TÜRKÇE
ENGLISH
Information
| Unit | FACULTY OF ENGINEERING |
| ELECTRICAL-ELECTRONIC ENGINEERING PR. (ENGLISH) | |
| Code | EEE203 |
| Name | Complex Calculus |
| Term | 2018-2019 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 |
| Label | C Compulsory |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Prof. Dr. SAMİ ARICA |
| Course Instructor |
Prof. Dr. SAMİ ARICA
(Güz)
(A Group)
(Ins. in Charge)
|
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
Resources
Notes
Complex Analysis. John M. Howie. (April 20, 2007). Springer.
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 | - | Has capability in those fields of mathematics and physics that form the foundations of engineering. | 0 |
| PLO02 | - | Grasps the main knowledge in the basic topics of electrical and electronic engineering. | 0 |
| PLO03 | - | Comprehends the functional integrity of the knowledge gathered in the fields of basic engineering and electrical-electronics engineering. | 3 |
| PLO04 | - | Identifies problems and analyzes the identified problems based on the gathered professional knowledge. | 0 |
| PLO05 | - | Formulates and solves a given theoretical problem using the knowledge of basic engineering. | 3 |
| PLO06 | - | Has aptitude for computer and information technologies | 0 |
| PLO07 | - | Knows English at a level adequate to comprehend the main points of a scientific text, either general or about his profession, written in English. | 3 |
| PLO08 | - | Has the ability to apply the knowledge of electrical-electronic engineering to profession-specific tools and devices. | 0 |
| PLO09 | - | Has the ability to write a computer code towards a specific purpose using a familiar programming language. | 0 |
| PLO10 | - | Has the ability to work either through a purpose oriented program or in union within a group where responsibilities are shared. | 2 |
| PLO11 | - | Has the aptitude to identify proper sources of information, reaches them and uses them efficiently. | 3 |
| PLO12 | - | Becomes able to communicate with other people with a proper style and uses an appropriate language. | 0 |
| PLO13 | - | Internalizes the ethical values prescribed by his profession in particular and by the professional life in general. | 0 |
| PLO14 | - | Has consciousness about the scientific, social, historical, economical and political facts of the society, world and age lived in. | 0 |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Review of complex numbers. | Textbook reading/Problem solving. | |
| 2 | Review of complex numbers (continued). | Textbook reading/Problem solving. | |
| 3 | Complex functions and mappings: limits, continuity, differentiability, analyticity; Cauchy-Riemann equations; harmonic functions . | Textbook reading/Problem solving. | |
| 4 | Complex functions and mappings: limits, continuity, differentiability, analyticity; Cauchy-Riemann equations; harmonic functions (continued). | Textbook reading/Problem solving. | |
| 5 | Complex functions and mappings: limits, continuity, differentiability, analyticity; Cauchy-Riemann equations; harmonic functions (continued). | Textbook reading/Problem solving. | |
| 6 | Elementary functions: exponential transformations, trigonometric, and hyperbolic functions; multi-valued functions, logarithmic and power functions. | Textbook reading/Problem solving. | |
| 7 | Elementary functions: exponential transformations, trigonometric, and hyperbolic functions; multi-valued functions, logarithmic and power functions (continued). | Textbook reading/Problem solving. | |
| 8 | Midterm Exam I | Textbook reading/Problem solving. | |
| 9 | Complex integration, Cauchy´s Integral Theorem, Cauchy´s Integral Formula and consequences. | Textbook reading/Problem solving. | |
| 10 | Complex integration, Cauchy´s Integral Theorem, Cauchy´s Integral Formula and consequences (continued). | Textbook reading/Problem solving. | |
| 11 | Complex integration, Cauchy´s Integral Theorem, Cauchy´s Integral Formula and consequences (continued). | Textbook reading/Problem solving. | |
| 12 | Midterm Exam II. Taylor and Laurent series, classification of singularities. | Textbook reading/Problem solving. | |
| 13 | Residues, the Residue Theorem, evaluation of improper real integrals using the Residue Theorem | Textbook reading/Problem solving. | |
| 14 | Residues, the Residue Theorem, evaluation of improper real integrals using the Residue Theorem (continued). | Textbook reading/Problem solving. | |
| 15 | Conformal mappings and applications. | Textbook reading/Problem solving. | |
| 16 | Final Exam. | Textbook reading/Problem solving. | |
| 17 | Final Exam. | Textbook reading/Problem solving. |
Assessment (Exam) Methods and Criteria
| Assessment Type | Midterm / Year Impact | End of Term / End of Year Impact |
|---|---|---|
| 1. Midterm Exam | 100 | 40 |
| General Assessment | ||
| Midterm / Year Total | 100 | 40 |
| 1. Final Exam | - | 60 |
| Grand Total | - | 100 |
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 | ||