ECTS - Complex Analysis
Complex Analysis (MATH346) Course Detail
| Course Name | Course Code | Season | Lecture Hours | Application Hours | Lab Hours | Credit | ECTS |
|---|---|---|---|---|---|---|---|
| Complex Analysis | MATH346 | 6. Semester | 4 | 0 | 0 | 4 | 7 |
| Pre-requisite Course(s) |
|---|
| MATH251 |
| Course Language | English |
|---|---|
| Course Type | Compulsory Departmental Courses |
| Course Level | Bachelor’s Degree (First Cycle) |
| 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 | |
|---|---|
| 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 | Acquires skills to use the advanced theoretical and applied knowledge obtained at the mathematics bachelors program to do further academic and scientific research in both mathematics-based graduate programs and public or private sectors. | X | ||||
| 2 | Transplants and applies the theoretical and applicable knowledge gained in their field to the secondary education by using suitable tools and devices. | X | ||||
| 3 | Acquires the skill of choosing, using and improving problem solving techniques which are needed for modeling and solving current problems in mathematics or related fields by using the obtained knowledge and skills. | X | ||||
| 4 | Acquires analytical thinking and uses time effectively in the process of deduction | X | ||||
| 5 | Acquires basic software knowledge necessary to work in the computer science related fields and together with the skills to use information technologies effectively. | X | ||||
| 6 | Obtains the ability to collect data, to analyze, interpret and use statistical methods necessary in decision making processes. | X | ||||
| 7 | Acquires the level of knowledge to be able to work in the mathematics and related fields and keeps professional knowledge and skills up-to-date with awareness in the importance of lifelong learning. | X | ||||
| 8 | Takes responsibility in mathematics related areas and has the ability to work affectively either individually or as a member of a team. | 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 the ability to communicate ideas with peers supported by qualitative and quantitative data. | X | ||||
| 11 | Has professional and 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 | ||