|
|
MATH
302
Functional
Analysis II
|
|
Instructor:
|
Assoc. Prof. Dr. Murat Adývar
|
|
Office:
|
Room:
424
|
|
Office
Hours:
|
Wed-Fri
13:00-14:30 (or by appointment)
|
|
e-Mail:
|
murat.adivar@ieu.edu.tr
|
|
Phone:
|
(232)
488 83 77
|
|
Class
Hours:
|
Thursday
08:30-11:20
Classroom: C 407
|
|
Announcements:
Announcements
will be given in class and posted to the course web site. Students should
regularly check the web site for new and updated announcements.
Objectives:
|
|
This
two-tier course provides deep understanding of introductory functional
analysis. The objective of this course is
to cover fundamental theorems of functional analysis such as Hahn-Banach
theorem, Open mapping theorem, Closed graph theorem, Baire’s category theorem, Banach fixed point
theorem, and their
applications.
|
|
Course
Outline:
|
|
1
|
Hilbert Spaces: Hilbert-Adjoint
operator
|
|
2
|
Self-Adjoint, Unitary and Normal Operators
|
|
3
|
Fundamental Theorems for Normed and Banach
Spaces: Zorn’s Lemma,
Hahn-Banach theorem
|
|
4
|
Hahn-Banach
theorem for complex and normed spaces, and it’s application to C[a,b].
|
|
5
|
Adjoint operator
|
|
6
|
Reflexive spaces
|
|
7
|
Category theorem, Uniform boundedness
theorem, and applications.
|
|
8
|
Convergence:
Strong and weak convergence
|
|
9
|
Convergence of sequences of operators and
functionals.
|
|
10
|
Open mapping theorem, Closed linear operators
and closed graph theorem
|
|
11
|
Banach fixed point theorem: Application of Banach’s theorem to linear
equations
|
|
12
|
Application of
Banach’s theorem to linear equations, Application of Banach’s theorem to
differential equations, Application of Banach’s theorem to integral
equations
|
|
13
|
Approximation
theory: Approximation in normed spaces, uniqueness,
strict convexity
|
|
14
|
Uniform
approximation, Chebyshev polynomials, Approximation in Hilbert spaces
|
|
|
Textbook:
Erwin Kreyszig, Introductory Functional
Analysis with Applications by Wiley.
|
|
Reference
Book:
Walter Rudin, Functional Analysis
2/E, International Series in Pure and Applied Mathematics
|
|
Articles:
Will
be handed out in class as needed.
|
|
Assignments:
Homework
and reading assignments will be given in class.
|
|
Evaluation:
Students
will receive a final letter grade according to the scale shown below,
formulated with the percentages in the below table. Performance shown in
homework, quizzes, exams and participation make up an important part of
instructor's final opinion.
|
|
Grading
|
Percent
|
|
Midterm
|
40
|
|
Final
|
40
|
|
Homeworks
|
5
|
|
Attendance&Participation
|
5
|
|
Quizzes
|
10
|
|
|
Attendance:
Attendance is required at all times. Students are
expected to come to class fully prepared to discuss textbook readings and
course assignments.
|
|
|