| Course Description |
|
| Course Name |
: |
Theory of Complex Functions |
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| Course Code |
: |
EE-529 |
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| Course Type |
: |
Optional |
|
| Level of Course |
: |
Second Cycle |
|
| Year of Study |
: |
1 |
|
| Course Semester |
: |
Fall (16 Weeks) |
|
| ECTS |
: |
6 |
|
| Name of Lecturer(s) |
: |
Assoc.Prof.Dr. TURGUT İKİZ
|
|
| Learning Outcomes of the Course |
: |
The student, upon succesful completion of this course
Calculates the integral of a complex function for specific values of the parameters of the integrand.
|
|
| Mode of Delivery |
: |
Face-to-Face |
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| Prerequisites and Co-Prerequisites |
: |
None |
|
| Recommended Optional Programme Components |
: |
None |
|
| Aim(s) of Course |
: |
Introducing the concepts of functions of a complex variable and analytic function. Comprehending the series expansion of analytic functions about singular points. Giving the analytic functions in boundary-value problems. Comprehending the determination of the approximate solution of the integral equations under some considerations |
|
| Course Contents |
: |
The concepts of functions of complex variables. The derivative and integral of a compex functions. Cauchy’s integral. Series expansions of analytic functions. Taylor and Laurent’s series. Residues theorem. Conformal mapping. Analytic functions in the solutions of boundary-value problems. Saddle point method. Wiener-Hopf method. |
|
| Language of Instruction |
: |
English |
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| Work Place |
: |
Classroom |
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Course Outline /Schedule (Weekly) Planned Learning Activities |
| Week | Subject | Student's Preliminary Work | Learning Activities and Teaching Methods |
|
1 |
Kompleks değişkenli fonksiyon kavramı. Kompleks değişkenli bir fonksiyonun türevi ve integrali. |
Review of the complex variables cource |
Lecture, discussion |
|
2 |
Cauchy’s integral and its applications. |
Review of the previous lecture and preparation of the next course |
Lecture, discussion |
|
3 |
The concepts of analytic function and the series expansion of analytic functions. Analytic continuation. |
Review of the previous lecture and preparation of the next course |
Lecture, discussion |
|
4 |
Laurent series and singularities. |
Review of the previous lecture and preparation of the next course |
Lecture, discussion |
|
5 |
Residue theorem and its applications. |
Review of the previous lecture and preparation of the next course |
Lecture, discussion |
|
6 |
Conformal mapping |
Review of the previous lecture and preparation of the next course |
Lecture, discussion |
|
7 |
Midterm examination |
Review of all of the previous course |
Written examination |
|
8 |
Boundary-value problems; Dirichlet ve Nouman problemleri |
Preparation of the next course |
Lecture, discussion |
|
9 |
Fundamentals of the operational calculus; Laplace transform
|
Review of the previous lecture and preparation of the next course |
Lecture, discussion |
|
10 |
Solutions of the linear differential equations by operational method |
Review of the previous lecture and preparation of the next course |
Lecture, discussion |
|
11 |
Saddle point method |
Preparation of the course |
Lecture, discussion |
|
12 |
Application of the saddle point method |
Review of the previous lecture and preparation of the next course |
Lecture, discussion |
|
13 |
Application of the saddle point method |
Review of the previous lecture and preparation of the next course |
Simulation |
|
14 |
Wiener-Hopf metod |
Preparation of the course |
Lecture, discussion |
|
15 |
Application of the Wiener-Hopf metod |
Review of the previous lecture and preparation of the next course |
Simulation |
|
16/17 |
Final examination |
Review of all of the previous course |
Written examination |
|
|
| Contribution of the Course to Key Learning Outcomes |
| # | Key Learning Outcome | Contribution* |
|
1 |
Communicates with people in an appropriate language and style. |
3 |
|
2 |
Specializes by furthering his knowledge level at least in one of the basic subfields of electiral-electronic engineering. |
5 |
|
3 |
Grasps the integrity formed by the topics involved in the field of specialization. |
5 |
|
4 |
Grasps and follows the existing literature in the field of specialization. |
5 |
|
5 |
Comprehends the interdisciplinary interaction of his field with other fields. |
5 |
|
6 |
Has the aptitude to pursue theoretical and experimental work. |
2 |
|
7 |
Forms a scientific text by compiling the knowledge obtained from research. |
4 |
|
8 |
Works in a programmed manner within the framework set by the advisor on the thesis topic, in accordance with the logical integrity required by this topic. |
5 |
|
9 |
Performs a literature search in scientific databases; in particular, to scan the databases in an appropriate manner, to list and categorize the listed items. |
5 |
|
10 |
Has English capability at a level adequate to read and understand a scientific text in his field of specialization, written in English. |
5 |
|
11 |
Compiles his/her knowledge in his/her field of specialization. in a presentation format, and presents in a clear and effective way. |
5 |
|
12 |
Writes a computer code aimed at a specific purpose, in general, and related with his/her field of specialization, in particular |
5 |
|
13 |
Pursues research ın new topics based on his/her existing research experıence. |
5 |
|
14 |
Gives guidance in environments where problems related with his/her field need to be solved, and takes initiative. |
4 |
|
15 |
Develops and evaluates projects, policies and processes in his field of specialization. |
5 |
| * Contribution levels are between 0 (not) and 5 (maximum). |
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