| Course Description |
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| Course Name |
: |
Complex Analysis |
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| Course Code |
: |
MT 433 |
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| Course Type |
: |
Optional |
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| Level of Course |
: |
First Cycle |
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| Year of Study |
: |
4 |
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| Course Semester |
: |
Fall (16 Weeks) |
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| ECTS |
: |
5 |
|
| Name of Lecturer(s) |
: |
Asst.Prof.Dr. NAZAR ŞAHİN ÖĞÜŞLÜ
|
|
| Learning Outcomes of the Course |
: |
Calculates certain integrals of some special types of complex functions.
Writes and proves the sum of series formulas.
Is able to find the sum of the series.
Explains the relationship between zeros and poles of a complex function in an area.
Finds the number of zeros and poles of a complex function in an area.
Decides whether a function conformal and can apply on curves.
Explains the relationship between the convergence of an infinite multiplication with convergence of an infinite series.
Calculates some of the infinite multiplication.
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|
| Mode of Delivery |
: |
Face-to-Face |
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| Prerequisites and Co-Prerequisites |
: |
None |
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| Recommended Optional Programme Components |
: |
None |
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| Aim(s) of Course |
: |
Calculate certain integrals of some special types of complex functions, write and prove that the sum of series formulas, find the sum of the series, explain the relationship between zeros and poles of a complex function in an area, find the number of zeros and poles of a complex function in an area, decide whether a function conformal and can apply on curves, explain the relationship between the convergence of an infinite multiplication with convergence of an infinite series, calculate some of the infinite multiplication. |
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| Course Contents |
: |
Integrals, sum of series, poles and zeros, conformal mappings, infinite multiplication |
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| Language of Instruction |
: |
Turkish |
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| Work Place |
: |
Department of Mathematics Classrooms |
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|
Course Outline /Schedule (Weekly) Planned Learning Activities |
| Week | Subject | Student's Preliminary Work | Learning Activities and Teaching 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 |
Lecture and discussion |
|
2 |
Integrals |
Review of the relevant pages from sources |
Lecture and discussion |
|
3 |
Calculation of definite integrals contaning sine and cosine expressions. |
Review of the relevant pages from sources |
Lecture and discussion |
|
4 |
Definite integrals of multi-valued functions. |
Review of the relevant pages from sources |
Lecture and discussion |
|
5 |
Cauchy principal value and trigonometric integrals. |
Review of the relevant pages from sources |
Lecture and discussion |
|
6 |
Proof of formulas of the sum of series. |
Review of the relevant pages from sources |
Lecture and discussion |
|
7 |
Applications related to the calculation of the sum of series. |
Review of the relevant pages from sources |
Lecture and discussion |
|
8 |
Written exam |
topics discussed in the lecture notes and sources again |
Written exam |
|
9 |
Mittag-Leffler´s theorem, proof and applications. |
Review of the relevant pages from sources |
Lecture and discussion |
|
10 |
Proof of formulas related to the relationship between zeros and poles and its applications. |
Review of the relevant pages from sources |
Lecture and discussion |
|
11 |
Rouche´s theorem and its applications. |
Review of the relevant pages from sources |
Lecture and discussion |
|
12 |
Conformal mappings. |
Review of the relevant pages from sources |
Lecture and discussion |
|
13 |
Applications related to conformal mappings |
Review of the relevant pages from sources |
Lecture and discussion |
|
14 |
Definition and properties of infinite products. |
Review of the relevant pages from sources |
Lecture and discussion |
|
15 |
Some applications related to infinite products. |
Review of the relevant pages from sources |
Lecture and discussion |
|
16/17 |
Written exam |
Review of the topics discussed in the lecture notes and sources again |
Written exam |
|
|
| Contribution of the Course to Key Learning Outcomes |
| # | Key Learning Outcome | Contribution* |
|
1 |
Is able to prove Mathematical facts encountered in secondary school. |
5 |
|
2 |
Recognizes the importance of basic notions in Algebra, Analysis and Topology |
5 |
|
3 |
Develops maturity of mathematical reasoning and writes and develops mathematical proofs. |
5 |
|
4 |
Is able to express basic theories of mathematics properly and correctly both written and verbally |
3 |
|
5 |
Recognizes the relationship between different areas of Mathematics and ties between Mathematics and other disciplines. |
4 |
|
6 |
Expresses clearly the relationship between objects while constructing a model |
4 |
|
7 |
Draws mathematical models such as formulas, graphs and tables and explains them |
5 |
|
8 |
Is able to mathematically reorganize, analyze and model problems encountered. |
5 |
|
9 |
Knows at least one computer programming language |
5 |
|
10 |
Uses effective scientific methods and appropriate technologies to solve problems |
0 |
|
11 |
Knows programming techniques and is able to write a computer program |
0 |
|
12 |
Is able to do mathematics both individually and in a group. |
0 |
|
13 |
Has sufficient knowledge of foreign language to be able to understand Mathematical concepts and communicate with other mathematicians |
0 |
|
14 |
In addition to professional skills, the student improves his/her skills in other areas of his/her choice such as in scientific, cultural, artistic and social fields |
0 |
| * Contribution levels are between 0 (not) and 5 (maximum). |
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