| PSYCHOLOGY | |||||
| 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) | Develop close interest in human mind and behavior, and attain critical thinking skills (in particular the ability to evaluate psychological theories using empirical evidence), as well as appreciating psychology as an evidence based science. | |
| 2) | Gain a biopsychosocial understanding of human behavior, namely, the biological, psychological, social determinants of behavior. | |
| 3) | Acquire theoretical and applied knowledge and learn about basic psychological concepts and perspectives | |
| 4) | Familiarize with methodology and data evaluation techniques by being aware of scientific research methods (i.e. correlational, experimental, longitudinal, case study). | |
| 5) | Employ ethical sensitivity while doing assessment, research or working with groups. | |
| 6) | Familiarize with the essential perspectives of psychology (cognitive, developmental, clinical, social, behavioral, and biological). | |
| 7) | Get the opportunity and skills to evaluate qualitative and quantitative data, write reports, and present them. | |
| 8) | Attain preliminary knowledge for psychological measurement and evaluation. | |
| 9) | To have a basic knowledge of other disciplines (e.g. sociology, history, political science, communication studies, philosophy, anthropology, literature, law, art, etc) that can contribute to psychology and to be able to make use of this knowledge in understanding and interpreting of psychological process. | 3 |