Course Information
SemesterCourse Unit CodeCourse Unit TitleL+PCreditNumber of ECTS Credits
8MATH452FUNCTIONAL ANALYSIS3+036

Course Details
Language of Instruction English
Level of Course Unit First Cycle
Department / Program MATHEMATICS
Mode of Delivery Face to Face
Type of Course Unit Elective
Objectives of the Course To introduce students with basic notations and concepts related with the abstract spaces and linear operators. To show the use of theoretical knowledge in solving some applied problems. To motivate students to do research and use different literature when learning the course. To give elementary background for more advanced study in Functional analysis.
Course Content Metric spaces. Banach and Hilbert Spaces. Linear Operators on Normed Spaces, Bounded and Compact Operators. Spaces of Linear Operators and Convergence. Fundamental Theorems for Normed and Banach Spaces: Hanh-Banach Theorem, Uniform Boundedness Theorem, Open Mapping Theorem, Closed Graph Theorem. Linear Functionals on Hilbert Spaces and Riesz Representation Theorem. Adjoint, Self-adjoint, Unitary and Normal Operators. Spectrum and Resolvent of an Operator. Spectral Properties of Bounded and Compact Operators. Unbounded Operators and Their Basic Properties.
Course Methods and Techniques
Prerequisites and co-requisities None
Course Coordinator None
Name of Lecturers ŞİRİN ATILGAN BÜYÜKAŞIK
Assistants None
Work Placement(s) No

Recommended or Required Reading
Resources Walter Rudin, “Functional Analysis”, McGraw-Hill,Inc.
E. Kreyszig, “Introductory Functional Analysis with Applications”, John-Wiley &Sons.
L. Debnath, P. Mikusinski, “Introduction to Hilbert spaces with Applications”, Third edition.
I. Gohberg, S. Goldberg, “Basic Operator Theory”, Birkhauser.
A. N. Kolmogorov, S.V. Fomin, “Introductory Real Analysis”, Dover Publications,INC.

Course Category

Planned Learning Activities and Teaching Methods
Activities are given in detail in the section of "Assessment Methods and Criteria" and "Workload Calculation"

Assessment Methods and Criteria
In-Term Studies Quantity Percentage
Midterm exams 2 % 50
Quizzes 0 % 0
Homeworks 5 % 5
Other activities 0 % 0
Laboratory works 0 % 0
Projects 1 % 5
Final examination 1 % 40
Total
9
% 100

ECTS Allocated Based on Student Workload
Activities Quantity Duration Total Work Load
Weekly Course Time 1 36 36
Outside Activities About Course (Attendance, Presentation, Midterm exam,Final exam, Quiz etc.) 1 99 99
Exams and Exam Preparations 1 57 57
Total Work Load   Number of ECTS Credits 6 192

Course Learning Outcomes: Upon the successful completion of this course, students will be able to:
NoLearning Outcomes
1 To know the structure of Banach and Hilbert spaces
2 To be able to classify linear operators according to their behavior and basic properties
3 To understand the fundamental theorems for normed and Banach spaces and be able to use them
4 To know the definition of a spectrum of an operator. To be able to find the spectrum and spectral properties of some special operators
5 To be able to define and give examples of unbounded operators


Weekly Detailed Course Contents
WeekTopicsStudy MaterialsMaterials
1 Metric Spaces, Convergence, Completeness, Compactness Chapter 1
2 Banach spaces Chapter 2
3 Hilbert Spaces, Separable Spaces, Orthogonal Expansions Chapter 3
4 Bounded and Compact Linear Operators, Sequences of Operators Chapter 2
5 Hahn-Banach Theorem Chapter 4.2
6 Uniform Boundedness Theorem Chapter 4.7
7 Open Mapping and Closed Graph Theorem Chapter 4.12 and 4.13
8 Linear Functionals on Inner Product Spaces Chapter 3.8
9 Riesz Representation, Adjoint of a Bounded Operator Chapter 3.9
10 Self-Adjoint, Unitary and Normal Operators Chapter 3.10
11 Spectrum and Resolvent Chapter 7
12 Spectral Properties of Bounded and Compact Operators Chapter 7
13 Unbounded Operators Chapter 10
14 Unbounded Operators with Applications Chapter 10


Contribution of Learning Outcomes to Programme Outcomes
P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 P11 P12 P13 P14
C1 3
C2 3
C3 3 3
C4 3 3
C5 3

Contribution: 0: Null 1:Slight 2:Moderate 3:Significant 4:Very Significant


https://obs.iyte.edu.tr/oibs/bologna/progCourseDetails.aspx?curCourse=163213&lang=en