COURSE INTRODUCTION AND APPLICATION INFORMATION


Course Name
Functional Analysis I
Code
Semester
Theory
(hour/week)
Application/Lab
(hour/week)
Local Credits
ECTS
MATH 301
Fall
3
0
3
5
Prerequisites
None
Course Language
English
Course Type
Required
Course Level
First Cycle
Mode of Delivery -
Teaching Methods and Techniques of the Course
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 understand general properties of metric and normed spaces and explain the relationship between them.
  • will be able to explain similarities and differences between function, functional and operator.
  • will be able to clarify some important notions of vector spaces such as: seperability, completeness and incompleteness.
  • will be able to explain convergence, limit and being Cauchy sequence by using functional analysis tools.
  • will be able to understand the properties of linear operators and its important aplications whether they are defined on finite or infinite dimension .
  • will be able to define continuity and boundedness for operators, functions and functionals and clarify differences of this examples.
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 Managment Skills Courses
Transferable Skill Courses

 

WEEKLY SUBJECTS AND RELATED PREPARATION STUDIES

Week Subjects Required Materials
1 Metric Spaces (Introduction and examples) Erwin Kreyszig, “Introductory Functional Analysis with Applications” by Wiley.
2 Topology: Open set, Closed set, Neighborhood, Topological space, Dense and separable sets, Continuous functions on metric spaces Erwin Kreyszig, “Introductory Functional Analysis with Applications” by Wiley.
3 Sequences: boundedness, convergence, limit of a sequence, Cauchy Sequence, Seperability Erwin Kreyszig, “Introductory Functional Analysis with Applications” by Wiley.
4 Completeness and incompleteness (Examples and proofs). Erwin Kreyszig, “Introductory Functional Analysis with Applications” by Wiley.
5 Review Erwin Kreyszig, “Introductory Functional Analysis with Applications” by Wiley.
6 Completeness and incompleteness (Examples and proofs). Erwin Kreyszig, “Introductory Functional Analysis with Applications” by Wiley.
7 Completion of metric spaces. Erwin Kreyszig, “Introductory Functional Analysis with Applications” by Wiley.
8 Vector spaces, subspace, dimension, Hamel basis. Erwin Kreyszig, “Introductory Functional Analysis with Applications” by Wiley.
9 Review Erwin Kreyszig, “Introductory Functional Analysis with Applications” by Wiley.
10 Normed spaces and Banach Spaces Erwin Kreyszig, “Introductory Functional Analysis with Applications” by Wiley.
11 Further properties of Normed spaces Erwin Kreyszig, “Introductory Functional Analysis with Applications” by Wiley.
12 Finite dimensional Normed spaces and subspaces, Equivalent norms Erwin Kreyszig, “Introductory Functional Analysis with Applications” by Wiley.
13 Compactness and finite dimension, Maxmin theorem Erwin Kreyszig, “Introductory Functional Analysis with Applications” by Wiley.
14 Linear operators Erwin Kreyszig, “Introductory Functional Analysis with Applications” by Wiley.
15 Some properties and applications of bounded and linear operators. Erwin Kreyszig, “Introductory Functional Analysis with Applications” by Wiley.
16 Review of the Semester  
Course Notes/Textbooks The extracts above and exercises will be given.
Suggested Readings/Materials Walter Rudin, Functional Analysis 2/E, International Series in Pure and Applied Mathematics.

 

EVALUATION SYSTEM

Semester Activities Number Weigthing
Participation
Laboratory / Application
Field Work
Quizzes / Studio Critiques
Portfolio
Homework / Assignments
10
15
Presentation / Jury
Project
Seminar / Workshop
Oral Exam
Midterm
2
50
Final Exam
1
35
Total

Weighting of Semester Activities on the Final Grade
12
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
5
1
Field Work
Quizzes / Studio Critiques
Portfolio
Homework / Assignments
10
1
Presentation / Jury
Project
Seminar / Workshop
Oral Exam
Midterms
2
25
Final Exams
1
30
    Total
143

 

COURSE LEARNING OUTCOMES AND PROGRAM QUALIFICATIONS RELATIONSHIP

#
Program Competencies/Outcomes
* Contribution Level
1
2
3
4
5
1 To have a grasp of basic mathematics, applied mathematics and theories and applications of statistics. X
2 To be able to use theoretical and applied knowledge acquired in the advanced fields of mathematics and statistics, X
3 To be able to define and analyze problems and to find solutions based on scientific methods, X
4 To be able to apply mathematics and statistics in real life with interdisciplinary approach and to discover their potentials, X
5 To be able to acquire necessary information and to make modeling in any field that mathematics is used and to improve herself/himself, X
6 To be able to criticize and renew her/his own models and solutions, X
7 To be able to tell theoretical and technical information easily to both experts in detail and nonexperts in basic and comprehensible way, X
8

To be able to use international resources in English and in a second foreign language from the European Language Portfolio (at the level of B1) effectively and to keep knowledge up-to-date, to communicate comfortably with colleagues from Turkey and other countries, to follow periodic literature,

X
9

To be familiar with computer programs used in the fields of mathematics and statistics and to be able to use at least one of them effectively at the European Computer Driving Licence Advanced Level,

X
10

To be able to behave in accordance with social, scientific and ethical values in each step of the projects involved and to be able to introduce and apply projects in terms of civic engagement,

X
11 To be able to evaluate all processes effectively and to have enough awareness about quality management by being conscious and having intellectual background in the universal sense, X
12

By having a way of abstract thinking, to be able to connect concrete events and to transfer solutions, to be able to design experiments, collect data, and analyze results by scientific methods and to interfere,

X
13

To be able to continue lifelong learning by renewing the knowledge, the abilities and the compentencies which have been developed during the program, and being conscious about lifelong learning,

14

To be able to adapt and transfer the knowledge gained in the areas of mathematics and statistics to the level of secondary school,

15

To be able to conduct a research either as an individual or as a team member, and to be effective in each related step of the project, to take role in the decision process, to plan and manage the project by using time effectively.

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

 

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