YAŞAR UNIVERSITY
SCIENCE AND LETTERS FACULTY
MATHEMATICS DEPARTMENT
COURSE SYLLABUS
Course
Code
Semester
Math 501
Fall
Course Title
Functional Analysis I
Course Hour/Week
Theory
3
Practice
0
Yaşar Credit
ECTS
3
8
Course Type
1. Compulsory Courses
X
1.1. Programme Compulsory Courses
1.2. University Compulsory Courses (UFND)
1.3. YÖK (Higher Education Council) Compulsory Courses
2. Elective Courses
2.1. Program Elective Courses
2.2. University Elective Courses
3. Prerequisites Courses
3.1. Compulsory Prerequisites Courses
3.2. Elective Prerequisites Courses
Language of Instruction
English
Level of Course
Undergraduate (First Cycle)
Prerequisites Course(s) (compulsory)
-
Special Pre-Conditions of the Course
(recommended)
-
Course Coordinator
Assist.Prof.Dr. Şahlar Meherrem
Course Instructor(s)
Assist.Prof.Dr. Şahlar Meherrem
Mail: sahlar.meherrem@yasar.edu.tr
Web: smaharramov.edu.tr
Mail: sahlar.meherrem@yasar.edu.tr
Web: smaharramov.edu.tr
Course Assistant(s)/Tutor (s)
Aim(s) of the Course
Learning Outcomes of the Course
Course Content
COURSE OUTLINE/SCHEDULE (Weekly)
Preliminary Preparation
Week
Topics
Methodology and
Implementation
(theory, practice,
assignment etc.)
1
Metrics and Norms
John K. Hunter and Bruno
Nachtergaele, Applied Analysis,
Lecture Notes,
Chapter 1
2
Convergence, Upper and Lower bounds,
Open and Closed Sets, Continuity
John K. Hunter and Bruno
Nachtergaele,Applied Analysis,
Lecture Notes
Chapter 1
Theory and Practice
The Completion of the Metric spaces
John K. Hunter and Bruno
Nachtergaele, Applied Analysis,
Lecture Notes
Chapter 1
Theory and Practice
John K. Hunter and Bruno
Nachtergaele, Applied Analysis,
Lecture Notes
Chapter 1
Theory and Practice
3
4
5
6
Compactness and Totally boundedness
Continuous Functions
Compact subsets of C(K)
Convergence of Functions,
Theory and Practice
John K. Hunter and Bruno
Nachtergaele,
Applied Analysis, Lecture Notes
Chapter 1 and Chapter 2
John K. Hunter and Bruno
Nachtergaele,
Applied Analysis, Lecture Notes
Chapter 1 and Chapter 2
Theory and Practice
Theory and Practice
7
Spaces of Continuous Functions
John K. Hunter and Bruno
Nachtergaele,
Applied Analysis, Lecture Notes
Chapter1 and Chapter 2
8
Preparation for Midterm 50 min and
Midterm 90 min
17.11.2015, 14.30-16.00
John K. Hunter and Bruno
Nachtergaele,
Applied Analysis, Lecture Notes
Theory and Practice
John K. Hunter and Bruno
Nachtergaele,
Applied Analysis, Lecture Notes
Chapter3
Theory and Practice
Banach Spaces
John K. Hunter and Bruno
Nachtergaele,
Applied Analysis, Lecture Notes
Chapter5
Theory and Practice
Hilbert Spaces
John K. Hunter and Bruno
Nachtergaele, Applied Analysis,
Lecture Notes
Chapter6
Theory and Practice
Bounded Linear Operators on Hilbert Spaces
John K. Hunter and Bruno
Nachtergaele, Applied Analysis,
Lecture Notes,
Chapter8
Theory and Practice
Bounded Linear Operators on Hilbert Spaces
John K. Hunter and Bruno
Nachtergaele, Applied Analysis,
Lecture Notes,
Chapter8
Theory and Practice
Contraction Mapping theorem, Fixed Points of
9
10
11
12
13
Dynamical Systems
14
Spectrum of Baunded Linear operators
15
Final Exam
John K. Hunter and Bruno
Nachtergaele, Applied Analysis,
Lecture Notes
Chapter 9
1)
2)
Required Course Material (s) /Reading(s)/Text Book (s)
3)
4)
Theory and Practice
John K. Hunter and Bruno Nachtergaele,
Applied Analysis, Lecture Notes, (Main Book)
Elements of Functional Analysis, L.A. Lusternik and
V. J. Sobolev, John Willey and Sons, 1974
Elements of the Theory of Functions and
Functional Analysis by A. Kolmogorov and S
.Fomin, Dover Publication, 1999
Applied Functional Analysis, Eberhard Zeidler,
Springer, 1995
Recommended Course Material (s)/Reading(s)/Other
ASSESSMENT
Semester Activities/ Studies
NUMBER
WEIGHT in %
Mid- Term
1
40
Attendance
14
3
Quiz
4
5
Assignment (s)
2
2
Project
-
-
Laboratory
-
-
Field Studies (Technical Visits)
-
-
Presentation/ Seminar
-
-
Practice (Laboratory, Virtual Court, Studio Studies etc.)
-
-
Other (Placement/Internship etc.)
-
-
TOTAL
100
Contribution of Semester Activities/Studies to the Final Grade
50
Contribution of Final Examination/Final Project/ Dissertation to the Final Grade
50
TOTAL
100
CONTRIBUTION OF LEARNING OUTCOMES TO PROGRAMME OUTCOMES
No Programme Outcomes
Level of
Contribution (1lowest/ 5highest)
1
1
2
3
4
5
2
3
4
x
To read and identify the basic notions and to obtain results as using them
To illustrate the given concepts with examples
To conclude results by using basic definitions
To demonstrate mathematical proofs clearly and correctly
To solve problems by analyzing mathematical theories, notions and data
5
x
x
x
x
6
7
8
To transfer the knowledge and solution offers related in the field
x
To use abstract thinking competence
x
To compare the given fundamental notions
x
ECTS /STUDENT WORKLOAD
NUMBER
UNIT
HOUR
TOTAL
(WORKLOAD)
Course Teaching Hour (14 weeks* total course hours)
14
Week
3
42
Preliminary Preparation and finalizing of course notes,
further self- study
14
2
28
Assignment (s)
3
3
9
ACTIVITIES
Presentation/ Seminars
Week
Number
Number
Quiz and Preparation for the Quiz
3
Number
3
9
Mid- Term(s)
1
Number
12
12
20
20
Project (s)
Number
Field Studies (Technical Visits, Investigate Visit etc.)
Number
Practice (Laboratory, Virtual Court, Studio Studies etc.)
Number
Final Examination/ Final Project/ Dissertation and
Preparation
Other (Placement/Internship etc.)
1
Number
Number
Total Workload
120
Total Workload/ 25
4.8
ECTS
5
ETHICAL RULES WITH REGARD TO THE COURSE (IF AVAILABLE)
ASSESSMENT and EVALUATION METHODS:
Final Grades will be determined according to the Yaşar University Associate Degree, Bachelor Degree and Graduate
Degree Education and Examination Regulation
PREPARED BY
Assist.Prof.Dr. Şahlar Meherrem
UPDATED
09.12.2011
APPROVED