FACULTY OF ARTS AND SCIENCES

Department of Mathematics

MATH 441 | Course Introduction and Application Information

Course Name
Functional Analysis I
Code
Semester
Theory
(hour/week)
Application/Lab
(hour/week)
Local Credits
ECTS
MATH 441
Fall
3
0
3
6

Prerequisites
None
Course Language
English
Course Type
Required
Course Level
First Cycle
Mode of Delivery -
Teaching Methods and Techniques of the Course Q&A
Lecture / Presentation
Course Coordinator -
Course Lecturer(s)
Assistant(s)
Course Objectives This twotier course provides deep understanding of introductory functional analysis. The objective of this course is to cover fundamental topics of functional analysis such as General results about metric spaces: Cauchy sequences, completeness and completion, Normed and Banach spaces: Elementary properties and results.
Learning Outcomes The students who succeeded in this course;
  • will be able to explain the general properties of metric and normed spaces and the relationships between them.
  • will be able to explain similarities and differences between function, functional and operator.
  • will be able to illustrate concepts such as separability, completeness and complement of vector spaces.
  • will be able to define convergence, limit and being Cauchy sequence by using functional analysis tools.
  • will be able to analyze the properties of linear operators defined in finite and infinite dimensions and the important applications of these properties.
  • will be able to define the concepts of continuity and limitation for operator, function and functional.
Course Description This course aims to teach basic theory and applications of Functional Analysis

 



Course Category

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 Metric spaces, Topology: Open set, closed set, neighborhood, topological space, dense and separable sets, continuous functions in metric space. Erwin Kreyszig, “Introductory Functional Analysis with Applications” by Wiley, 1989.ISBN-13: 978- 0471504597 Section 1.1,1.2,1.3
2 Sequences: boundedness, convergence, limit of the sequence, Cauchy series, separability. Erwin Kreyszig, “Introductory Functional Analysis with Applications” by Wiley, 1989.ISBN-13: 978- 0471504597 Section 1.4
3 Completeness, completeness of metric space Erwin Kreyszig, “Introductory Functional Analysis with Applications” by Wiley, 1989.ISBN-13: 978- 0471504597 Section1.5
4 Vector spaces: subspace, dimension, Hamel bases Erwin Kreyszig, “Introductory Functional Analysis with Applications” by Wiley, 1989.ISBN-13: 978- 0471504597 Section 2.1
5 Normed spaces, Banach spaces Erwin Kreyszig, “Introductory Functional Analysis with Applications” by Wiley, 1989.ISBN-13: 978- 0471504597 Section 2.2
6 Properties of normed spaces Erwin Kreyszig, “Introductory Functional Analysis with Applications” by Wiley, 1989.ISBN-13: 978- 0471504597 Section 2.3
7 Finite dimensional norm spaces and subspaces, equivalent norms. Erwin Kreyszig, “Introductory Functional Analysis with Applications” by Wiley, 1989.ISBN-13: 978- 0471504597 Section 2.4
8 Compactness and finite size, max min theorem. Erwin Kreyszig, “Introductory Functional Analysis with Applications” by Wiley, 1989.ISBN-13: 978- 0471504597 Section 2.5
9 Linear operators and some of their properties, some properties and applications of bounded and linear operators Erwin Kreyszig, “Introductory Functional Analysis with Applications” by Wiley, 1989.ISBN-13: 978- 0471504597 Section 2.6-2.7
10 Linear Functionals Erwin Kreyszig, “Introductory Functional Analysis with Applications” by Wiley, 1989.ISBN-13: 978- 0471504597 Section 2.8
11 Inner product space and Hilbert space Erwin Kreyszig, “Introductory Functional Analysis with Applications” by Wiley, 1989.ISBN-13: 978- 0471504597 Section 3.1
12 Properties of inner product space Erwin Kreyszig, “Introductory Functional Analysis with Applications” by Wiley, 1989.ISBN-13: 978- 0471504597 Section 3.2
13 Orthogonal and orthonormal sets. Key features Erwin Kreyszig, “Introductory Functional Analysis with Applications” by Wiley, 1989.ISBN-13: 978- 0471504597 Section 3.3-3.4
14 General Review Erwin Kreyszig, “Introductory Functional Analysis with Applications” by Wiley, 1989.ISBN-13: 978- 0471504597
15 Semester review
16 Final exam

 

Course Notes/Textbooks

Erwin Kreyszig, “Introductory Functional Analysis with Applications” by Wiley, 1989.ISBN-13: 978-0471504597 

Suggested Readings/Materials

'' Functional Analysis'',by Walter Rudin McGraw-Hill Science/Engineering/Math; 2nd edition ,1991,ISBN-13:978-0070542365

 

EVALUATION SYSTEM

Semester Activities Number Weigthing
Participation
Laboratory / Application
Field Work
Quizzes / Studio Critiques
Portfolio
Homework / Assignments
Presentation / Jury
Project
Seminar / Workshop
Oral Exams
Midterm
2
60
Final Exam
1
40
Total

Weighting of Semester Activities on the Final Grade
2
60
Weighting of End-of-Semester Activities on the Final Grade
1
40
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
5
70
Field Work
0
Quizzes / Studio Critiques
0
Portfolio
0
Homework / Assignments
0
Presentation / Jury
0
Project
0
Seminar / Workshop
0
Oral Exam
0
Midterms
2
20
40
Final Exam
1
22
22
    Total
180

 

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.

X
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.

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.

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.

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.

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.

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

 


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