CANKIRI KARATEKIN UNIVERSITY

Bologna Information System

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

INTRODUCTION TO FUNCTIONAL ANALYSIS | MAT403 | FALL | 4+0 | C | 8 |

Learning Outcomes | 1-To explain metric spaces, complete metric spaces and properties of complete metric spaces 2-To explain some basic structures like open-closed sets and limit of sequences 3-To explain the concepts of normed spaces, linear operators and linear functionals on normed spaces 4-To explain the fundamental theorems of functional analysis like hahn-banach theorem, banach steinhauss theorem, open mapping and closed graphs theorems |

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

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

Classroom study (Pre-study, practice) | 12 | 7 | 84 | |

Assignments | 10 | 2 | 14 | 28 |

Short-Term Exams (exam + preparation) | 10 | 2 | 15 | 30 |

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

Project | 0 | 0 | 0 | 0 |

Laboratory | 0 | 0 | 0 | 0 |

Final exam (exam + preparation) | 50 | 1 | 20 | 20 |

Other | 0 | 0 | 0 | 0 |

Total Workload (hours) | 234 | |||

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

ECTS Credit | 8 |

Week | Topics | Study Metarials |

1 | Metric and Metric spaces, neighborhood of a point , open and closed sets in metric spaces | |

2 | Sequences in metric spaces and their convergence, Hölder and Minkowski inequalities, Classical sequence spaces | |

3 | Complete metric spaces, First and second countable metric spaces, Baire Category Theorem | |

4 | Continuous functions between metric spaces and their properties | |

5 | Vector space, subspace, norm, normed space, Banach space, examples of normed spaces, | |

6 | Finite dimensional normed spaces | |

7 | Bounded and continuous linear operators | |

8 | Linear operators and functionals in finite dimensional spaces, Normed operator spaces, Dual space | |

9 | Hahn-Banach Teorem, Hahn-Banach Theorem for normed spaces | |

10 | Applications of bounded linear functionals defined on continuous function spaces, Reflexive spaces | |

11 | Banach-Steinhaus Theorem and its applications | |

12 | Open Mapping Theorem and its applications | |

13 | Closed linear operators | |

14 | Closed Graph theorem and its applications |

Prerequisites | - |

Language of Instruction | Turkish |

Course Coordinator | Prof. Dr. Hüseyin IRMAK |

Instructors |
1-)Doktor Öğretim Üyesi Gülsüm Ulusoy Ada |

Assistants | - |

Resources | Fonksiyonel Analize Giriş I, Erwin Kreyszig den uyarlayan Prof. Dr. Öner Çakar, Ankara Üniversitesi Yayınları, 2007. |

Supplementary Book | [1] Yüksel SOYKAN, Fonksiyonel Analiz, Nobel yayın dağıtım. 2008, Ankara. [2] Erdoğan S. Şuhubi, Fonksiyonel analiz, İTÜ vakfı yayınları, 2001. [3] Tosun Terzioğlu, Fonksiyonel Analizin Yöntemleri, Matematik Vakfı, 1998. |

Document | Lecture notes |

Goals | - |

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 | 5 |

4 | To be able to relate the gained mathematical acquisitions with different disciplines and apply in real life | 2 |

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 | 5 |

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 | 3 |

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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