ECTS - Functional Analysis
Functional Analysis (MATH357) Course Detail
| Course Name | Course Code | Season | Lecture Hours | Application Hours | Lab Hours | Credit | ECTS |
|---|---|---|---|---|---|---|---|
| Functional Analysis | MATH357 | Area Elective | 3 | 0 | 0 | 3 | 6 |
| Pre-requisite Course(s) |
|---|
| MATH251 |
| Course Language | English |
|---|---|
| Course Type | Elective Courses |
| Course Level | Natural & Applied Sciences Master's Degree |
| 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 | 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 | ||
| 1 | Has the ability to apply scientific knowledge gained in the undergraduate education and to expand and extend knowledge in the same or in a different area. | X | ||||
| 2 | Has the ability to obtain, to evaluate, to interpret and to apply information by doing scientific research. | X | ||||
| 3 | Can apply gained knowledge and problem solving abilities in inter-disciplinary research. | X | ||||
| 4 | Has the ability to work independently within research area, to state the problem, to develop solution techniques, to solve the problem, to evaluate the obtained results and to apply them when necessary. | X | ||||
| 5 | Takes responsibility individually and as a team member to improve systematic approaches to produce solutions in unexpected complicated situations related to the area of study. | X | ||||
| 6 | Can develop strategies, implement plans and principles on the area of study and can evaluate obtained results within the framework. | X | ||||
| 7 | Can develop and extend the knowledge in the area and to use them with scientific, social and ethical responsibility. | X | ||||
| 8 | Has the ability to follow recent developments within the area of research, to support research with scientific arguments and data, to communicate the information on the area of expertise in a systematically by means of written report and oral/visual presentation. | 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 software and hardware knowledge in the area of expertise, and has proficient information and communication technology knowledge. | X | ||||
| 11 | Has professional 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 | ||