ECTS - Functional Analysis
Functional Analysis (MATH357) Course Detail
| Course Name | Course Code | Season | Lecture Hours | Application Hours | Lab Hours | Credit | ECTS |
|---|---|---|---|---|---|---|---|
| Functional Analysis | MATH357 | 7. Semester | 3 | 0 | 0 | 3 | 6 |
| Pre-requisite Course(s) |
|---|
| MATH251 |
| Course Language | English |
|---|---|
| Course Type | Elective Courses |
| Course Level | Bachelor’s Degree (First Cycle) |
| Mode of Delivery | Face To Face |
| Learning and Teaching Strategies | Lecture, Question and Answer, Problem Solving. |
| Course Lecturer(s) |
|
| Course Objectives | The aim of the course is providing a familiarity to concepts of the functional analysis, such as norm, compactness and convergence. |
| Course Learning Outcomes |
The students who succeeded in this course;
|
| Course Content | Vector spaces, Hamel basis, linear operators, equations in operators, ordered vector spaces, extension of positive linear functionals, convex functions, Hahn-Banach Theorem, The Minkowski functional, Separation Theorem, metric spaces, continuity and uniform continuity, completeness, Baire Theorem, normed spaces, Banach spaces, the algebra of bounde |
Weekly Subjects and Releated Preparation Studies
| Week | Subjects | Preparation |
|---|---|---|
| 1 | Metric Spaces Open Sets, Closed Sets | pp. 2--22 |
| 2 | Convergence, Cauchy Sequence, Completeness | pp. 23--44 |
| 3 | Vector Spaces, Normed Spaces Banach Spaces | pp. 50--66 |
| 4 | Further Properties of Normed Spaces Finite Dimensional Normed Spaces and Subspaces | pp. 67--75 |
| 5 | Compactness and Finite Dimensional Linear Operators | pp. 77--90 |
| 6 | Bounded and Continuous Linear Operators, Linear Functional | pp. 91--110 |
| 7 | Midterm Exam | |
| 8 | Linear Operators and Functionals on Finite Dimensional Spaces Normed Spaces of Operators, Dual Spaces | pp. 111--125 |
| 9 | Hahn-Banach Theorem Hahn-Banach Theorem for Complex Valued Vector Spaces and Normed Spaces | pp. 213--224 |
| 10 | Application to Bounded Linear Functionals on C[a,b] | pp. 225--230 |
| 11 | Adjoint Operator | pp. 231--238 |
| 12 | Reflexive Spaces | pp. 239-245 |
| 13 | Midterm Exam | |
| 14 | Category Theorems Uniform Boundedness Theorem | pp. 246--254 |
| 15 | Strong and Weak Convergence Convergence of Sequence of Operators and Functionals | pp.256-268 |
| 16 | Review |
Sources
| Course Book | 1. Introductory Functional Analysis with Applications, E. Kreyszig, 1978, John Wiley and Sons Inc. ISBN 0-471-5073-8 |
|---|---|
| Other Sources | 2. Elements of the Theory of Functions and Functional Analysis, A.N. Kolmogorov and S.V. Fomin, Dover, NY, 1999. ISBN: 0-486-40683-0 |
| 3. Functional Analysis, G.Bachman and L. Narici , Dover, 1991, ISBN: 0-486-40251-7 |
Evaluation System
| Requirements | Number | Percentage of Grade |
|---|---|---|
| Attendance/Participation | - | - |
| Laboratory | - | - |
| Application | - | - |
| Field Work | - | - |
| Special Course Internship | - | - |
| Quizzes/Studio Critics | - | - |
| Homework Assignments | - | - |
| Presentation | - | - |
| Project | - | - |
| Report | - | - |
| Seminar | - | - |
| Midterms Exams/Midterms Jury | 2 | 60 |
| Final Exam/Final Jury | 1 | 40 |
| Toplam | 3 | 100 |
| Percentage of Semester Work | 60 |
|---|---|
| Percentage of Final Work | 40 |
| Total | 100 |
Course Category
| Core Courses | |
|---|---|
| Major Area Courses | X |
| 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 | ||
| 1 | Acquires skills to use the advanced theoretical and applied knowledge obtained at the mathematics bachelors program to do further academic and scientific research in both mathematics-based graduate programs and public or private sectors. | X | ||||
| 2 | Transplants and applies the theoretical and applicable knowledge gained in their field to the secondary education by using suitable tools and devices. | X | ||||
| 3 | Acquires the skill of choosing, using and improving problem solving techniques which are needed for modeling and solving current problems in mathematics or related fields by using the obtained knowledge and skills. | X | ||||
| 4 | Acquires analytical thinking and uses time effectively in the process of deduction. | X | ||||
| 5 | Acquires basic software knowledge necessary to work in the computer science related fields and together with the skills to use information technologies effectively. | X | ||||
| 6 | Obtains the ability to collect data, to analyze, interpret and use statistical methods necessary in decision making processes. | X | ||||
| 7 | Acquires the level of knowledge to be able to work in the mathematics and related fields and keeps professional knowledge and skills up-to-date with awareness in the importance of lifelong learning. | X | ||||
| 8 | Takes responsibility in mathematics related areas and has the ability to work affectively either individually or as a member of a team. | X | ||||
| 9 | Has proficiency in English language and has the ability to communicate with colleagues and to follow the innovations in mathematics and related fields. | X | ||||
| 10 | Has the ability to communicate ideas with peers supported by qualitative and quantitative data. | X | ||||
| 11 | Has professional and ethical consciousness and responsibility which takes into account the universal and social dimensions in the process of data collection, interpretation, implementation and declaration of results in mathematics and its applications. | X | ||||
ECTS/Workload Table
| Activities | Number | Duration (Hours) | Total Workload |
|---|---|---|---|
| Course Hours (Including Exam Week: 16 x Total Hours) | 16 | 3 | 48 |
| Laboratory | |||
| Application | |||
| Special Course Internship | |||
| Field Work | |||
| Study Hours Out of Class | 14 | 3 | 42 |
| Presentation/Seminar Prepration | |||
| Project | |||
| Report | |||
| Homework Assignments | 5 | 4 | 20 |
| Quizzes/Studio Critics | |||
| Prepration of Midterm Exams/Midterm Jury | 2 | 12 | 24 |
| Prepration of Final Exams/Final Jury | 1 | 16 | 16 |
| Total Workload | 150 | ||