COURSE INTRODUCTION AND APPLICATION INFORMATION


Course Name
Functional Analysis II
Code
Semester
Theory
(hour/week)
Application/Lab
(hour/week)
Local Credits
ECTS
MATH 302
Fall/Spring
3
0
3
6
Prerequisites
 MATH 301To attend the classes (To enrol for the course and get a grade other than NA or W)
Course Language
English
Course Type
Service Course
Course Level
First Cycle
Mode of Delivery -
Teaching Methods and Techniques of the Course
Course Coordinator -
Course Lecturer(s)
Assistant(s)
Course Objectives This course provides deep understanding of introductory functional analysis. The objective of this course is to cover fundamental theorems of functional analysis such as HahnBanach theorem, Open mapping theorem, Closed graph theorem, Baire’s  category theorem, Banach fixed point theorem, and their applications.
Learning Outcomes The students who succeeded in this course;
  • will be able to define inner product spaces and explain the relationship between Hilbert spaces, Banach spaces and metric spaces.
  • will be able to know properties of orthogonal sets
  • will be able to know the differences between convergences of sequences of operators and functionals.
  • will be able to understand and apply fundamental theorems of functional analysis
  • will be able to understand and compare strong convergence and weak convergence
Course Description This course aims to teach basic theory and applications of Functional Analysis.

 



Course Category

Core Courses
Major Area Courses
Supportive Courses
Media and Managment Skills Courses
Transferable Skill Courses

 

WEEKLY SUBJECTS AND RELATED PREPARATION STUDIES

Week Subjects Required Materials
1 Inner product spaces and their properties, Hilbert Spaces Erwin Kreyszig, “Introductory Functional Analysis with Applications” by Wiley.
2 Inner product spaces and their properties, Hilbert Spaces Erwin Kreyszig, “Introductory Functional Analysis with Applications” by Wiley.
3 Orthogonal complements and direct sums Erwin Kreyszig, “Introductory Functional Analysis with Applications” by Wiley.
4 Orthogonal complements and direct sums Erwin Kreyszig, “Introductory Functional Analysis with Applications” by Wiley.
5 Orthonormal sets and sequences Erwin Kreyszig, “Introductory Functional Analysis with Applications” by Wiley.
6 Fourier series and their properties Erwin Kreyszig, “Introductory Functional Analysis with Applications” by Wiley.
7 Total orthonormal sets and sequences Erwin Kreyszig, “Introductory Functional Analysis with Applications” by Wiley.
8 Representation of functionals on Hilbert spaces Erwin Kreyszig, “Introductory Functional Analysis with Applications” by Wiley.
9 Hilbert-Adjoint operator Erwin Kreyszig, “Introductory Functional Analysis with Applications” by Wiley.
10 Self-adjoint, unitary and normal operators Erwin Kreyszig, “Introductory Functional Analysis with Applications” by Wiley.
11 Fundamental theorems of functional analysis: Zorn's lemma, Hahn-Banach theorem and Banach fixed point theorem Erwin Kreyszig, “Introductory Functional Analysis with Applications” by Wiley.
12 Fundamental theorems of functional analysis: Baire category theorem, Uniform boundedness theorem, Open mapping theorem and Banach fixed point theorem Erwin Kreyszig, “Introductory Functional Analysis with Applications” by Wiley.
13 Weak and strong convergence Erwin Kreyszig, “Introductory Functional Analysis with Applications” by Wiley.
14 Convergence of sequences of operators and functionals Erwin Kreyszig, “Introductory Functional Analysis with Applications” by Wiley.
15 Course Review
16 Course Review
Course Notes/Textbooks

Erwin Kreyszig, “Introductory Functional Analysis with Applications” by Wiley.

Suggested Readings/Materials Walter Rudin, Functional Analysis 2/E, International Series in Pure and Applied Mathematics.

 

EVALUATION SYSTEM

Semester Activities Number Weigthing
Participation
1
10
Laboratory / Application
Field Work
Quizzes / Studio Critiques
6
15
Portfolio
Homework / Assignments
Presentation / Jury
Project
Seminar / Workshop
Oral Exam
Midterm
1
35
Final Exam
1
40
Total

Weighting of Semester Activities on the Final Grade
8
60
Weighting of End-of-Semester Activities on the Final Grade
1
40
Total

ECTS / WORKLOAD TABLE

Semester Activities Number Duration (Hours) Workload
Course Hours
(Including exam week: 16 x total hours)
16
3
48
Laboratory / Application Hours
(Including exam week: 16 x total hours)
16
Study Hours Out of Class
14
3
Field Work
Quizzes / Studio Critiques
3
Portfolio
Homework / Assignments
2
Presentation / Jury
Project
Seminar / Workshop
Oral Exam
Midterms
2
28
Final Exams
1
36
    Total
182

 

COURSE LEARNING OUTCOMES AND PROGRAM QUALIFICATIONS RELATIONSHIP

#
Program Competencies/Outcomes
* Contribution Level
1
2
3
4
5

*1 Lowest, 2 Low, 3 Average, 4 High, 5 Highest

 

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