| EUROPEAN UNION RELATIONS | |||||
| Bachelor | TR-NQF-HE: Level 6 | QF-EHEA: First Cycle | EQF-LLL: Level 6 | ||
| Course Code | Course Name | Semester | Theoretical | Practical | Credit | ECTS |
| MAT4051 | Advanced Complex Analysis | Spring | 3 | 0 | 3 | 6 |
| This catalog is for information purposes. Course status is determined by the relevant department at the beginning of semester. |
| Language of instruction: | English |
| Type of course: | Non-Departmental Elective |
| Course Level: | Bachelor’s Degree (First Cycle) |
| Mode of Delivery: | Face to face |
| Course Coordinator : | |
| Recommended Optional Program Components: | There is none. |
| Course Objectives: | To study advanced studies and applications in the theory of functions of a complex variable. |
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The students who have succeeded in this course; Grap residue theorem and its applications in evaluation of reel integrals Explain general principles of theory of conformal mappings. Grab Laplace and Fourier Transforms. |
| Concept of Residue, Residue Theorem. Applications of Residue Theorem to Real Integrals. Argument Principle, Rouche and Hurwitz Theorems. Infınıte Products, Weierstrass Formula. Representation Entire and Meromorphic Functions as an Infınıte Product, Mittag-Leffler Formula. Concept of Analytic Continuity, Analytic Continuity of an Analytic Function. Weierstrass Method of Analytic Continuity. General Principle of Conformal Mappings. Riemann Mapping Theorem. Riemann-Schwarz Symmetry Principle, Christoffel-Schwarz Formula. Functions Denoted by Cauchy Kernel. Regularity of an Integral Depending on a Parameter. Laplace Transform. Fourier Transform. |
| Week | Subject | Related Preparation |
| 1) | Concept of Residue, Residue Theorem. | |
| 2) | Applications of Residue Theorem to Real Integrals. | |
| 3) | Argument Principle, Rouche and Hurwitz Theorems. | |
| 4) | Infınıte Products, Weierstrass Formula. | |
| 5) | Representation Entire and Meromorphic Functions as an Infınıte Product, Mittag-Leffler Formula. | |
| 6) | Concept of Analytic Continuity, Analytic Continuity of an Analytic Function. | |
| 7) | Weierstrass Method of Analytic Continuity. | |
| 8) | General Principle of Conformal Mappings. | |
| 9) | Riemann Mapping Theorem. | |
| 10) | Riemann-Schwarz Symmetry Principle, Christoffel-Schwarz Formula. | |
| 11) | Functions Denoted by Cauchy Kernel. | |
| 12) | Regularity of an Integral Depending on a Parameter. | |
| 13) | Laplace Transform. | |
| 14) | Fourier Transform. |
| Course Notes / Textbooks: | A.I. Markushevich “Theory of Functions of a Complex Variable” Ruel V. Churchill, James Ward Brown, “Complex variables and applications” |
| References: | . |
| Semester Requirements | Number of Activities | Level of Contribution |
| Attendance | 16 | % 0 |
| Homework Assignments | 7 | % 10 |
| Midterms | 2 | % 50 |
| Final | 1 | % 40 |
| Total | % 100 | |
| PERCENTAGE OF SEMESTER WORK | % 60 | |
| PERCENTAGE OF FINAL WORK | % 40 | |
| Total | % 100 | |
| Activities | Number of Activities | Duration (Hours) | Workload |
| Course Hours | 14 | 3 | 42 |
| Study Hours Out of Class | 14 | 2 | 28 |
| Homework Assignments | 7 | 2 | 14 |
| Midterms | 2 | 10 | 20 |
| Final | 1 | 21 | 21 |
| Total Workload | 125 | ||
| No Effect | 1 Lowest | 2 Low | 3 Average | 4 High | 5 Highest |
| Program Outcomes | Level of Contribution | |
| 1) | To be able to examine, interpret data and assess ideas with the scientific methods in the area of EU studies. | 2 |
| 2) | To be able to inform authorities and institutions in the area of EU studies, to be able to transfer ideas and proposals supported by quantitative and qualitative data about the problems. | 2 |
| 3) | To be introduced to and to get involved in other disciplines that EU studies are strongly related with (political science, international relations, law, economics, sociology, etc.) and to be able to conduct multi-disciplinary research and analysis on European politics. | 3 |
| 4) | To be able to evaluate current news on European Union and Turkey-EU relations and identify, analyze current issues relating to the EU’s politics and policies. | 2 |
| 5) | To be able to use English in written and oral communication in general and in the field of EU studies in particular. | 1 |
| 6) | To have ethical, social and scientific values throughout the processes of collecting, interpreting, disseminating and implementing data related to EU studies. | 1 |
| 7) | To be able to assess the historical development, functioning of the institutions and decision-making system and common policies of the European Union throughout its economic and political integration in a supranational framework. | 2 |
| 8) | To be able to evaluate the current legal, financial and institutional changes that the EU is going through. | 2 |
| 9) | To explain the dynamics of enlargement processes of the EU by identifying the main actors and institutions involved and compare previous enlargement processes and accession process of Turkey. | 2 |
| 10) | To be able to analyze the influence of the EU on political, social and economic system of Turkey. | 2 |
| 11) | To acquire insight in EU project culture and to build up project preparation skills in line with EU format and develop the ability to work in groups and cooperate with peers. | 2 |
| 12) | To be able to recognize theories and concepts used by the discipline of international relations and relate them to the historical development of the EU as a unique post-War political project. | 3 |