| AMERICAN CULTURE AND LITERATURE | |||||
| 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) | Upon graduation, students will acquire key skills and attributes to conduct research to use research tools, to solve problems, to communicate effectively and to transfer skills to the workplace. | |
| 2) | Upon graduation, students will have developed the ability to discuss key issues in fluent English. | |
| 3) | Upon graduation, students will have developed the ability to compose written documents in English with a mature prose style. | 4 |
| 4) | Upon graduation, students will have gained broad knowledge of the American and English literary canons. | 4 |
| 5) | Upon graduation, students will have developed the ability to analyze, synthesize and criticize sophisticated works of American and English literature. | 4 |
| 6) | Upon graduation, students will have achieved in depth the understanding of contemporary American culture. | 3 |
| 7) | Upon graduation, students will have developed the ability to draw links among diverse literary texts and documents and establish critical connections and adopt an interdisciplinary attitude. | 3 |
| 8) | Upon graduation, students will be able to develop new projects individually or in teams. | 3 |
| 9) | Upon graduation, students will be able to apply their knowledge into their lives for interdisciplinary problem-solving and solutions. | 4 |