Akademik Dersler - Tanıtım


Code - Course Title	MAT404 - Functional Analysis II
Course Type	Required Courses
Language of Instruction	Türkçe
Laboratory + Practice	3+0
ECTS	5.0
Course Instructor(s)	PROFESÖR DOKTOR NEDİM DEĞİRMENCİ
Mode of Delivery	The mode of delivery of this course is Face to face
Prerequisites	There is no prerequisite or co-requisite for this course.
Courses Recomended	Abstract Mathematics 1,2, Analysis 3,4, Topology 1,2, Linear Algebra 1,2
Required or Recommended Resources	Gazi Yayınevi Kreyszig, E (1989) Introductory Functional Analysis with Applications. J.WILEY & SONS Bryan P. and Martin A Youngson (2000) Linear Functional Analysis,Springer, Bayraktar, M. (2006) Fonksiyonel Analiz, Gazi Yayınevi Yüksel Soykan, Fonksiyonel Analiz
Recommended Reading List
Assessment methods and criteria	Written exam
Work Placement	N/A
Sustainability Development Goals

Weeks	Topics
Week - 1	Bounded linear operators
Week - 2	Bounded linear operators: bounded linear functionals
Week - 3	Dual Spaces
Week - 4	Dual Spaces
Week - 5	Hahn-Banach Theorem
Week - 6	Hahn Banach Theorem
Week - 7	Existence of bounded linear functionals
Week - 8	Inner product spaces
Week - 9	Inner Product Spaces
Week - 10	Properties of Hilbert Spaces
Week - 11	Properties of Hilbert Spaces: Orthogonality
Week - 12	Properties of Hilbert Spaces: Orthogonality
Week - 13	Orthonormal sets, Gram-Schmidt orthogonalization process
Week - 14	Bessel's inequality, Parseval identity, Fourier Coefficients

Assessment Method and Passing Requirements
	Quamtity	Percentage (%)
1.Midterm Exam	1	20
2.Midterm Exam	1	30
Final Exam	1	50
Toplam (%)		100