Nevşehir Hacı Bektaş Veli University Course Catalogue
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| Year/Semester of Study | 1 / Spring Semester | ||||
| Level of Course | 2nd Cycle Degree Programme | ||||
| Type of Course | Optional | ||||
| Department | ELECTRICAL AND ELECTRONICS ENGINEERING (MASTER) | ||||
| Pre-requisities and Co-requisites | None | ||||
| Mode of Delivery | Face to Face | ||||
| Teaching Period | 14 Weeks | ||||
| Name of Lecturer | ALİ KÜRŞAD GÖRÜR (kgorur@nevsehir.edu.tr) | ||||
| Name of Lecturer(s) | |||||
| Language of Instruction | Turkish | ||||
| Work Placement(s) | None | ||||
| Objectives of the Course | |||||
| To get knowledge and skills about the basic theroy of complex variable functions and some application, differentiation and integration in the complex plane, Cauchy integral theorems, Taylor and Laurent series, Residue theorem,Conformal mapping and application. | |||||
| Learning Outcomes | PO | MME | |
| The students who succeeded in this course: | |||
| LO-1 | Perform basic mathematical operations with complex numbers |
PO-1 Sufficient knowledge in mathematics, science and engineering related to their branches; the ability to apply theoretical and practical knowledge in these areas to model and solve engineering problems. PO-2 The ability to identify, formulate, and solve complex engineering problems; selecting and applying appropriate analysis and modeling methods for this purpose. PO-3 The ability to design a complex system, process, device or product under realistic constraints and conditions to meet specific requirements; the ability to apply modern design methods for this purpose. (Realistic constraints and conditions include such issues as economy, environmental issues, sustainability, manufacturability, ethics, health, safety, social and political issues, according to the nature of design.) PO-4 Ability to develop, select and use modern techniques and tools necessary for engineering applications; ability to use information technologies effectively. PO-5 Ability to design experiments, conduct experiments, collect data, analyze and interpret results for examination of engineering problems. |
Examination |
| LO-2 | Work with functions in complex plane and Riemann Surfaces |
PO-1 Sufficient knowledge in mathematics, science and engineering related to their branches; the ability to apply theoretical and practical knowledge in these areas to model and solve engineering problems. PO-2 The ability to identify, formulate, and solve complex engineering problems; selecting and applying appropriate analysis and modeling methods for this purpose. PO-3 The ability to design a complex system, process, device or product under realistic constraints and conditions to meet specific requirements; the ability to apply modern design methods for this purpose. (Realistic constraints and conditions include such issues as economy, environmental issues, sustainability, manufacturability, ethics, health, safety, social and political issues, according to the nature of design.) PO-4 Ability to develop, select and use modern techniques and tools necessary for engineering applications; ability to use information technologies effectively. PO-5 Ability to design experiments, conduct experiments, collect data, analyze and interpret results for examination of engineering problems. |
Examination |
| LO-3 | To be informed about the derivative and integration of functions in complex plane |
PO-1 Sufficient knowledge in mathematics, science and engineering related to their branches; the ability to apply theoretical and practical knowledge in these areas to model and solve engineering problems. PO-2 The ability to identify, formulate, and solve complex engineering problems; selecting and applying appropriate analysis and modeling methods for this purpose. PO-3 The ability to design a complex system, process, device or product under realistic constraints and conditions to meet specific requirements; the ability to apply modern design methods for this purpose. (Realistic constraints and conditions include such issues as economy, environmental issues, sustainability, manufacturability, ethics, health, safety, social and political issues, according to the nature of design.) PO-4 Ability to develop, select and use modern techniques and tools necessary for engineering applications; ability to use information technologies effectively. PO-5 Ability to design experiments, conduct experiments, collect data, analyze and interpret results for examination of engineering problems. |
Examination |
| PO: Programme Outcomes MME:Method of measurement & Evaluation |
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| Course Contents | ||
| Complex plane and functions in complex plane.Analytical functions.Power series. Conformal mapping. Complex derivation. Complex integration.Singularities. Residues.Cauchy theorems. Taylor and Laurent series. | ||
| Weekly Course Content | ||
| Week | Subject | Learning Activities and Teaching Methods |
| 1 | Introduction the complex plane and basic arithmetic and geometric representations. | Lecture, question and answer, discussion |
| 2 | Introduction the functions in complex plane and Riemann Sheet, power functions and their inverses. | Lecture, question and answer, discussion |
| 3 | Exponential functions and logarithm | Lecture, question and answer, discussion |
| 4 | Trigonometric functions and their inverses, the order of branch points. | Lecture, question and answer, discussion |
| 5 | Derivation in complex plane, Cauchy-Riemann equations | Lecture, question and answer, discussion |
| 6 | The geometrical meaning of derivation and conformal mapping | Lecture, question and answer, discussion |
| 7 | Complex line integrals and Cauchy ingtegral theorem | Lecture, question and answer, discussion |
| 8 | mid-term exam | |
| 9 | Applications of the Cauchy formula and some results | Lecture, question and answer, discussion |
| 10 | Residue concept and its applications | Lecture, question and answer, discussion |
| 11 | Types of singularities and some theorems | Lecture, question and answer, discussion |
| 12 | Taylor and Laurent series expansions | Lecture, question and answer, discussion |
| 13 | Entire functions | Lecture, question and answer, discussion |
| 14 | Analytical continuation | Lecture, question and answer, discussion |
| 15 | Analytical continuation | Lecture, question and answer, discussion |
| 16 | final exam | |
| Recommend Course Book / Supplementary Book/Reading | ||
| 1 | 1- M. İdemen, "Kompleks Değişkenli Fonksiyonlar Teorisi", İ.T.Ü. yayınları, 1992. | |
| 2 | 2- R. V. Churchill, Complex Variables and Applications, McGraw-Hill,1960. | |
| 3 | 3- M.O. Gonzalez, "Classical Complex Analysis, Marcell Dekker, Inc., 1992. | |
| 4 | 4- Kompleks Analiz ve Uygulamaları, Dennis G. Zill, Patrick D. Shanahan | |
| Required Course instruments and materials | ||
| Projection, computer. | ||
| Assessment Methods | |||
| Type of Assessment | Week | Hours | Weight(%) |
| mid-term exam | 8 | 1 | 40 |
| Other assessment methods | |||
| 1.Oral Examination | |||
| 2.Quiz | |||
| 3.Laboratory exam | |||
| 4.Presentation | |||
| 5.Report | |||
| 6.Workshop | |||
| 7.Performance Project | |||
| 8.Term Paper | |||
| 9.Project | |||
| final exam | 16 | 1 | 60 |
| Student Work Load | |||
| Type of Work | Weekly Hours | Number of Weeks | Work Load |
| Weekly Course Hours (Theoretical+Practice) | 3 | 14 | 42 |
| Outside Class | |||
| a) Reading | 3 | 12 | 36 |
| b) Search in internet/Library | 3 | 12 | 36 |
| c) Performance Project | 0 | ||
| d) Prepare a workshop/Presentation/Report | 2 | 8 | 16 |
| e) Term paper/Project | 0 | ||
| Oral Examination | 0 | ||
| Quiz | 0 | ||
| Laboratory exam | 0 | ||
| Own study for mid-term exam | 3 | 8 | 24 |
| mid-term exam | 1 | 1 | 1 |
| Own study for final exam | 3 | 8 | 24 |
| final exam | 1 | 1 | 1 |
| 0 | |||
| 0 | |||
| Total work load; | 180 | ||