CANKIRI KARATEKIN UNIVERSITY

Bologna Information System

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

COMPLEX ANALYSIS I | MAT301 | FALL | 4+0 | Fac./ Uni. | C | 8 |

Learning Outcomes | 1-To be able to do algebraic operations related to complex numbers 2-To be able to do certain geometric operations in complex space 3-To be able to apply theorems related to sequences and cauchy sequences 4-To be able to explain the concepts functions and transformations in complex space 5-To be able to express basic theorems related to limit, continuity and uniform continuity in complex space 6-To be able to apply convergence tests to complex series |

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

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

Classroom study (Pre-study, practice) | 14 | 8 | 112 | |

Assignments | 0 | 0 | 0 | 0 |

Short-Term Exams (exam + preparation) | 20 | 4 | 8 | 32 |

Midterm exams (exam + preparation) | 30 | 1 | 12 | 12 |

Project | 0 | 0 | 0 | 0 |

Laboratory | 0 | 0 | 0 | 0 |

Final exam (exam + preparation) | 50 | 1 | 16 | 16 |

Other | 0 | 0 | 0 | 0 |

Total Workload (hours) | 228 | |||

Total Workload (hours) / 30 (s) | 7,6 ---- (8) | |||

ECTS Credit | 8 |

Week | Topics | Study Metarials |

1 | Introduction to complex numbers and basic operations. | |

2 | Construction of complex numbers and certain geometric properties. | |

3 | Certain algebric operations in complex plane. | |

4 | Topologic operations in complex plane / I. Short Exam | |

5 | Sequences in complex plane, related definitions, theorems and applications. | |

6 | Cauchy sequences in complex plane, related definitions, theorems and applications. | |

7 | Certain functions in the complex plane and some applications / II. Short Exam | |

8 | Certain transformations in the complex plane and some applications. | |

9 | The concept of limit in complex plane and related theorems, some applications. | |

10 | Certain roles of complex sequences for limits and related theorems, some applications / III. Short Exam | |

11 | Continuous in the complex plane, related theorems and certain applications. | |

12 | Complex function sequences and related definitions, their applications. | |

13 | The concept of complex series, basic concepts and theorems. | |

14 | Convergence and uniform convergence of complex series and related criterian / IV. Short Exam |

Prerequisites | - |

Language of Instruction | Turkish |

Course Coordinator | Assoc. 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 2. Calculus with Analytic Geometry, Silverman, R. A., Prentice Hall., 1985 3. Real and Complex Analysis, Rudin, W., McGraw-Hill., 1991 |

Document | Lecture notes |

Goals | To constitute complex numbers and complex plane, to introduce geometric, algebric and topologic properties of this plane, to introduce or determine concepts of analysis (comlex (number) sequence, Cauchy sequence, their convergences and divergences, certain complex functions, limit, series and convergence and divergence of them) and to apply their applications. |

Content | Introduction to complex numbers and basic operations on them, construction of complex numbers and some geometric properties of them, some algebraic operations on complex space, some topological properties of complex space, sequences in complex space and basic definitions theorems, applications related to them, Cauchy sequences in complex space and basic definitions, theorems and applications related to them, some functions on complex space and some applications, some transformations on complex space and some applications, concept of limit in complex space and related theorems, the concept of sequential limit in complex space and related theorems, the concept of uniform continuity in complex space and related theorems, sequences of complex valued functions and related definitions, the concept of complex series and related theorems, the convergence and uniform convergence of complex series and related criteria. |

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 | 5 |

3 | To be able to use the gained mathematical knowledge in the process of identifying the problem, analyzing and determining the solution steps | 5 |

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 | 4 |

9 | To adopt the necessity of learning constantly by observing the improvement of scientific accumulation over time | 2 |

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 | - |

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

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