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 | Fall | 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. |
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 develop an interest in the human mind and behavior, to be able to evaluate theories using empirical findings, to understand that psychology is an evidence-based science by acquiring critical thinking skills. | |
2) | To gain a biopsychosocial perspective on human behavior. To understand the biological, psychological, and social variables of behavior. | |
3) | To learn the basic concepts in psychology and the theoretical and practical approaches used to study them (e.g. basic observation and interview techniques). | |
4) | To acquire the methods and skills to access and write information using English as the dominant language in the psychological literature, to recognize and apply scientific research and data evaluation techniques (e.g. correlational, experimental, cross-sectional and longitudinal studies, case studies). | |
5) | To be against discrimination and prejudice; to have ethical concerns while working in research and practice areas. | |
6) | To recognize the main subfields of psychology (experimental, developmental, clinical, cognitive, social and industrial/organizational psychology) and their related fields of study and specialization. | |
7) | To acquire the skills necessary for analyzing, interpreting and presenting the findings as well as problem posing, hypothesizing and data collection, which are the basic elements of scientific studies. | |
8) | To gain the basic knowledge and skills necessary for psychological assessment and evaluation. | |
9) | To acquire basic knowledge of other disciplines (medicine, genetics, biology, economics, sociology, political science, communication, philosophy, anthropology, literature, law, art, etc.) that will contribute to psychology and to use this knowledge in the understanding and interpretation of psychological processes. | |
10) | To develop sensitivity towards social problems; to take responsibility in activities that benefit the field of psychology and society. | |
11) | To have problem solving skills and to be able to develop the necessary analytical approaches for this. | |
12) | To be able to criticize any subject in business and academic life and to be able to express their thoughts. |