Information Package / Course Catalogue
Functional Analysis I
Course Code: MAT401
Course Type: Required
Couse Group: First Cycle (Bachelor's Degree)
Education Language: Turkish
Work Placement: N/A
Theory: 2
Prt.: 2
Credit: 3
Lab: 0
ECTS: 6
Objectives of the Course

1. Introducing the concepts of metric spaces, vector spaces and normed spaces and the relationships between them 2. Teaching the concept of Banach spaces 3. Generalizing the topics and methods of mathematical analysis, geometry, and linear algebra to infinite-dimensional spaces

Course Content

Linear spaces, Linear transformations, Metric spaces, Normed spaces, Norm of linear bounded transformation, Banach spaces

Name of Lecturer(s)
Assoc. Prof. Emrah YILDIRIM
Learning Outcomes
1.Understanding the concepts of linear space, linear transformation
2.Be able to define the concept of metric space
3.Understanding the concepts of convergence, continuity, Cauchy series and the relationships between them
4.Understanding the concept of normed space and its properties
5.Defining bounded linear transformation normed spaces
6.Understanding the definition of Banach space
Recommended or Required Reading
1.Introductory Functional Analysis with Applications, Erwin Kreyszig
2.Fonksiyonel Analiz, Yüksel Soykan, Nobel Akademik Yayıncılık
Weekly Detailed Course Contents
Week 1 - Theoretical & Practice
Course introduction, Reminding basic concepts about linear spaces
Week 2 - Theoretical & Practice
Linear transformations, examples
Week 3 - Theoretical & Practice
General reminders and examples about metric spaces
Week 4 - Theoretical & Practice
Concepts of continuity, convergence, Couchy series sequence in metric spaces and the relations between them
Week 5 - Theoretical & Practice
Problem solutions 1
Week 6 - Theoretical & Practice
Relations between normed spaces, metric spaces, normed spaces, metric spaces and topological spaces
Week 7 - Theoretical & Practice
Function spaces, sequence spaces, sample problem solutions
Week 8 - Theoretical & Practice
Continuity and convergence in normed spaces
Week 9 - Theoretical & Practice
B(X,Y) dual space, operator norm
Week 10 - Theoretical & Practice
Banach spaces
Week 11 - Theoretical & Practice
Equivalent Norms
Week 12 - Theoretical & Practice
Cauchy series in normed spaces, Banach spaces
Week 13 - Theoretical & Practice
Examples of finite and infinite dimensional Banach spaces
Week 14 - Theoretical & Practice
Series in normed spaces, Schauder basis
Assessment Methods and Criteria
Type of AssessmentCountPercent
Midterm Examination1%40
Final Examination1%60
Workload Calculation
ActivitiesCountPreparationTimeTotal Work Load (hours)
Lecture - Theory142256
Lecture - Practice142256
Midterm Examination115217
Final Examination120222
TOTAL WORKLOAD (hours)151
Contribution of Learning Outcomes to Programme Outcomes
PÇ-1
PÇ-2
PÇ-3
PÇ-4
PÇ-5
PÇ-6
PÇ-7
PÇ-8
PÇ-9
PÇ-10
PÇ-11
PÇ-12
PÇ-13
PÇ-14
PÇ-15
PÇ-16
PÇ-17
PÇ-18
OÇ-1
4
4
5
5
3
2
3
2
OÇ-2
4
4
5
5
3
2
3
2
OÇ-3
4
4
5
5
3
2
3
2
OÇ-4
4
4
5
5
3
2
3
2
OÇ-5
4
4
5
5
3
2
3
2
OÇ-6
4
4
5
5
3
2
3
2
Adnan Menderes University - Information Package / Course Catalogue
2026