GRADUATE COURSE DETAILS
Course Title:
Functional Analysis I
Code :
FMT5102
Lecture
Application
42
0
Education and Teaching Methods
Home
Laboratuary
Project/
Field Study work
0
Semester
Course Type
0
Other
Total
198
240
0
Autumn
Basic
Scientific
Course
Objectives
Institute: Instute of Science
Field: Mathematics
Credits
Credit
ECTS
T+A+L=Credit
3
Language
Turkish/English
Technical
Elective
Scientific
8
Social
Elective
To introduce fundamental concepts and theorems of Functional analysis.
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•
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Learning
Outcomes
and
Competences
•
•
•
•
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Textbook
and /or
References
To learn the concepts Banach space and Hilbert space,
To learn the concepts orthogonal set and orthonormal base,
To learn the concept bounded linear operator,
To learn the uniform boundedness principle, open mapping theorem and closed graph
theorem,
To learn the Hahn-Banach theorem,
To learn the concept quotient space.
Barbara D. MacCluer, Elementary Functional Analysis, Springer (2009).
J. B. Conway, A Course in Functional Analysis, Springer (1985).
W. Rudin, Functional Analysis, McGraw Hill (1991).
ASSESSMENT CRITERIA
Theoretical Courses
If any,
mark as
(X)
Project Course and Graduation Study
If any,
mark as
(X)
Percent
(%)
Midterm Exams
Midterm Exams
Quizzes
Midterm Controls
Homeworks
Term Paper
Term Paper
(Projects,reports,
….)
Oral Examination
Laboratory Work
Final Exam
Final Exam
X
100
Other
Other
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Subjects
Hilbert Spaces
Normed Spaces
Orthogonality
The Geometry of Hilbert Spaces
Linear Functionals
Orthonormal Bases
Bounded Linear Transformations
Adjoints of Operators on Hilbert Spaces
Dual Spaces
Adjoints of Operators on Banach Spaces
The Hahn-Banach Theorem
Uniform Boundedness Principle
Open Mapping and Closed Graph Theorems
Quotent Spaces
Instructors
Assoc. Prof. Ali GÜVEN
e-mail
ag_guven@yahoo.com
Website
http://matematik.balikesir.edu.tr/
1
Percent
(%)