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 | Ph.D. |
| 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 | Is independently able to build a problem in the area of study, solve the problem by developing solution techniques and assess the solutions. | X | ||||
| 2 | Is capable of creating a groundwork in the fundamental branches of mathematics as well as in his/her research area | X | ||||
| 3 | follows the latest national and international literature in Mathematics and in his/her area of research; and uses them in his/her related studies | X | ||||
| 4 | observes and adopts the scientific ethical values in his/her professional and social life | X | ||||
| 5 | presents in Turkish and English in academic/scientific events the results of his/her research or the latest studies and findings on a special topic and participates in discussions | X | ||||
| 6 | Develops skills to work independently or as a member of a team | X | ||||
| 7 | Develops competences in the areas of creative and critical thinking, problem solving and producing original studies. Follows recent scientific studies, is capable of making an analysis, synthesis and assessment of the knowledge acquired | X | ||||
| 8 | Is open to lifelong improvement of his/her acquired knowledge, skills and competences. | X | ||||
| 9 | Is able to apply the acquired knowledge and problem-solving skills to interdisciplinary studies, proposes different solution methods to problems in terms of mathematical models and from a mathematical point of view | X | ||||
| 10 | Uses the mathematical based softwares, informatics and communication technologies for scientific purposes | X | ||||
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 | ||