ECTS - Complex Analysis
Complex Analysis (MATH346) Course Detail
| Course Name | Course Code | Season | Lecture Hours | Application Hours | Lab Hours | Credit | ECTS |
|---|---|---|---|---|---|---|---|
| Complex Analysis | MATH346 | Area Elective | 4 | 0 | 0 | 4 | 7 |
| Pre-requisite Course(s) |
|---|
| MATH251 |
| 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 | The course is designed to provide necessary backgrounds in Complex Analysis for students of Mathematics, Engineering and Physical Sciences. The topics covered by this course have numerous applications in Differential Equations, Inverse Scattering Problems, Matrix Theory, Operator Theory, Probability Theory, Elliptic Functions, Classical Special Functions, Approximation Theory, Orthogonal Polynomials, Fourier Analysis, Filter Theory, System Theory, etc. |
| Course Learning Outcomes |
The students who succeeded in this course;
|
| Course Content | Complex Nnumbers and elementary functions, analytic functions and integration, sequences, series and singularities of complex functions, residue calculus and applications of contour integration, conformal mappings and applications. |
Weekly Subjects and Releated Preparation Studies
| Week | Subjects | Preparation |
|---|---|---|
| 1 | Complex Numbers and Their Properties, Elementary Functions, Limits, Continuity. | pp. 1-53 |
| 2 | Complex Differentiation, Applications to Ordinary Differential Equations. | pp. 53-59 |
| 3 | The Cauchy-Riemann Equations, Ideal Fluid Flow, Multi-valued Functions, The Notion of the Riemann Surface of an Analytic Function. | pp. 60-85 |
| 4 | Complex Integration, Cauchy’s Theorem, Cauchy’s Integral Formula. | pp. 111-158 |
| 5 | Applications of Cauchy’s Integral Formula, Liouville, Morera, Maximum-Modules Theorems. | pp. 158-175 |
| 6 | Mid-Term Examination | |
| 7 | Complex Series, Taylor Series, Laurent Series. | pp. 175-197 |
| 8 | Singularities of Complex Functions, Infinite Products. | pp. 221-247 |
| 9 | Mittag-Leffler Expansions, Differential Equations on the Complex Plane. | s. 158-195 (in other Refernces [1].) |
| 10 | Cauchy Residue Theorem, Evaluation of Definite Integrals, Principal Value Integrals. | pp. 251-267 |
| 11 | 11. Week Integrals with Branch Points, the Argument Principal | pp. 270-283 |
| 12 | Rouche’s Theorem, Fourier and Laplace Transforms. | pp. 284-298 |
| 13 | Conformal Transformations, Critical Points and Inverse Mappings. | pp. 343-360 |
| 14 | Mapping Theorems. pp. 341-345 (in [1]) | pp. 341-345 (in other References [1].) |
| 15 | Bilinear Transformations. | pp. 299-313 |
Sources
| Course Book | 1. Complex Variables and Applications, by J. W. Brown and R.V. Churchill, McGraw Hill, 2003. |
|---|---|
| Other Sources | 2. Complex Variables: Introduction and Applications, by M.J. Ablowitz and A.S. Fokas, Cambridge Texts in Applied Mathematics. Cambridge University Press, 1997. |
| 3. A Collection of Problems on Complex Analysis, by L.I. Volkovyski et al Dover Pub., 1991. |
Evaluation System
| Requirements | Number | Percentage of Grade |
|---|---|---|
| Attendance/Participation | - | - |
| Laboratory | - | - |
| Application | - | - |
| Field Work | - | - |
| Special Course Internship | - | - |
| Quizzes/Studio Critics | - | - |
| Homework Assignments | 5 | 10 |
| Presentation | - | - |
| Project | - | - |
| Report | - | - |
| Seminar | - | - |
| Midterms Exams/Midterms Jury | 2 | 50 |
| Final Exam/Final Jury | 1 | 40 |
| Toplam | 8 | 100 |
| Percentage of Semester Work | 60 |
|---|---|
| Percentage of Final Work | 40 |
| 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 | Has the ability to apply scientific knowledge gained in the undergraduate education and to expand and extend knowledge in the same or in a different area. | X | ||||
| 2 | Has the ability to obtain, to evaluate, to interpret and to apply information by doing scientific research. | X | ||||
| 3 | Can apply gained knowledge and problem solving abilities in inter-disciplinary research. | X | ||||
| 4 | Has the ability to work independently within research area, to state the problem, to develop solution techniques, to solve the problem, to evaluate the obtained results and to apply them when necessary. | X | ||||
| 5 | Takes responsibility individually and as a team member to improve systematic approaches to produce solutions in unexpected complicated situations related to the area of study. | X | ||||
| 6 | Can develop strategies, implement plans and principles on the area of study and can evaluate obtained results within the framework. | X | ||||
| 7 | Can develop and extend the knowledge in the area and to use them with scientific, social and ethical responsibility. | X | ||||
| 8 | Has the ability to follow recent developments within the area of research, to support research with scientific arguments and data, to communicate the information on the area of expertise in a systematically by means of written report and oral/visual presentation. | X | ||||
| 9 | Has proficiency in English language and has the ability to communicate with colleagues and to follow the innovations in mathematics and related fields. | X | ||||
| 10 | Has software and hardware knowledge in the area of expertise, and has proficient information and communication technology knowledge. | X | ||||
| 11 | Has professional ethical consciousness and responsibility which takes into account the universal and social dimensions in the process of data collection, interpretation, implementation and declaration of results in mathematics and its applications. | X | ||||
ECTS/Workload Table
| Activities | Number | Duration (Hours) | Total Workload |
|---|---|---|---|
| Course Hours (Including Exam Week: 16 x Total Hours) | 16 | 4 | 64 |
| Laboratory | |||
| Application | |||
| Special Course Internship | |||
| Field Work | |||
| Study Hours Out of Class | 14 | 4 | 56 |
| Presentation/Seminar Prepration | |||
| Project | |||
| Report | |||
| Homework Assignments | 5 | 7 | 35 |
| Quizzes/Studio Critics | |||
| Prepration of Midterm Exams/Midterm Jury | 2 | 15 | 30 |
| Prepration of Final Exams/Final Jury | 1 | 25 | 25 |
| Total Workload | 210 | ||