COURSE UNIT TITLE

: FUNCTIONAL ANALYSIS

Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS
OMT 4021 FUNCTIONAL ANALYSIS COMPULSORY 3 0 0 5

Offered By

Mathematics Teacher Education

Level of Course Unit

First Cycle Programmes (Bachelor's Degree)

Course Coordinator

ASSOCIATE PROFESSOR ADEM ÇELIK

Offered to

Mathematics Teacher Education

Course Objective

To introduce with norm and inner product concept, to examine relation between metric norm and inner product, to teach operator and functional concept

Learning Outcomes of the Course Unit

1   To be able to look limit and continuity in normed space
2   To be able to comprehend the importance of Banach space
3   To be able to comprehend the importance of inner product spaces and Hilbert space
4   To be able to comprehend relations between metric, inner product and norm
5   To be able to comprehend relations between function, operator, and functional

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description
1 To be remembered vector space concept and its properties, exemplifications
2 Norm and normed vector spaces, exemplifications
3 Sphere in normed vector spaces, exemplifications
4 Convergent sequence in normed vector spaces, Cauchy sequence in normed vector spaces
5 Continuity in functions, equivalent norm concept in normed vector spaces
6 Relation between metric and norm
7 Complete normed vector spaces (Banach space), exemplifications
8 Midterm exam
9 Inner product and inner product spaces, exemplifications
10 Sphere in inner product spaces, exemplifications
11 Complete inner product spaces (Hilbert spaces), exemplifications
12 Relation between metric, norm and inner product
13 Relation between operator and linear operator, Bounded linear operator and its properties
14 Functional concept and dual space concept
15 Final exam

Recomended or Required Reading

:Fonksiyonel Analiz Yöntemleri, Tosun Terzioğlu;
Fonksiyonel Analize Giriş, S. Ahmet Kılıç, Musa Erdem; Fonksiyonel Analiz, Binali Musayev, Murat Alp

Planned Learning Activities and Teaching Methods

lecture based instruction, question-answer, group working

Assessment Methods

SORTING NUMBER SHORT CODE LONG CODE FORMULA
1 MTE MIDTERM EXAM
2 STT TERM WORK (SEMESTER)
3 FINS FINAL EXAM
4 FCGR FINAL COURSE GRADE (RESIT) MTE * 0.30 + STT * 0.10 + FINS * 0.60
5 RST RESIT
6 FCGR FINAL COURSE GRADE (RESIT) MTE * 0.40 + RST * 0.60

Further Notes About Assessment Methods

None

Assessment Criteria

To be announced.

Language of Instruction

Turkish

Course Policies and Rules

To be announced.

Contact Details for the Lecturer(s)

adem.celik@deu.edu.tr

Office Hours

To be announced.

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours)
Lectures 13 3 39
Preparations before/after weekly lectures 13 2 26
Preparation for midterm exam 1 15 15
Preparation for final exam 1 20 20
Preparing assignments 1 7 7
Preparing presentations 1 2 2
Final 1 2 2
Midterm 1 2 2
TOTAL WORKLOAD (hours) 113

Contribution of Learning Outcomes to Programme Outcomes

PO/LOPO.1PO.2PO.3PO.4PO.5PO.6PO.7PO.8PO.9PO.10PO.11PO.12PO.13PO.14PO.15PO.16PO.17PO.18
LO.1552
LO.2552
LO.3552
LO.4552
LO.5552