Nevşehir Hacı Bektaş Veli University Course Catalogue

Information Of Programmes

FACULTY OF LETTERS & SCIENCE / MAT440 - MATHEMATICS

Code: MAT440 Course Title: FUNCTIONAL ANALYSIS II Theoretical+Practice: 4+0 ECTS: 6
Year/Semester of Study 4 / Spring Semester
Level of Course 1st Cycle Degree Programme
Type of Course Optional
Department MATHEMATICS
Pre-requisities and Co-requisites None
Mode of Delivery Face to Face
Teaching Period 14 Weeks
Name of Lecturer NECDET BATIR (nbatir@nevsehir.edu.tr)
Name of Lecturer(s) NECDET BATIR,
Language of Instruction Turkish
Work Placement(s) None
Objectives of the Course
This course is designed to provide students with basic knowledge of functional analysis.

Learning Outcomes PO MME
The students who succeeded in this course:
LO-1 Hahn-Banach and open mapping theorem and Closed linear operator, closed graph theorem are known. PO-11 With the knowledge he gain, they determine the learning needs of those working under him, execute the musts of graduate education.
Examination
LO-2 Inner product space, closed subspaces and Complete subspaces are known. PO-11 With the knowledge he gain, they determine the learning needs of those working under him, execute the musts of graduate education.
Examination
LO-3 The minimum vector and vertical projection, Conjugate of an Hilbert operator and s-Linear transformation of two variables are known. PO-11 With the knowledge he gain, they determine the learning needs of those working under him, execute the musts of graduate education.
Examination
LO-4 Banach Algebra, Disk Algebra, Regular and singular elements, Topological zero divisor, Spectrum, Spectral radius, Ideals and quotient algebras are known. PO-11 With the knowledge he gain, they determine the learning needs of those working under him, execute the musts of graduate education.
Examination
PO: Programme Outcomes
MME:Method of measurement & Evaluation

Course Contents
Weekly Course Content
Week Subject Learning Activities and Teaching Methods
1 Hahn-Banach and open mapping theorem To speech face to face
2 Closed linear operator, closed graph theorem To speech face to face
3 Inner product space, closed subspaces To speech face to face
4 Complete subspaces To speech face to face
5 The minimum vector and vertical projection, To speech face to face
6 Conjugate of an Hilbert operator To speech face to face
7 s-Linear transformation of two variables To speech face to face
8 mid-term exam
9 Banach Algebra To speech face to face
10 Disk Algebra To speech face to face
11 Regular and singular elements To speech face to face
12 Topological zero divisor To speech face to face
13 Spectrum To speech face to face
14 Spectral radius To speech face to face
15 Ideals and quotient algebras To speech face to face
16 final exam
Recommend Course Book / Supplementary Book/Reading
1 Fonksiyonel Analiz, Mustafa Bayraktar
Required Course instruments and materials
The books of Functional Analysis

Assessment Methods
Type of Assessment Week Hours Weight(%)
mid-term exam 8 2 40
Other assessment methods
1.Oral Examination
2.Quiz
3.Laboratory exam
4.Presentation
5.Report
6.Workshop
7.Performance Project
8.Term Paper
9.Project
final exam 16 2 60

Student Work Load
Type of Work Weekly Hours Number of Weeks Work Load
Weekly Course Hours (Theoretical+Practice) 3 15 45
Outside Class
       a) Reading 3 15 45
       b) Search in internet/Library 3 15 45
       c) Performance Project 0
       d) Prepare a workshop/Presentation/Report 0
       e) Term paper/Project 0
Oral Examination 0
Quiz 0
Laboratory exam 0
Own study for mid-term exam 2 8 16
mid-term exam 2 1 2
Own study for final exam 5 6 30
final exam 2 1 2
0
0
Total work load; 185