Functional Analysis (MAE719)

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General

School	School of Science
Academic Unit	Department of Mathematics
Level of Studies	Undergraduate
Course Code	MAE719
Semester	7
Course Title	Functional Analysis
Independent Teaching Activities	Lectures (Weekly Teaching Hours: 3, Credits: 6)
Course Type	Special Background
Prerequisite Courses	-
Language of Instruction and Examinations	Greek
Is the Course Offered to Erasmus Students	Yes ( in English)
Course Website (URL)	See eCourse, the Learning Management System maintained by the University of Ioannina.

Learning Outcomes

Learning outcomes

The goal of this course is: To familiarize the student with the notions, the basic theorems and the techniques concerning normed vector spaces, Banach spaces, Hilbert spaces, bounded linear operators between them and the dual spaces. After completing this course the student will be able to recognize if a given normed linear space is a Banach space, to compute the norm of a bounded linear operator, to use the basic theorems of Functional analysis (Hahn-Banach theorem and its consequences, Open mapping theorem, Closed graph theorem, Banach-Steinhaus theorem, Uniform Boundedness Principle).

General Competences

Αnalyse and combine data and information using various technologies. Working independently and in groups. Free, creative, analytic, and conclusive thinking. Decision making.

Syllabus

Linear spaces and algebraic bases (Hamel bases). Linear operators. Normed linear spaces. Banach spaces and classical examples. Finite dimensional spaces. Bounded linear operators, bounded linear functionals and computation of their norm. Dual space. Conjugate operators. Hahn Banach theorem and its consequences. The second dual space. Reflexive spaces. Baire's category theorem and some of its consequences in Functional Analysis (Open Mapping Theorem, Closed graph Theorem, Uniform Boundedness Principle, Banach-Steinhaus Theorem). Elements from Hilbert spaces.

Teaching and Learning Methods - Evaluation

Delivery	Teaching on the blackboard from the teacher
Use of Information and Communications Technology	-
Teaching Methods	Activity Semester Workload Lectures 39 Individual study 78 Solving exercises-homework 33 Course total 150
Student Performance Evaluation	Exams in the end of the semester (mandatory), intermediate exams (optional), assignments of exercises during the semester (optional).

Attached Bibliography

See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:

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