MATHEMATICS (TURKISH, PHD) | |||||
PhD | TR-NQF-HE: Level 8 | QF-EHEA: Third Cycle | EQF-LLL: Level 8 |
Course Code | Course Name | Semester | Theoretical | Practical | Credit | ECTS |
MAT4054 | Functional Analysis II | Fall | 3 | 0 | 3 | 6 |
The course opens with the approval of the Department at the beginning of each semester |
Language of instruction: | En |
Type of course: | Departmental Elective |
Course Level: | |
Mode of Delivery: | Face to face |
Course Coordinator : | Dr. Öğr. Üyesi TUĞCAN DEMİR |
Course Objectives: | This twotier course aims to provide deep understanding of introductory functional analysis. |
The students who have succeeded in this course; The students who succeeded in this course; o will be able to understand the need for functional analysis and infinite dimensional vector spaces. o will be able to compare the notions of Metric, Banach and Hilbert spaces. o will be able to construct formal proofs. o will be able to compare function,functional and operator. o will be able to derive the dual space of a given Banach space. o will be able to explain representation of functionals on Hilbert spaces. |
This course aims to teach basic theory and applications of Functional Analysis |
Week | Subject | Related Preparation | |
1) | Introduction: Metric Space, Open set, Closed set, Neighborhood. | ||
2) | Sequences: Boundedness, Convergence, Cauchy Sequence, Seperability. | ||
3) | Completeness and Completion of Metric Spaces. | ||
4) | Examples. Completeness Proofs. | ||
5) | Vector spaces: Subspace, Dimension, Hamel Basis. | ||
6) | Normed Spaces, Banach Spaces: Normed Space, Banach Space, Further Properties of Normed Spaces. | ||
7) | Finite Dimensional Normed Spaces and Subspaces, Compactness and Finite Dimension. | ||
8) | Linear Operators: Some Properties. | ||
9) | Applications of Bounded and Linear Operators. | ||
10) | Functionals: Linear Functionals, Normed Spaces of Operators | ||
11) | Dual Space: Algebric Dual and Continuous Dual. | ||
12) | Inner Product Spaces, Hilbert Spaces: Inner Product Space Hilbert Space, Further Properties of Inner Product Spaces, Parallelogram Law. | ||
13) | Orthogonal Complements and Direct Sums. | ||
14) | Orthonormal Sets and Sequences, Total Orthonormal Sets and Sequences, representation of Functionals on Hilbert Spaces, Hilbert adjoint Operator. |
Course Notes: | Erwin Kreyszig, “Introductory Functional Analysis with Applications” by Wiley. |
References: | Tosun Terzioğlu, Fonksiyonel analizin yöntemleri, İstanbul: Matematik Vakfı 1998 |
Semester Requirements | Number of Activities | Level of Contribution |
Attendance | % 0 | |
Laboratory | % 0 | |
Application | % 0 | |
Field Work | % 0 | |
Special Course Internship (Work Placement) | % 0 | |
Quizzes | 3 | % 15 |
Homework Assignments | % 0 | |
Presentation | % 0 | |
Project | % 0 | |
Seminar | % 0 | |
Midterms | 2 | % 45 |
Preliminary Jury | % 0 | |
Final | 1 | % 40 |
Paper Submission | % 0 | |
Jury | % 0 | |
Bütünleme | % 0 | |
Total | % 100 | |
PERCENTAGE OF SEMESTER WORK | % 60 | |
PERCENTAGE OF FINAL WORK | % 40 | |
Total | % 100 |
Activities | Number of Activities | Duration (Hours) | Workload |
Course Hours | 14 | 3 | 42 |
Laboratory | 0 | 0 | 0 |
Application | 0 | 0 | 0 |
Special Course Internship (Work Placement) | 0 | 0 | 0 |
Field Work | 0 | 0 | 0 |
Study Hours Out of Class | 14 | 2 | 28 |
Presentations / Seminar | 1 | 10 | 10 |
Project | 0 | 0 | 0 |
Homework Assignments | 0 | 0 | 0 |
Quizzes | 3 | 2 | 6 |
Preliminary Jury | 0 | ||
Midterms | 2 | 10 | 20 |
Paper Submission | 0 | ||
Jury | 0 | ||
Final | 1 | 19 | 19 |
Total Workload | 125 |
No Effect | 1 Lowest | 2 Low | 3 Average | 4 High | 5 Highest |
Program Outcomes | Level of Contribution |