CANKIRI KARATEKIN UNIVERSITY

Bologna Information System

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

COMPLEX ANALYSIS II | MAT302 | SPRING | 4+0 | C | 7 |

Learning Outcomes | 1-To explain derivative of complex functions and related theorems. 2-To explain cauchy riemann equations and their applications. 3-To calculate complex integrals. 4-To determine rezidues and improper integrals. 5-To determine zeros and poles of complex functions. 6-To explain important theorems (morera, liouville etc). |

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 | 2 | 12 | 24 |

Short-Term Exams (exam + preparation) | 10 | 2 | 12 | 24 |

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) | 208 | |||

Total Workload (hours) / 30 (s) | 6,93 ---- (7) | |||

ECTS Credit | 7 |

Week | Topics | Study Metarials |

1 | Certain basic foreknowledge, introduction to elementer complex functions | |

2 | Derivatives of elementer complex functions and related theorems | |

3 | Analytic functions and their derivatives | |

4 | Cauchy-Riemann equations and their applications | |

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

6 | Concept of complex integral, basic definitions, related theorems | |

7 | Cauchy Goursat theorem, related theorem, certain applications | |

8 | Cauchy Integral formulas, related theorems and applications | |

9 | Morera theorem | |

10 | Maksimum modulus theorem, Liouville theorem and fundemental theorem of algebra Goursat theorem and related results | |

11 | Taylor and Laurent Series | |

12 | Zeros and poles of analytic functions, rezidue and related theorems | |

13 | Rezidues and related theorems, concepts of improper integrals | |

14 | Some applications of improper integrals |

Prerequisites | COMPLEX ANALYSIS I |

Language of Instruction | Turkish |

Course Coordinator | Prof. Dr. Hüseyin IRMAK |

Instructors | - |

Assistants | - |

Resources | Complex variables and applications - 6th ed., Brown, J. W., McGraw-Hill., 2005. |

Supplementary Book | [1] Theory and problems of complex analysis, Schaum`s Outlines Series, Spiegel, M., Metric Editions , 1986 [2] Calculus with Analytic Geometry, Silverman, R. A., Prentice Hall., 1985 . [3] Real and Complex Analysis, Rudin, W., McGraw-Hill., 1991. [4] Complex variable with applicatins, Ponnusamy, S. and Silverman, H., Birkhauser, Berlin, 2006. |

Document | Lecture notes |

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

Content | - |

Program Learning Outcomes | Level of Contribution | |

1 | To have a grasp of theoretical and applied knowledge in main fields of mathematics | 5 |

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 | 4 |

4 | To be able to relate the gained mathematical acquisitions with different disciplines and apply in real life | 3 |

5 | To have the qualification of studying independently in a problem or a project requiring mathematical knowledge | 3 |

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 | 4 |

8 | To be able to determine what sort of knowledge the problem met requires and guide the process of learning this knowledge | 5 |

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 | 4 |

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 | 4 |

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

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