TÜRKÇE
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Information
| Code | EEE203 |
| Name | Complex Calculus |
| Term | 2024-2025 Academic Year |
| Semester | 3. Semester |
| Duration (T+A) | 3-0 (T-A) (17 Week) |
| ECTS | 5 ECTS |
| National Credit | 3 National Credit |
| Teaching Language | İngilizce |
| Level | Lisans Dersi |
| Type | Normal |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Prof. Dr. SAMİ ARICA |
| Course Instructor |
Gökay DİŞKEN
(A Group)
(Ins. in Charge)
Duygu Nazan GENÇOĞLAN (A Group) (Asst. Ins.) |
Course Goal / Objective
In this course, functions of a complex variable, continuity, limits, derivative and contour integrals of the functions are discussed. In other words, the topic is an extension of calculus to the functions of a complex variable.
Course Content
Review of complex numbers. Complex functions and mappings: limits, continuity, differentiability, analyticity, Cauchy Riemann equations, harmonic functions. Elementary functions: exponential transformations, trigonometric, and hyperbolic functions, multi-valued functions, logarithmic and power functions. Complex integration, Cauchy's Integral Theorem, Cauchy's Integral Formula and consequences. Taylor and Laurent series, classification of singularities. Residues, the Residue Theorem, evaluation of improper real integrals using the Residue Theorem. Conformal mappings and applications.
Course Precondition
There are no prerequisites for the course.
Resources
Fundamentals of Complex Analysis with Applications to Engineering, Science, and Mathematics. Edward B. Saff Edward B. Saff, Arthur David Snider. 3 edition (January 10, 2003). Prentice Hall. Complex Analysis, A First Course with Applications. Dennis G. Zill and Patrick D. Shanahan. Third Edition (2015). Jones & Bartlett Learning.
Notes
No suggested additional course notes.
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Understand complex functions , analyticity; Cauchy-Riemann equations; harmonic functions. |
| LO02 | Learn exponential, trigonometric, and hyperbolic functions; multi-valued functions, logarithmic and power functions. |
| LO03 | Compute complex integrals, apply Cauchy's Integral Theorem, Cauchy's Integral Formula and consequences. |
| LO04 | Realize Residues, the Residue Theorem, evaluate improper real integrals using the Residue Theorem. |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | Bilgi - Kuramsal, Olgusal | Adequate knowledge in mathematics, science and engineering subjects pertaining to the relevant discipline; ability to use theoretical and applied knowledge in these areas in complex engineering problems. | 5 |
| PLO02 | Bilgi - Kuramsal, Olgusal | Ability to identify, formulate, and solve complex engineering problems; ability to select and apply proper analysis and modeling methods for this purpose. | 3 |
| PLO03 | Bilgi - Kuramsal, Olgusal | Ability to design a complex system, process, device or product under realistic constraints and conditions, in such a way as to meet the desired result; ability to apply modern design methods for this purpose. | |
| PLO04 | Bilgi - Kuramsal, Olgusal | Ability to devise, select, and use modern techniques and tools needed for analyzing and solving complex problems encountered in engineering practice; ability to employ computer programming techniques, and information technologies effectively. | |
| PLO05 | Bilgi - Kuramsal, Olgusal | Ability to design and conduct experiments, gather data, analyze and interpret results for investigating complex engineering problems or discipline specific research questions. | |
| PLO06 | Bilgi - Kuramsal, Olgusal | Ability to work efficiently in intra-disciplinary and multi-disciplinary teams; ability to work individually. | |
| PLO07 | Bilgi - Kuramsal, Olgusal | Ability to communicate effectively, both orally and in writing; knowledge of a minimum of one foreign language; ability to write effective reports and comprehend written reports, prepare design and production reports, make effective presentations, | |
