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11111
COURSE INTRODUCTION AND APPLICATION INFORMATION
| Course Name | |
| Code | Semester | Theory (hour/week) | Application/Lab (hour/week) | Local Credits | ECTS |
|---|---|---|---|---|---|
| Fall/Spring |
| Prerequisites |
| ||||||||
| Course Language | |||||||||
| Course Type | Service Course | ||||||||
| Course Level | - | ||||||||
| Mode of Delivery | - | ||||||||
| Teaching Methods and Techniques of the Course | Problem SolvingQ&A | ||||||||
| Course Coordinator | - | ||||||||
| Course Lecturer(s) | |||||||||
| Assistant(s) | |||||||||
| Course Objectives | |
| Learning Outcomes | The students who succeeded in this course;
|
| Course Description |
|
| Core Courses | |
| Major Area Courses | ||
| Supportive Courses | ||
| Media and Managment Skills Courses | ||
| Transferable Skill Courses |
WEEKLY SUBJECTS AND RELATED PREPARATION STUDIES
| Week | Subjects | Required Materials |
| 1 | Inner product spaces and their properties, Hilbert Spaces | Erwin Kreyszig, “Introductory Functional Analysis with Applications” by Wiley. |
| 2 | Inner product spaces and their properties, Hilbert Spaces | Erwin Kreyszig, “Introductory Functional Analysis with Applications” by Wiley. |
| 3 | Orthogonal complements and direct sums | Erwin Kreyszig, “Introductory Functional Analysis with Applications” by Wiley. |
| 4 | Orthogonal complements and direct sums | Erwin Kreyszig, “Introductory Functional Analysis with Applications” by Wiley. |
| 5 | Orthonormal sets and sequences | Erwin Kreyszig, “Introductory Functional Analysis with Applications” by Wiley. |
| 6 | Fourier series and their properties | Erwin Kreyszig, “Introductory Functional Analysis with Applications” by Wiley. |
| 7 | Total orthonormal sets and sequences | Erwin Kreyszig, “Introductory Functional Analysis with Applications” by Wiley. |
| 8 | Representation of functionals on Hilbert spaces | Erwin Kreyszig, “Introductory Functional Analysis with Applications” by Wiley. |
| 9 | Hilbert-Adjoint operator | Erwin Kreyszig, “Introductory Functional Analysis with Applications” by Wiley. |
| 10 | Self-adjoint, unitary and normal operators | Erwin Kreyszig, “Introductory Functional Analysis with Applications” by Wiley. |
| 11 | Fundamental theorems of functional analysis: Zorn's lemma, Hahn-Banach theorem and Banach fixed point theorem | Erwin Kreyszig, “Introductory Functional Analysis with Applications” by Wiley. |
| 12 | Fundamental theorems of functional analysis: Baire category theorem, Uniform boundedness theorem, Open mapping theorem and Banach fixed point theorem | Erwin Kreyszig, “Introductory Functional Analysis with Applications” by Wiley. |
| 13 | Weak and strong convergence | Erwin Kreyszig, “Introductory Functional Analysis with Applications” by Wiley. |
| 14 | Convergence of sequences of operators and functionals | Erwin Kreyszig, “Introductory Functional Analysis with Applications” by Wiley. |
| 15 | Course Review | |
| 16 | Course Review |
| Course Notes/Textbooks | Erwin Kreyszig, “Introductory Functional Analysis with Applications” by Wiley. |
| Suggested Readings/Materials | Walter Rudin, Functional Analysis 2/E, International Series in Pure and Applied Mathematics. |
EVALUATION SYSTEM
| Semester Activities | Number | Weigthing |
| Participation | 1 | 10 |
| Laboratory / Application | ||
| Field Work | ||
| Quizzes / Studio Critiques | 6 | 15 |
| Portfolio | ||
| Homework / Assignments | ||
| Presentation / Jury | ||
| Project | ||
| Seminar / Workshop | ||
| Oral Exam | ||
| Midterm | 1 | 35 |
| Final Exam | 1 | 40 |
| Total |
| Weighting of Semester Activities on the Final Grade | 8 | 60 |
| Weighting of End-of-Semester Activities on the Final Grade | 1 | 40 |
| Total |
ECTS / WORKLOAD TABLE
| Semester Activities | Number | Duration (Hours) | Workload |
|---|---|---|---|
| Course Hours (Including exam week: 16 x total hours) | 16 | 3 | 48 |
| Laboratory / Application Hours (Including exam week: 16 x total hours) | 16 | ||
| Study Hours Out of Class | 14 | 3 | |
| Field Work | |||
| Quizzes / Studio Critiques | 3 | ||
| Portfolio | |||
| Homework / Assignments | 2 | ||
| Presentation / Jury | |||
| Project | |||
| Seminar / Workshop | |||
| Oral Exam | |||
| Midterms | 2 | 28 | |
| Final Exams | 1 | 36 | |
| Total | 182 |
COURSE LEARNING OUTCOMES AND PROGRAM QUALIFICATIONS RELATIONSHIP
| # | Program Competencies/Outcomes | * Contribution Level | ||||
1 | 2 | 3 | 4 | 5 | ||
*1 Lowest, 2 Low, 3 Average, 4 High, 5 Highest