APPLIED MATHEMATICS (TURKISH, THESIS) | |||||
Master | TR-NQF-HE: Level 7 | QF-EHEA: Second Cycle | EQF-LLL: Level 7 |
Course Code | Course Name | Semester | Theoretical | Practical | Credit | ECTS |
MAT5009 | Functional Analysis I | Fall Spring |
3 | 0 | 3 | 12 |
This catalog is for information purposes. Course status is determined by the relevant department at the beginning of semester. |
Language of instruction: | Turkish |
Type of course: | Departmental Elective |
Course Level: | |
Mode of Delivery: | Face to face |
Course Coordinator : | Assoc. Prof. ERSİN ÖZUĞURLU |
Recommended Optional Program Components: | None |
Course Objectives: | This course provides deep understanding of introductory functional analysis. The objective of this course is to cover fundamental theorems of functional analysis such as HahnBanach theorem, Open mapping theorem, Closed graph theorem, Baire’s category theorem, Banach fixed point theorem, and their applications. |
The students who have succeeded in this course; The students who succeeded in this course; o will be able to know the essential theorems such as Open mapping theorem, Closed graph theorem, Baire’s category theorem, and Banach fixed point theorem of functional analysis and to be aware of the important applications of these theorems. o will be able to compare strong and weak convergence. o will be able to know the differences between convergences of sequences of operators and functionals. |
This course aims to teach basic theory and applications of Functional Analysis. |
Week | Subject | Related Preparation |
1) | Hilbert Spaces: HilbertAdjoint Operator. | |
2) | SelfAdjoint, Unitary and Normal Operators. | |
3) | Fundamental Theorems for Normed and Banach Spaces: Zorn’s Lemma,HahnBanach Theorem. | |
4) | HahnBanach Theorem for Complex and Normed Spaces, and It’s Application to C[a,b]. | |
5) | Adjoint Operator. | |
6) | Reflexive Spaces. | |
7) | Category Theorem, Uniform Boundedness Theorem, and Applications. | |
8) | Convergence: Strong and Weak Convergence. | |
9) | Convergence of Sequences of Operators and Functionals. | |
10) | Open Mapping theorem. | |
11) | Closed Linear Operators and Closed Graph Theorem. | |
12) | Banach Fixed Point Theorem: Application of Banach’s Theorem to Linear Equations. | |
13) | Application of Banach’s Theorem to Linear Equations, Differential Equations, and Integral Equations. | |
14) | Approximation Theory: Approximation in Normed Spaces, Uniqueness and Strict Convexity. Uniform Approximation, Chebyshev Polynomials, Approximation in Hilbert Spaces. |
Course Notes / Textbooks: | Walter Rudin, Functional Analysis 2/E, International Series in Pure and Applied Mathematics. |
References: | Erwin Kreyszig, “Introductory Functional Analysis with Applications” by Wiley. |
Semester Requirements | Number of Activities | Level of Contribution |
Homework Assignments | 7 | % 30 |
Presentation | 1 | % 30 |
Final | 1 | % 40 |
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 |
Presentations / Seminar | 1 | 40 | 40 |
Homework Assignments | 7 | 13 | 91 |
Final | 1 | 27 | 27 |
Total Workload | 200 |
No Effect | 1 Lowest | 2 Low | 3 Average | 4 High | 5 Highest |
Program Outcomes | Level of Contribution |