| PLO08 | Bilgi - Kuramsal, Olgusal | Recognition of the need for lifelong learning; ability to access information, to follow developments in science and technology, and to continue to educate him/herself. | 3 |
| PLO09 | Bilgi - Kuramsal, Olgusal | Consciousness to behave according to ethical principles and professional and ethical responsibility; knowledge on standards used in engineering practice. | |
| PLO10 | Bilgi - Kuramsal, Olgusal | Knowledge about business life practices such as project management, risk management, and change management; awareness in entrepreneurship, innovation; knowledge about sustainable development. | |
| PLO11 | Bilgi - Kuramsal, Olgusal | Knowledge about the global and social effects of engineering practices on health, environment, and safety, and contemporary issues of the century reflected into the field of engineering; awareness of the legal consequences of engineering solutions. | |
| PLO12 | Bilgi - Kuramsal, Olgusal | Ability to apply the knowledge of electrical-electronics engineering to profession-specific tools and devices. | 3 |
| PLO13 | Bilgi - Kuramsal, Olgusal | Having consciousness about the scientific, social, historical, economical and political facts of the society, world and age lived in. |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Review of complex numbers. Part - 1 | Textbook reading/Problem solving. | Öğretim Yöntemleri: Anlatım |
| 2 | Review of complex numbers. Part -2 | Textbook reading/Problem solving. | Öğretim Yöntemleri: Anlatım |
| 3 | Complex functions and mappings: limits, continuity, differentiability, analyticity;Cauchy-Riemann equations; harmonic functions. Part - 1. | Textbook reading/Problem solving. | Öğretim Yöntemleri: Anlatım |
| 4 | Complex functions and mappings: limits, continuity, differentiability, analyticity;Cauchy-Riemann equations; harmonic functions. Part - 2. | Textbook reading/Problem solving. | Öğretim Yöntemleri: Anlatım |
| 5 | Complex functions and mappings: limits, continuity, differentiability, analyticity;Cauchy-Riemann equations; harmonic functions. Part - 3. | Textbook reading/Problem solving. | Öğretim Yöntemleri: Anlatım |
| 6 | Elementary functions: exponential transformations, trigonometric, and hyperbolicfunctions; multi-valued functions, logarithmic and power functions. Part - 1. | Textbook reading/Problem solving. | Öğretim Yöntemleri: Anlatım |
| 7 | Elementary functions: exponential transformations, trigonometric, and hyperbolicfunctions; multi-valued functions, logarithmic and power functions. Part - 2. | Textbook reading/Problem solving. | Öğretim Yöntemleri: Anlatım |
| 8 | Mid-Term Exam | Textbook reading/Problem solving. | Ölçme Yöntemleri: Yazılı Sınav |
| 9 | Complex integration, Cauchy's Integral Theorem, Cauchy's Integral Formula and consequences. Part - 1. | Textbook reading/Problem solving. | Öğretim Yöntemleri: Anlatım |
| 10 | Complex integration, Cauchy's Integral Theorem, Cauchy's Integral Formula and consequences. Part - 2. | Textbook reading/Problem solving. | Öğretim Yöntemleri: Anlatım |
| 11 | Complex integration, Cauchy's Integral Theorem, Cauchy's Integral Formula and consequences. Part - 3. | Textbook reading/Problem solving. | Öğretim Yöntemleri: Anlatım |
| 12 | Midterm Exam II. Taylor and Laurent series, classification of singularities. | Textbook reading/Problem solving. | Öğretim Yöntemleri: Anlatım |
| 13 | Residues, the Residue Theorem, evaluation of improper real integrals using the Residue Theorem. Part - 1. | Textbook reading/Problem solving. | Öğretim Yöntemleri: Anlatım |
| 14 | Residues, the Residue Theorem, evaluation of improper real integrals using the Residue Theorem. Part - 2. | Textbook reading/Problem solving. | Öğretim Yöntemleri: Anlatım |
| 15 | Conformal mappings and applications. | Textbook reading/Problem solving. | Öğretim Yöntemleri: Anlatım |
| 16 | Term Exams | Textbook reading/Problem solving. | Ölçme Yöntemleri: Yazılı Sınav |
| 17 | Term Exams | Textbook reading/Problem solving. | 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 | 2 | 2 |
| Final Exam | 1 | 2 | 2 |
| Total Workload (Hour) | 116 | ||
| Total Workload / 25 (h) | 4,64 | ||
| ECTS | 5 ECTS | ||