ECTS - Complex Analysis
Complex Analysis (MATH552) Course Detail
| Course Name | Course Code | Season | Lecture Hours | Application Hours | Lab Hours | Credit | ECTS |
|---|---|---|---|---|---|---|---|
| Complex Analysis | MATH552 | Area Elective | 3 | 0 | 0 | 3 | 5 |
| Pre-requisite Course(s) |
|---|
| N/A |
| Course Language | English |
|---|---|
| Course Type | Elective Courses |
| Course Level | Natural & Applied Sciences Master's Degree |
| Mode of Delivery | Face To Face |
| Learning and Teaching Strategies | Lecture, Question and Answer, Team/Group. |
| Course Lecturer(s) |
|
| Course Objectives | This course is designed to provide necessary backgrounds and further knowledge in Complex Analysis for graduate students of Mathematics. The topics covered by this course have numerous applications in pure and applied mathematics. |
| Course Learning Outcomes |
The students who succeeded in this course;
|
| Course Content | Analytic functions as mappings, conformal mappings, complex integration, harmonic functions, series and product developments, entire functions, analytic continuation, algebraic functions. |
Weekly Subjects and Releated Preparation Studies
| Week | Subjects | Preparation |
|---|---|---|
| 1 | The algebra of complex numbers. Introduction to the concept of analytic function. Elementary theory of power series. | pp. 1-42 |
| 2 | Elementary point set topology: sets and elements, metric spaces, connectedness, compactness, continuous functions, topological spaces. | pp. 50-67 |
| 3 | Conformality. Elementary conformal mappings. Elementary Riemann surfaces. | pp. 68-97 |
| 4 | Fundamental theorems of complex integration. Cauchy’s integral formula. | pp. 101-120 |
| 5 | Local properties of analytic functions: removable singularities, Taylor’s formula, zeros and poles, the local mapping, the maximum principle. | pp. 124-133 |
| 6 | Mid-Term Examination | |
| 7 | The general form of Cauchy’s theorem. Multiply connected regions | pp. 137-144 |
| 8 | The calculus of residues: the residue theorem, the argument principle, evaluation of definite integrals. | pp. 147-153 |
| 9 | Harmonic functions. | pp. 160-170 |
| 10 | Power series expansions. The Laurent series. Partial fractions and factorization. | pp. 173-199 |
| 11 | Entire functions. | pp. 205-206 |
| 12 | Normal families of analytic functions. | pp. 210-217 |
| 13 | Analytic continuation. | pp. 275-287 |
| 14 | Algebraic functions. | pp. 291-294 |
| 15 | Picard’s theorem. | pp. 297 |
| 16 | Final Examination |
Sources
| Course Book | 1. L. V. Ahlfors, Complex Analysis, 2nd ed., McGraw-Hill, New York 1966. |
|---|---|
| Other Sources | 2. A. I. Markuschevich, Theory of Functions of a Complex Variable, 1985. |
| 3. A J. W. Brown and R. V. Churcill, Complex Variables and Applications, McGraw-Hill, New York, 2003. |
Evaluation System
| Requirements | Number | Percentage of Grade |
|---|---|---|
| Attendance/Participation | - | - |
| Laboratory | - | - |
| Application | - | - |
| Field Work | - | - |
| Special Course Internship | - | - |
| Quizzes/Studio Critics | - | - |
| Homework Assignments | 5 | 15 |
| Presentation | - | - |
| Project | - | - |
| Report | - | - |
| Seminar | - | - |
| Midterms Exams/Midterms Jury | 2 | 50 |
| Final Exam/Final Jury | 1 | 35 |
| Toplam | 8 | 100 |
| Percentage of Semester Work | 65 |
|---|---|
| Percentage of Final Work | 35 |
| Total | 100 |
Course Category
| Core Courses | X |
|---|---|
| Major Area Courses | |
| Supportive Courses | |
| Media and Managment Skills Courses | |
| Transferable Skill Courses |
The Relation Between Course Learning Competencies and Program Qualifications
| # | Program Qualifications / Competencies | Level of Contribution | ||||
|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | ||
| 1 | Ability to carry out advanced research activities, both individual and as a member of a team | |||||
| 2 | Ability to evaluate research topics and comment with scientific reasoning | |||||
| 3 | Ability to initiate and create new methodologies, implement them on novel research areas and topics | |||||
| 4 | Ability to produce experimental and/or analytical data in systematic manner, discuss and evaluate data to lead scintific conclusions | |||||
| 5 | Ability to apply scientific philosophy on analysis, modelling and design of engineering systems | |||||
| 6 | Ability to synthesis available knowledge on his/her domain to initiate, to carry, complete and present novel research at international level | |||||
| 7 | Contribute scientific and technological advancements on engineering domain of his/her interest area | |||||
| 8 | Contribute industrial and scientific advancements to improve the society through research activities | |||||
ECTS/Workload Table
| Activities | Number | Duration (Hours) | Total Workload |
|---|---|---|---|
| Course Hours (Including Exam Week: 16 x Total Hours) | |||
| Laboratory | |||
| Application | |||
| Special Course Internship | |||
| Field Work | |||
| Study Hours Out of Class | 14 | 3 | 42 |
| Presentation/Seminar Prepration | |||
| Project | |||
| Report | |||
| Homework Assignments | 5 | 2 | 10 |
| Quizzes/Studio Critics | |||
| Prepration of Midterm Exams/Midterm Jury | 2 | 7 | 14 |
| Prepration of Final Exams/Final Jury | 1 | 11 | 11 |
| Total Workload | 77 | ||