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Information
| Code | EE529 |
| Name | Theory of Complex Functions |
| Term | 2024-2025 Academic Year |
| Semester | . Semester |
| Duration (T+A) | 3-0 (T-A) (17 Week) |
| ECTS | 6 ECTS |
| National Credit | 3 National Credit |
| Teaching Language | İngilizce |
| Level | Yüksek Lisans Dersi |
| Type | Normal |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Prof. Dr. TURGUT İKİZ |
Course Goal / Objective
To understand the concept of complex function, to solve some important integrals using complex plane, to solve some scattering problems usimg the princple of abalytic continuation.
Course Content
Functions in complex plane, derivative in complex plane, integral in complex plane, Cauchy Formula and some results, exact functions, analytic continuation, Hilbert and Wiener Hopf problems.
Course Precondition
None
Resources
The Theory of Complex Functions
Notes
The theory of Functions with complex variables
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Ability to communicate with people in an appropriate language and style |
| LO02 | To be able to search for literature in scientific databases; in particular, the ability to properly and accurately scan databases and evaluate and categorize listed items. |
| LO03 | To be able to work on the thesis topic in a programmatic way, in accordance with the logical integrity required by the subject, within the framework determined by the advisor. |
| LO04 | To understand the concept of the function on complex plane |
| LO05 | To understand and be able to apply analytic continuation |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | Bilgi - Kuramsal, Olgusal | Being able to specialize in at least one of the branches that form the foundations of electrical-electronic engineering by increasing the level of knowledge beyond the undergraduate level. | 3 |
| PLO02 | Bilgi - Kuramsal, Olgusal | To comprehend the integrity of all the subjects included in the field of specialization. | 3 |
| PLO03 | Bilgi - Kuramsal, Olgusal | Knowing and following the current scientific literature in the field of specialization | |
| PLO04 | Bilgi - Kuramsal, Olgusal | To be able to comprehend the interdisciplinary interaction of the field with other related branches. | |
| PLO05 | Bilgi - Kuramsal, Olgusal | Ability to do theoretical and experimental work | |
| PLO06 | Bilgi - Kuramsal, Olgusal | To create a complete scientific text by compiling the information obtained from the research. | 3 |
| PLO07 | Bilgi - Kuramsal, Olgusal | To work on the thesis topic programmatically, following the logical integrity required by the subject within the framework determined by the advisor. | 3 |
| PLO08 | Bilgi - Kuramsal, Olgusal | To search for literature in scientific databases, particularly the ability to correctly and accurately scan databases and evaluate and categorize listed items. | 4 |
| PLO09 | Bilgi - Kuramsal, Olgusal | Knowledge of English at a level that can easily read and understand a scientific text written in English in the field of specialization | 5 |
| PLO10 | Bilgi - Kuramsal, Olgusal | Compile information on his/her expertise in a presentation format and present it understandably and effectively. | |
| PLO11 | Bilgi - Kuramsal, Olgusal | Ability to write a computer program in a familiar programming language, generally for a specific purpose, specifically related to the field of expertise. | 4 |
| PLO12 | Bilgi - Kuramsal, Olgusal | Being able to guide and take the initiative in environments that require solving problems related to the field | 3 |
| PLO13 | Yetkinlikler - İletişim ve Sosyal Yetkinlik | Ability to communicate with people in an appropriate language | |
| PLO14 | Yetkinlikler - Öğrenme Yetkinliği | To be able to produce projects, policies, and processes in the field of expertise and to evaluate these elements | |
| PLO15 | Yetkinlikler - Öğrenme Yetkinliği | Ability to research new topics based on existing research experience | 5 |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | The Regions and Functions in complex plane and the Riemann surfaces | review of complex analysis | Öğretim Yöntemleri: Anlatım, Tartışma |
| 2 | Some special functions in complex plane | Review of previous lecture | Öğretim Yöntemleri: Anlatım |
| 3 | Derivative in complex plane, regular functions and Cauchy Riemann equations | Review of previous lecture | Öğretim Yöntemleri: Anlatım |
| 4 | Integration in complex plane, Cauchy's theorem, | Review of previous lecture | Öğretim Yöntemleri: Anlatım |
| 5 | Cauchy's Formula and some importanr results | Review of previous lecture | Öğretim Yöntemleri: Anlatım |
| 6 | Taylor's and Laurent's series | Review of previous lecture | Öğretim Yöntemleri: Anlatım |
| 7 | A general discussion on Taylor's and Laurent's series | Review of previous lectures | Öğretim Yöntemleri: Tartışma |
| 8 | Mid-Term Exam | Review | Ölçme Yöntemleri: Yazılı Sınav |
| 9 | Exact functions | Review | Öğretim Yöntemleri: Anlatım |
| 10 | The integral properties of the Exact functions | Review of previous lecture | Öğretim Yöntemleri: Anlatım, Tartışma |
| 11 | Analytic Continuation | Review of previous lecture | Öğretim Yöntemleri: Anlatım |
| 12 | Weierstrass Method for abalytic continuation | Review of previous lecture | Öğretim Yöntemleri: Anlatım |
| 13 | Singular points and the limits of analytic continuation | Review of previous lecture | Öğretim Yöntemleri: Anlatım |
| 14 | Hilbert's and Wiener Hopf's Problems | Review of previous lecture | Öğretim Yöntemleri: Anlatım |
| 15 | A discussion on exact function and analytic continuation | Review of previous lectures | Öğretim Yöntemleri: Tartışma |
| 16 | Term Exams | Reviev | Ölçme Yöntemleri: Ödev |
| 17 | Term Exams | Review | Ölçme Yöntemleri: Yazılı Sınav |
Student Workload - ECTS
| Works | Number | Time (Hour) | Workload (Hour) |
|---|---|---|---|
| Course Related Works | |||
| Class Time (Exam weeks are excluded) | 14 | 3 | 42 |
| Out of Class Study (Preliminary Work, Practice) | 14 | 5 | 70 |
| Assesment Related Works | |||
| Homeworks, Projects, Others | 0 | 0 | 0 |
| Mid-term Exams (Written, Oral, etc.) | 1 | 15 | 15 |
| Final Exam | 1 | 30 | 30 |
| Total Workload (Hour) | 157 | ||
| Total Workload / 25 (h) | 6,28 | ||
| ECTS | 6 ECTS | ||