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Course Information

Course's Contribution to Prog.

ECTS- Workload Calculation Tool

Program Information

Course Title | Code | Semester | Laboratory+Practice (Hour) | Pool | Type | ECTS |

Complex Analysis II | MATH302 | SPRING | 4+0 | C | 7 |

Learning Outcomes | 1-Comments derivative of complex functions and related theorems. 2-Analyzes Cauchy Riemann equations and their applications. 3-Solves complex integrals. 4-Solves rezidues and improper integrals. |

Activity | Percentage (100) | Number | Time (Hours) | Total Workload (hours) |

Course Duration (Weeks x Course Hours) | 14 | 4 | 56 | |

Classroom study (Pre-study, practice) | 14 | 5 | 70 | |

Assignments | 10 | 1 | 20 | 20 |

Short-Term Exams (exam + preparation) | 10 | 1 | 20 | 20 |

Midterm exams (exam + preparation) | 30 | 1 | 16 | 16 |

Project | 0 | 0 | 0 | 0 |

Laboratory | 0 | 0 | 0 | 0 |

Final exam (exam + preparation) | 50 | 1 | 18 | 18 |

Other | 0 | 0 | 0 | 0 |

Total Workload (hours) | 200 | |||

Total Workload (hours) / 30 (s) | 6,67 ---- (7) | |||

ECTS Credit | 7 |

Week | Topics | Study Metarials |

1 | Certain basic foreknowledge, introduction to elementer complex functions | R1) Lecture Notes |

2 | Derivatives of elementer complex functions and related theorems | R1) Lecture Notes |

3 | Analytic functions and their derivatives | R1) Lecture Notes |

4 | Cauchy-Riemann equations and their applications | R1) Lecture Notes |

5 | Harmonic functions, w(t) curves in complex plane, countours, domains. | R1) Lecture Notes |

6 | Concept of complex integral, basic definitions, related theorems | R1) Lecture Notes |

7 | Cauchy Goursat theorem, related theorem, certain applications | R1) Lecture Notes |

8 | Midterm exams | |

9 | Cauchy Integral formulas, related theorems and applications | R1) Lecture Notes |

10 | Morera theorem | R1) Lecture Notes |

11 | Maksimum modulus theorem, Liouville theorem and fundemental theorem of algebra Goursat theorem and related results | R1) Lecture Notes |

12 | Taylor and Laurent Series | R1) Lecture Notes |

13 | Zeros and poles of analytic functions, rezidue and related theorems | R1) Lecture Notes |

14 | Rezidues and related theorems, concepts of improper integrals | R1) Lecture Notes |

15 | Some applications of improper integrals | R1) Lecture Notes |

Prerequisites | - |

Language of Instruction | English |

Coordinator | Assoc. Prof. Dr. Faruk POLAT |

Instructors | - |

Assistants | - |

Resources | R1: Lecture notes R2: Brown, J. W., Complex variables and applications - 6th ed., McGraw-Hill., 2005. R3: Spiegel, M., Theory and problems of complex analysis, Schaum`s Outlines Series, Metric Editions. R4: Silverman, R. A., Calculus with Analytic Geometry, Prentice Hall., 1985. |

Supplementary Book | [1]: Rudin, W., Real and Complex Analysis, McGraw-Hill., 1991. [2]: Complex variable with applicatins, Ponnusamy, S. and Silverman, H., Birkhauser, Berlin, 2006. |

Goals | To introduce elementer functions, their derivatives, integrals and to apply them to complex functions and to know important theorems. |

Content | Elementary functions, their derivatives, Cauchy-Riemann equations, Harmonic functions, w(t) curves in complex plane, their perimeters, their domains, Complex integral notion , Cauchy Goursat theorem, Cauchy integral formula, Liouville theorem and Fundamental Theorem of Algebra, Taylor and Laurent Series, Zeros, polar points and residue of Analytic functions. |

Program Learning Outcomes | Level of Contribution | |

1 | To have a grasp of theoretical and applied knowledge in main fields of mathematics | 3 |

2 | To have the ability of abstract thinking | 4 |

3 | To be able to use the gained mathematical knowledge in the process of identifying the problem, analyzing and determining the solution steps | 3 |

4 | To be able to relate the gained mathematical acquisitions with different disciplines and apply in real life | - |

5 | To have the qualification of studying independently in a problem or a project requiring mathematical knowledge | - |

6 | To be able to work compatibly and effectively in national and international groups and take responsibility | - |

7 | To be able to consider the knowledge gained from different fields of mathematics with a critical approach and have the ability to improve the knowledge | - |

8 | To be able to determine what sort of knowledge the problem met requires and guide the process of learning this knowledge | - |

9 | To adopt the necessity of learning constantly by observing the improvement of scientific accumulation over time | - |

10 | To be able to transfer thoughts on issues related to mathematics, proposals for solutions to the problems to the expert and non-expert shareholders written and verbally | - |

11 | To be able to produce projects and arrange activities with awareness of social responsibility | - |

12 | To be able to follow publications in mathematics and exchange information with colleagues by mastering a foreign language at least European Language Portfolio B1 General Level | - |

13 | To be able to make use of the necessary computer softwares (at least European Computer Driving Licence Advanced Level), information and communication technologies for mathematical problem solving, transfer of thoughts and results | - |

14 | To have the awareness of acting compatible with social, scientific, cultural and ethical values | - |

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