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Course Information

Course Information

Course Title	Code	Semester	L+U Hour	Credits	ECTS
FUNCTIONAL ANALYSIS I	801500715050		3 + 0	3.0	8.0

Prerequisites

None

Language of Instruction	Turkish
Course Level	Graduate Degree
Course Type	Compulsory
Mode of delivery	Oral presentation, answer-question, discussion, solving problems
Course Coordinator
Instructors
Assistants
Goals	Normed Spaces, Hahn-Banach Theorem, Uniform Boundedness Theorem, Open Mapping Theorem, Closed Graph Theorem, Banach Fixed Point Theorem, Applications of Banach's Theorem to Linear Equations, Differential Equations and Integral Equations, Spectral Theory in Finite Dimentional Normed Spaces, Properties of Resolvent and Spectrum, Banach Algebras and their Properties
Course Content	Normed Spaces, Hahn-Banach Theorem, Uniform Boundedness Theorem, Open Mapping Theorem, Closed Graph Theorem, Banach Fixed Point Theorem, Applications of Banach's Theorem to Linear Equations, Differential Equations and Integral Equations, Spectral Theory in Finite Dimentional Normed Spaces, Properties of Resolvent and Spectrum, Banach Algebras and their Properties
Learning Outcomes	1) Hahn-Banach Theorem, Uniform .Boundedness Principle, Open Mapping Theorem and Closed Graph Theorem 2) Applications of four fundamental theorems 3) Learns Banach Fixed Point Theorem and studies its applications 4) Knows the spectral theory of linear operators in normed spaces and determines the spectrum and resolvent of a linear operator 5) Knows the basic properties of Banach algebras