Information Package / Course Catalogue - Adnan Menderes University

General Information Unit Staff Academic Information Programme Outcomes Course Structure Diagram Contact Information

Person Responsible for Information Package

Prof. Adnan MELEKOĞLU

Prof. Hülya İNCEBOZ

Prof. İnci EGE

Prof. Semra DOĞRUÖZ

Assoc. Prof. Berna ARSLAN

Assoc. Prof. Emrah YILDIRIM

Assoc. Prof. Korhan GÜNEL

Ins. Nihal GÜNEL

Lec. Ahmet GENÇ

Lec. Dilek AÇIKGÖZ KAYA

Lec. Erdal ÖZYURT

Lec. Muhammet Ali OKUR

Lec. Okan ARSLAN

Lec. Rıfat AŞLIYAN

Lec. Sibel KOÇER

Res. Assist. İclal GÖR

Res. Assist. Mehmet Soner PEHLİVAN

Functional Analysis II

Course Code	: MAT410
Course Type	: Area Elective
Couse Group	: First Cycle (Bachelor's Degree)
Education Language	: Turkish
Work Placement	: N/A

Theory	: 2
Prt.	: 2
Credit	: 3
Lab	: 0
ECTS	: 6

Objectives of the Course

Introduce the concepts of compactness, dual space, open transformation theorem and closed graph theorem, inner product space and Hilbert space

Course Content

Compactness, finite-dimensional normed spaces, inner product spaces, Hilbert spaces

Name of Lecturer(s)

Learning Outcomes

1.	Working on finite dimensional normed spaces
2.	Learning the concept of compactness in normed spaces
3.	Know the fundamental theorems of functional analysis
4.	Studying fixed point theorem and its applications
5.	Learning Hilbert spaces

Recommended or Required Reading

1.	Introductory Functional Analysis with Applications, Erwin Kreyszig
2.	Fonksiyonel Analiz (Functional Analysis), Yüksel Soykan

Weekly Detailed Course Contents

Week 1 - Theoretical

Finite-dimensional normed spaces

Week 2 - Theoretical

Compactness and finite dimensionality

Week 3 - Theoretical

Quotient spaces

Week 4 - Theoretical

Open transformation theorem, closed graph theorem

Week 5 - Theoretical

Dual spaces

Week 6 - Theoretical

Hahn–Banach theorem

Week 7 - Theoretical

Consequences of the Hahn-Banach theorem

Week 8 - Theoretical

Equivalent transformations

Week 9 - Theoretical

Reflective spaces

Week 10 - Theoretical

Baire's theorem and its consequences

Week 11 - Theoretical

Fixed point theorem and applications

Week 12 - Theoretical

Uniform boundary principle, inner product spaces

Week 13 - Theoretical

Hilbert spaces

Week 14 - Theoretical

Orthogonality in inner product and Hilbert spaces

Assessment Methods and Criteria

Type of Assessment	Count	Percent
Assignment	1	%4
Term Assignment	1	%6
Midterm Examination	1	%30
Final Examination	1	%60

Workload Calculation

Activities	Count	Preparation	Time	Total Work Load (hours)
Lecture - Theory	14	2	2	56
Lecture - Practice	14	2	2	56
Assignment	1	1	1	2
Term Project	1	2	1	3
Midterm Examination	1	14	2	16
Final Examination	1	20	2	22
TOTAL WORKLOAD (hours)				155

Contribution of Learning Outcomes to Programme Outcomes

	PÇ-1	PÇ-2	PÇ-3	PÇ-4	PÇ-5	PÇ-6	PÇ-7	PÇ-8	PÇ-9	PÇ-10	PÇ-11	PÇ-12	PÇ-13	PÇ-14	PÇ-15	PÇ-16	PÇ-17	PÇ-18
OÇ-1	3		4		4				4	2	2	3	2
OÇ-2	3		4		4				4	2	2	3	2
OÇ-3	3		4		4				4	2	2	3	2
OÇ-4	3		4		4				4	2	2	3	2
OÇ-5	3		4		4				4	2	2	3	2