcomes |
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* Contribution Level : 1 Very low 2 Low 3 Medium 4 High 5 Very High |
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