Akademik Dersler - Tanıtım


Code - Course Title	MAT532 - Functional Analysis
Course Type	Required Courses
Language of Instruction	Türkçe
Laboratory + Practice	3+0
ECTS	7.5
Course Instructor(s)
Mode of Delivery	The mode of delivery of this course is only Face to face
Prerequisites	There is no prerequisite or co-requisite for this course.
Courses Recomended	No recommendation
Required or Recommended Resources	E.Kreyszig, \\\"Introductory Functional Analysis with Applications\\\", John WILEY &Sons; 1989
Recommended Reading List	B.Rynne, M.Youngson,\\\" Linear Functional Analysis\\\", Springer,2000
Assessment methods and criteria	Clasical examine - Two midterm exams and Final exam
Work Placement	N/A
Sustainability Development Goals

Weeks	Topics
Week - 1	The fundamental topics of the functional analysis. An Introduction.
Week - 2	Linear operators.
Week - 3	Operator variable maps.
Week - 4	Bounded operators. Calculation of the Fredholm and Volterra operators.
Week - 5	The topologies in the linear continuous operators space.
Week - 6	Completness with respect to the bounded and pointwise convergence topologies. Banach-Steinhaus theorem.
Week - 7	Completness with respect to the bounded and pointwise convergence topologies. Banach-Steinhaus theorem.
Week - 8	Inverse operators. Existence theorems.
Week - 9	Applications of the inverse operators.
Week - 10	Banach homeomorphism theorem.
Week - 11	The space of the linear continuous functionals and its dual. The duals of the spaces s and C[a,b] and general forms of the linear continuous functionals defined in these spaces.
Week - 12	The duals of the spaces lp, Lp[a,b] and Hilbert space and general forms of the linear continuous functionals defined in these spaces.
Week - 13	Weak convergence in the normed spaces.
Week - 14	Weak convergence in lp, C[a,b], Lp[a,b] and Hilbert spaces.

Assessment Method and Passing Requirements
	Quamtity	Percentage (%)
Toplam (%)		0