ECTS - Functional Analysis
Functional Analysis (MATH557) Course Detail
| Course Name | Course Code | Season | Lecture Hours | Application Hours | Lab Hours | Credit | ECTS |
|---|---|---|---|---|---|---|---|
| Functional Analysis | MATH557 | 3 | 0 | 0 | 3 | 5 |
| Pre-requisite Course(s) |
|---|
| N/A |
| Course Language | English |
|---|---|
| Course Type | N/A |
| Course Level | Ph.D. |
| Mode of Delivery | Face To Face |
| Learning and Teaching Strategies | Lecture, Question and Answer, Team/Group. |
| Course Lecturer(s) |
|
| Course Objectives | Functional analysis is the generalization and geometrization of the fundamental concepts and methods of classical analysis. The techniques of functional analysis have many applications in various branches of pure and applied mathematics. This course gives a transparent expository treatment of the fundamentals of functional analysis, thus bringing the subject within the easy access of students. The course is designed for comprehending of the notions of linear operators, linear functionals on metric spaces and normed spaces. |
| Course Learning Outcomes |
The students who succeeded in this course; |
| Course Content | Sets and mappings, countable sets, metric spaces, complete metric spaces, Baire category theorem, compactness, connectednes, normed spaces, linear topological invariants, Hilbert spaces, Cauchy-Schwartz inequality, linear operators, bounded operators, unbounded operators, inverse operators, Hahn-Banach extension theorems, open mapping and closed gr |
Weekly Subjects and Releated Preparation Studies
| Week | Subjects | Preparation |
|---|
Sources
| Course Book | 1. L. A. Lusternik and V. I. Sobolev, Elements of Functional Analysis, Wiley, New York, 1974. |
|---|---|
| Other Sources | 2. E. Kreyszig, Introductory Functional Analysis with Applications, Wiley, New York, 1978. |
| 3. A. N. Kolmogorov and S. V. Fomin, Elements of the Theory of Functions and Funtional Analysis, Dover, New York, 1999. | |
| 4. R. Meise and D. Vogt, Introduction to functional analysis, Oxford University Press, New York, 1997. |
Evaluation System
| Requirements | Number | Percentage of Grade |
|---|---|---|
| Attendance/Participation | - | - |
| Laboratory | - | - |
| Application | - | - |
| Field Work | - | - |
| Special Course Internship | - | - |
| Quizzes/Studio Critics | - | - |
| Homework Assignments | 5 | 10 |
| Presentation | - | - |
| Project | - | - |
| Report | - | - |
| Seminar | - | - |
| Midterms Exams/Midterms Jury | 2 | 50 |
| Final Exam/Final Jury | 1 | 40 |
| Toplam | 8 | 100 |
| Percentage of Semester Work | |
|---|---|
| Percentage of Final Work | 100 |
| Total | 100 |
Course Category
| Core Courses | X |
|---|---|
| Major Area Courses | |
| Supportive Courses | |
| Media and Managment Skills Courses | |
| Transferable Skill Courses |
The Relation Between Course Learning Competencies and Program Qualifications
| # | Program Qualifications / Competencies | Level of Contribution | ||||
|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | ||
ECTS/Workload Table
| Activities | Number | Duration (Hours) | Total Workload |
|---|---|---|---|
| Course Hours (Including Exam Week: 16 x Total Hours) | |||
| Laboratory | |||
| Application | |||
| Special Course Internship | |||
| Field Work | |||
| Study Hours Out of Class | |||
| Presentation/Seminar Prepration | |||
| Project | |||
| Report | |||
| Homework Assignments | 5 | 2 | 10 |
| Quizzes/Studio Critics | |||
| Prepration of Midterm Exams/Midterm Jury | 2 | 7 | 14 |
| Prepration of Final Exams/Final Jury | 1 | 11 | 11 |
| Total Workload | 35 | ||