FACULTY OF ARTS AND SCIENCES
Department of Mathematics
SOCIAL MEDIA
MATH 442 | Course Introduction and Application Information
| Course Name |
Functional Analysis II
|
|
Code
|
Semester
|
Theory
(hour/week) |
Application/Lab
(hour/week) |
Local Credits
|
ECTS
|
|
MATH 442
|
Fall/Spring
|
3
|
0
|
3
|
7
|
| Prerequisites |
|
|||||||
| Course Language |
English
|
|||||||
| Course Type |
Elective
|
|||||||
| Course Level |
First Cycle
|
|||||||
| Mode of Delivery | face to face | |||||||
| Teaching Methods and Techniques of the Course | Problem SolvingQ&ALecture / Presentation | |||||||
| Course Coordinator | - | |||||||
| Course Lecturer(s) | ||||||||
| Assistant(s) | ||||||||
| Course Objectives | This course provides a 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. |
| Learning Outcomes |
The students who succeeded in this course;
|
| Course Description | This course aims to teach basic theory and applications of Functional Analysis. |
|
|
Core Courses |
X
|
| Major Area Courses | ||
| Supportive Courses | ||
| Media and Management Skills Courses | ||
| Transferable Skill Courses |
WEEKLY SUBJECTS AND RELATED PREPARATION STUDIES
| Week | Subjects | Related Preparation |
| 1 | Normed and Banach spaces (Review) | Erwin Kreyszig,“Introductory Functional Analysis with Applications”, (Wiley,1989). Section: 2 |
| 2 | Inner product spaces and their properties, Hilbert spaces | Erwin Kreyszig,“Introductory Functional Analysis with Applications”, (Wiley,1989). Section: 3.2, 3.3 |
| 3 | Orthogonal complements and direct sums | Erwin Kreyszig,“Introductory Functional Analysis with Applications”, (Wiley,1989). Section: 3.3 |
| 4 | Orthogonal complements and direct sums | Erwin Kreyszig,“Introductory Functional Analysis with Applications”, (Wiley,1989). Section: 3.4 |
| 5 | Orthonormal sets and sequences | Erwin Kreyszig,“Introductory Functional Analysis with Applications”, (Wiley,1989). Section: 3.8 |
| 6 | Fourier series and their properties | Erwin Kreyszig,“Introductory Functional Analysis with Applications”, (Wiley,1989). Section: 3.9 |
| 7 | Total orthonormal sets and sequences | Erwin Kreyszig,“Introductory Functional Analysis with Applications”, (Wiley,1989). Section: 3.10 |
| 8 | Representation of functionals on Hilbert spaces | Erwin Kreyszig,“Introductory Functional Analysis with Applications”, (Wiley,1989). Section: 4.1, 4.2 |
| 9 | Hilbert-Adjoint operator | Erwin Kreyszig,“Introductory Functional Analysis with Applications”, Wiley,1989. Section: 4.2, 4.3 |
| 10 | Self-adjoint, unitary and normal operators | Erwin Kreyszig,“Introductory Functional Analysis with Applications”, (Wiley,1989). Section: 4.7 |
| 11 | Fundamental theorems of functional analysis: Zorn's lemma, Hahn-Banach theorem and Banach fixed point theorem | Erwin Kreyszig,“Introductory Functional Analysis with Applications”, (Wiley,1989). Section: 4.7, |
| 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”, (Wiley,1989). Section: 4.13 |
| 13 | Weak and strong convergence | Erwin Kreyszig,“Introductory Functional Analysis with Applications”, (Wiley,1989). Section: 4.8 |
| 14 | Convergence of sequences of operators and functionals | Erwin Kreyszig,“Introductory Functional Analysis with Applications”, (Wiley,1989). Section: 4.9 |
| 15 | Semester review | |
| 16 | Final exam |
| Course Notes/Textbooks | Erwin Kreyszig, “Introductory Functional Analysis with Applications” , (Wiley, 1989). ISBN-13: 978-0471504597 |
| Suggested Readings/Materials | Walter Rudin ,'' Functional Analysis'', 2nd edition (McGraw-Hill Science/Engineering/Math,1991). ISBN-13:978-0070542365 |
EVALUATION SYSTEM
| Semester Activities | Number | Weigthing |
| Participation | ||
| Laboratory / Application | ||
