COURSE SYLLABUS

FUNCTIONAL ANALYSIS

1	Course Title:	FUNCTIONAL ANALYSIS
2	Course Code:	MAT4021
3	Type of Course:	Compulsory
4	Level of Course:	First Cycle
5	Year of Study:	4
6	Semester:	7
7	ECTS Credits Allocated:	8
8	Theoretical (hour/week):	2
9	Practice (hour/week) :	2
10	Laboratory (hour/week) :	0
11	Prerequisites:	none
12	Recommended optional programme components:	None
13	Language:	Turkish
14	Mode of Delivery:	Face to face
15	Course Coordinator:	Prof. Dr. OSMAN BİZİM
16	Course Lecturers:	Prof. Dr. Osman Bizim
17	Contactinformation of the Course Coordinator:	Uludağ Üniversitesi, Fen-Edebiyat Fakültesi Matematik Bölümü, Görükle Bursa-TÜRKİYE 0 224 294 17 50 / obizim@uludag.edu.tr
18	Website:
19	Objective of the Course:	The aim of the course is to make the students gain the fundamental concepts on functional analysis including metric spaces, normed spaces, and inner-product spaces. Further to give the connection among entire spaces, normed spaces and Hilbert spaces.
20	Contribution of the Course to Professional Development

Learning Outcomes:

1	Learns metric, normed, topologic and inner-product spaces and relation between them.;
2	Learns the Banach spaces and their properties.;
3	Learns the linear spaces, linear operators and their properties.;
4	Learns dual and algebraic dual spaces and their properties.;
5	Learns the Hilbert spaces and their properties.;

22	Course Content:

Week	Theoretical	Practical
1	Metric, normed, topologic and inner-product spaces and their properties	Examples of the Metric, normed, topologic and inner-product spaces.
2	Linear spaces and their properties	Examples of the Linear spaces
3	The Banach spaces and their properties	Examples of the Banach spaces.
4	The linear space of finite order and their properties.	Examples of the linear space of finite order and their properties.
5	The linear operators and their properties.	Examples of the linear operators.
6	The bounded and continued linear operators and their properties.	Examples of the bounded and continued linear operators
7	The linear bounded extensions and their properties.	Examples of the linear bounded extensions and Dual spaces
8	The algebraic dual space, linear operators in space of finite order and their properties.	Examples of the algebraic dual space and linear operators in space of finite order
9	The Hanh-Banach theorem	The applications of the Hanh-Banach theorem
10	The open-mapping and closed-graph theorems	The applications of the open-mapping and closed-graph theorems
11	The Hilbert spaces and their properties	Examples of the Hilbert spaces
12	The closed subspace, algebraic sum of the space and its properties	Examples of the closed subspace and algebraic sum of the spaces
13	The functional in Hilbert spaces and their properties.	Examples of the functional in Hilbert spaces
14	The linear operators with two variables and their properties	Examples of the linear operators with two variables

23	Textbooks, References and/or Other Materials:	[1] Fonksiyonel Analiz, M. Bayraktar, [2] Fonksiyonel Analiz’in Yöntemleri, T. Terzioğlu, [3] Functional Analysis, W. Rudin, [4] Fonksiyonel Analiz, B. Musayev, M. Alp.
24	Assesment

TERM LEARNING ACTIVITIES	NUMBER	PERCENT
Midterm Exam	1	40
Quiz	0	0
Homeworks, Performances	0	0
Final Exam	1	60
Total	2	100
Contribution of Term (Year) Learning Activities to Success Grade		40
Contribution of Final Exam to Success Grade		60
Total		100
Measurement and Evaluation Techniques Used in the Course
Information

ECTS / WORK LOAD TABLE

CONTRIBUTION OF LEARNING OUTCOMES TO PROGRAMME QUALIFICATIONS

LO: Learning Objectives

PQ: Program Qualifications

Contribution Level:

1 Very Low

2 Low

3 Medium

4 High

5 Very High