TÜRKÇE
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Information
| Code | MT433 |
| Name | Complex Analysis |
| Term | 2022-2023 Academic Year |
| Semester | 7. Semester |
| Duration (T+A) | 3-0 (T-A) (17 Week) |
| ECTS | 5 ECTS |
| National Credit | 3 National Credit |
| Teaching Language | Türkçe |
| Level | Lisans Dersi |
| Type | Normal |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Doç. Dr. NAZAR ŞAHİN ÖĞÜŞLÜ |
| Course Instructor |
Doç. Dr. NAZAR ŞAHİN ÖĞÜŞLÜ
(A Group)
(Ins. in Charge)
|
Course Goal / Objective
Calculate certain integrals of some special types of complex functions, find the sum of the some series, understand the relationship between zeros and poles of a complex function in an area, decide whether or not a map is conformal and know the convergence of an infinite multiplication.
Course Content
Integrals, sum of series, poles and zeros, conformal mappings, infinite multiplication
Course Precondition
No
Resources
KOMPLEKS FONKSİYONLAR TEORİSİ, Yazar: Prof.Dr. Turgut Başkan; KARMAŞIK FONKSİYONLAR KURAMI, Yazar: Prof.Dr. Ali Dönmez
Notes
COMPLEX VARIABLES AND APPLICATIONS, Authors: Ruel V. Churchill, James Ward Brown
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Calculates certain integrals of some special types of complex functions. |
| LO02 | Proves the sum of series formulas. |
| LO03 | Find the sum of the series. |
| LO04 | Explains the relationship between zeros and poles of a complex function in an area. |
| LO05 | Finds the number of zeros and poles of a complex function in an area. |
| LO06 | Decides whether a function conformal or not. |
| LO07 | Explains the relationship between the convergence of an infinite multiplication with convergence of an infinite series. |
| LO08 | Calculates some of the infinite multiplication. |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | Bilgi - Kuramsal, Olgusal | Comprehend the ability to prove the mathematical knowledge gained in secondary education on the basis of theoretical basis. | 5 |
| PLO02 | Bilgi - Kuramsal, Olgusal | Understands importance of basic consepts of Algebra, Analaysis and Topology. | 5 |
| PLO03 | Yetkinlikler - Öğrenme Yetkinliği | Mathematical reasoning demonstrates the ability to develop and write mathematical proofs by gaining maturity. | 5 |
| PLO04 | Bilgi - Kuramsal, Olgusal | Demonstrate the ability to express the basic theories of mathematics both correctly. | 5 |
| PLO05 | Bilgi - Kuramsal, Olgusal | Understands the relationship between the different fields of mathematics and its relation to other disciplines. | 4 |
| PLO06 | Bilgi - Kuramsal, Olgusal | Comprehends the ability to understand the relationships between the objects in the most understandable way while creating a model for any problem. | 4 |
| PLO07 | Bilgi - Kuramsal, Olgusal | Comprehend and explain mathematical models such as formulas, graphs, tables and schema. | 4 |
| PLO08 | Bilgi - Kuramsal, Olgusal | Demonstrate the ability to mathematically rearrange, analyze, and model the problems they encounter. | 5 |
| PLO09 | Bilgi - Kuramsal, Olgusal | Comprehends at least one of the computer programming languages. | |
| PLO10 | Bilgi - Kuramsal, Olgusal | Demonstrate the ability to use scientific methods and appropriate technologies effectively in problem solving. | 4 |
| PLO11 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Understands sufficient knowledge of foreign language to be able to understand Mathematical concepts and communicate with other mathematicians | |
| PLO12 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | In addition to their professional development, they demonstrate their ability to continuously improve themselves by identifying their educational needs in scientific, cultural, artistic and social areas in line with their interests and abilities. | 3 |
| PLO13 | Yetkinlikler - Öğrenme Yetkinliği | Understands the programming techniques and shows the ability to do programming. | |
| PLO14 | Yetkinlikler - Öğrenme Yetkinliği | Demonstrates the ability to study mathematics both independently and as a group. | 3 |
| PLO15 | Bilgi - Kuramsal, Olgusal | Demonstrate an awareness of the universal and social impacts and legal consequences of mathematical applications in the field of study. | 3 |
| PLO16 | Bilgi - Kuramsal, Olgusal | Demonstrate the ability to select, use and develop effectively for contemporary mathematical applications. | 3 |
| PLO17 | Bilgi - Kuramsal, Olgusal | It has ability of lifelong learning awareness, access to information, monitoring developments in science and technology and self-renewal ability. | 4 |
| PLO18 | Bilgi - Kuramsal, Olgusal | Gains the ability to use information technologies effectively for contemporary mathematical applications. | 3 |
| PLO19 | Bilgi - Kuramsal, Olgusal | Gains the ability to design, conduct experiments, field work, data collection, analysis, archiving, text solving and / or interpretation according to mathematics fields. | 3 |
| PLO20 | Bilgi - Kuramsal, Olgusal | Gains the consciousness of prefesional ethics and responsibility. | 5 |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | General information, derivative, Cauchy-Riemann equations, analytic functions, Cauchy-Gaursat theorem, series and residual calculations, brief review. | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 2 | Integrals | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 3 | Calculation of definite integrals contaning sine and cosine expressions. | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 4 | Definite integrals of multi-valued functions. | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 5 | Cauchy principal value and trigonometric integrals. | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 6 | Proof of formulas of the sum of series. | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 7 | Applications related to the calculation of the sum of series. | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 8 | Mid-Term Exam | topics discussed in the lecture notes and sources again | Ölçme Yöntemleri: Yazılı Sınav |
| 9 | Mittag-Lefflers theorem, proof and applications. | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 10 | Proof of formulas related to the relationship between zeros and poles and its applications. | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 11 | Rouche theorem and its applications. | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 12 | Conformal mappings. | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 13 | Applications related to conformal mappings | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 14 | Definition and properties of infinite products. | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 15 | Some applications related to infinite products. | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 16 | Term Exams | topics discussed in the lecture notes and sources again | Ölçme Yöntemleri: Yazılı Sınav |
| 17 | Term Exams | topics discussed in the lecture notes and sources again | 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 | 3 | 42 |
| Assesment Related Works | |||
| Homeworks, Projects, Others | 0 | 0 | 0 |
| Mid-term Exams (Written, Oral, etc.) | 1 | 12 | 12 |
| Final Exam | 1 | 18 | 18 |
| Total Workload (Hour) | 114 | ||
| Total Workload / 25 (h) | 4,56 | ||
| ECTS | 5 ECTS | ||