| Field Work | ||
| Quizzes / Studio Critiques | ||
| Portfolio | ||
| Homework / Assignments |
1
|
20
|
| Presentation / Jury | ||
| Project | ||
| Seminar / Workshop |
1
|
20
|
| Oral Exams | ||
| Midterm | ||
| Final Exam |
1
|
60
|
| Total |
| Weighting of Semester Activities on the Final Grade |
2
|
40
|
| Weighting of End-of-Semester Activities on the Final Grade |
1
|
60
|
| Total |
ECTS / WORKLOAD TABLE
| Semester Activities | Number | Duration (Hours) | Workload |
|---|---|---|---|
| Theoretical Course Hours (Including exam week: 16 x total hours) |
16
|
3
|
48
|
| Laboratory / Application Hours (Including exam week: '.16.' x total hours) |
16
|
0
|
|
| Study Hours Out of Class |
14
|
4
|
56
|
| Field Work |
0
|
||
| Quizzes / Studio Critiques |
0
|
||
| Portfolio |
0
|
||
| Homework / Assignments |
1
|
36
|
36
|
| Presentation / Jury |
0
|
||
| Project |
0
|
||
| Seminar / Workshop |
0
|
||
| Oral Exam |
0
|
||
| Midterms |
0
|
||
| Final Exam |
1
|
70
|
70
|
| Total |
210
|
COURSE LEARNING OUTCOMES AND PROGRAM QUALIFICATIONS RELATIONSHIP
|
#
|
Program Competencies/Outcomes |
* Contribution Level
|
||||
|
1
|
2
|
3
|
4
|
5
|
||
| 1 | To be able to have a grasp of basic mathematics, applied mathematics or theories and applications of statistics. |
X | ||||
| 2 | To be able to use advanced theoretical and applied knowledge, interpret and evaluate data, define and analyze problems, develop solutions based on research and proofs by using acquired advanced knowledge and skills within the fields of mathematics or statistics. |
|||||
| 3 | To be able to apply mathematics or statistics in real life phenomena with interdisciplinary approach and discover their potentials. |
X | ||||
| 4 | To be able to evaluate the knowledge and skills acquired at an advanced level in the field with a critical approach and develop positive attitude towards lifelong learning. |
|||||
| 5 | To be able to share the ideas and solution proposals to problems on issues in the field with professionals, non-professionals. |
|||||
| 6 | To be able to take responsibility both as a team member or individual in order to solve unexpected complex problems faced within the implementations in the field, planning and managing activities towards the development of subordinates in the framework of a project. |
X | ||||
| 7 | To be able to use informatics and communication technologies with at least a minimum level of European Computer Driving License Advanced Level software knowledge. |
X | ||||
| 8 | To be able to act in accordance with social, scientific, cultural and ethical values on the stages of gathering, implementation and release of the results of data related to the field. |
|||||
| 9 | To be able to possess sufficient consciousness about the issues of universality of social rights, social justice, quality, cultural values and also environmental protection, worker's health and security. |
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| 10 | To be able to connect concrete events and transfer solutions, collect data, analyze and interpret results using scientific methods and having a way of abstract thinking. |
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| 11 | To be able to collect data in the areas of Mathematics or Statistics and communicate with colleagues in a foreign language. |
|||||
| 12 | To be able to speak a second foreign language at a medium level of fluency efficiently. |
|||||
| 13 | To be able to relate the knowledge accumulated throughout the human history to their field of expertise. |
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*1 Lowest, 2 Low, 3 Average, 4 High, 5 Highest
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