Rapor Tarihi: 13.04.2026 03:07
| Course Title | Code | Language | Type | Semester | L+U Hour | Credits | ECTS |
|---|---|---|---|---|---|---|---|
| Functional Analysis | MAT405 | Turkish | Compulsory | 7. Semester | 3 + 0 | 3.0 | 5.0 |
| Prerequisite Courses | |
| Course Level | Undergraduate |
| Mode of delivery | Lecturing |
| Course Coordinator | Prof. Dr. Merve İLKHAN KARA |
| Instructor(s) | |
| Goals | The aim of this course is to introduce the fundamental concepts of functional analysis, starting from metric spaces to normed spaces, and to enable students to understand key notions such as convergence, continuity, completeness, and compactness. It also aims to develop analytical thinking and problem-solving skills within the framework of linear and normed spaces. |
| Course Content | This course begins with the definition, examples, and fundamental properties of metric spaces, followed by sequences, convergence, Cauchy sequences, and completeness. Complete metric spaces, continuity, and compactness are studied. The course then introduces linear spaces and normed spaces, including their definitions, examples, and basic properties. Convergence and completeness in normed spaces, Banach spaces, and finite-dimensional normed spaces are also covered. The course is supported by problem-solving sessions. |
| # | Öğrenme Kazanımı |
| 1 | Defines the concepts of normed spaces and metric spaces and explains their fundamental properties. |
| 2 | Applies appropriate theorems and methods to solve problems in normed and metric spaces. |
| 3 | Constructs mathematical proofs using the fundamental theorems of functional analysis. |
| 4 | Interprets the concepts of completeness, boundedness, convergence, being a Cauchy sequence within the context of functional analysis. |
| 5 | Develops analytical thinking skills on abstract structures by using mathematical proof techniques. |
| Week | Topics/Applications | Method |
|---|---|---|
| 1. Week | Metric spaces: Definition, examples, and basic properties | Preparation, After Class Study |
| 2. Week | Metric spaces: Definition, examples, and basic properties | Preparation, After Class Study |
| 3. Week | Sequences, convergence, Cauchy sequences, and completeness | Preparation, After Class Study, Research |
| 4. Week | Complete Metric spaces | Preparation, After Class Study, Research |
| 5. Week | Continuity, compactness in metric spaces | Preparation, After Class Study, Research |
| 6. Week | Problem solving | Other Activities |
| 7. Week | Definition, examples, and fundamental properties of linear spaces. | Preparation, After Class Study |
| 8. Week | Introduction to normed spaces and their relation to metrics | Preparation, After Class Study, Research |
| 9. Week | Normed spaces: Definition, examples, and basic properties | Preparation, After Class Study |
| 10. Week | Normed spaces: Definition, examples, and basic properties | Preparation, After Class Study, Research |
| 11. Week | Convergence in normed spaces, Cauchy sequences, and the concept of completeness. | Preparation, After Class Study |
| 12. Week | Banach spaces and their fundamental properties | Preparation, After Class Study, Research |
| 13. Week | Finite dimensional normed spaces | Preparation, After Class Study, Research |
| 14. Week | Problem solving | Other Activities |
| No | Program Requirements | Level of Contribution | |||||
|---|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | |||
| 1 | Possesses theoretical and applied knowledge of the fundamental areas of mathematics (Analysis and Function Theory, Algebra and Number Theory, Geometry, Applied Mathematics, Topology and Foundations of Mathematics, and Mathematical Logic). | ✔ | |||||
| 3 | Defines mathematical problems, selects appropriate methods, and solves them using analytical/numerical techniques. | ✔ | |||||
| 4 | Constructs mathematical expressions with logical integrity and reaches conclusions using proof methods. | ✔ | |||||
| Program Requirements | DK1 | DK2 | DK3 | DK4 | DK5 |
|---|---|---|---|---|---|
| PY1 | 5 | 5 | 5 | 5 | 5 |
| PY3 | 3 | 5 | 4 | 3 | 5 |
| PY4 | 4 | 3 | 3 | 2 | 4 |
| Ders Kitabı veya Notu | |
|---|---|
| Diğer Kaynaklar |
|
| ECTS credits and course workload | Quantity | Duration (Hour) | Total Workload (Hour) | |
|---|---|---|---|---|
|
Ders İçi |
Class Hours | 14 | 3 | 42 |
|
Ders Dışı |
Homework | 1 | 3 | 3 |
| Preparation, After Class Study | 12 | 3 | 36 | |
| Research | 7 | 2.5 | 17.5 | |
| Other Activities | 2 | 3 | 6 | |
|
Sınavlar |
Midterm | 1 | 1.5 | 1.5 |
| Midterm Preparation | 1 | 3 | 3 | |
| Homework | 1 | 3 | 3 | |
| Final | 1 | 1.5 | 1.5 | |
| Classroom Activities | 14 | 1 | 14 | |
| Total Workload | 127.5 | |||
| *AKTS = (Total Workload) / 25,5 | ECTS Credit of the Course | 5.0 | ||
