

Course Information
Course Unit Title 
: 
Functional Analysis I 
Course Unit Code 
: 
MAT407 
Type of Course Unit 
: 
Compulsory 
Level of Course Unit

: 
First Cycle 
Year of Study

: 
4 
Semester

: 
7.Semester 
Number of ECTS Credits Allocated

: 
6,00 
Name of Lecturer(s) 
: 


Course Assistants 
: 


Learning Outcomes of The Course Unit 
: 
Metric spaces, further examples of metric spaces, Hölder and Minkowski inequalities for sums completeness, completion of metric spaces normed spaces, Banach spaces, compactness and finite dimension linear operators and functionals, spaces of operators and dual spaces

Mode of Delivery 
: 
FaceToFace

Prerequisities and Corequisities Courses 
: 
Unavailable

Recommended Optional Programme Components 
: 
Unavailable

Course Contents 
: 
Metric Spaces: Metric space , examples of metric spaces , Hölder and Minkowski inequalities for sums. Completeness: Complete metric spaces and completion of a metric space. Normed spaces: Definition and examples, Banach spaces, vector space , properties of normed spaces, finite dimensional normed spaces and subspaces. Operators: Definition and examples, linear operators , bounded and continuous linear operators. Functionals: Linear functionals , linear operators and functionals on finite dimensional spaces, spaces of operators and dual spaces.

Languages of Instruction 
: 
TurkishEnglish

Course Goals 
: 
Metric spaces, further examples of metric spaces, Hölder and Minkowski inequalities for sums completeness, completion of metric spaces normed spaces, Banach spaces, compactness and finite dimension linear operators and functionals, spaces of operators and dual spaces

Course Aims 
: 
The main purpose of course is introduced an abstract branch of mathematics that originated from classical analysis

WorkPlacement 

Not Available


Recommended or Required Reading
Textbook

: 

Additional Resources

: 
Kreyszig, E.: Introductory Functional Analysis with Applications, John Wiley and Sons. Pub., 1989. Çakar, Ö.: Fonksiyonel Analize Giriş, AÜFF Yayınları, 3, 2002.

Material Sharing
Documents

: 

Assignments

: 

Exams

: 

Additional Material

: 


Planned Learning Activities and Teaching Methods
Lectures, Practical Courses, Presentation, Seminar, Project, Laboratory Applications (if necessary)


ECTS / Table Of Workload (Number of ECTS credits allocated)
Student workload surveys utilized to determine ECTS credits.

Activity

:


Course Duration (Excluding Exam Week)

:


Time Of Studying Out Of Class

:


Homeworks

:


Presentation

:


Project

:


Lab Study

:


Field Study

:


Visas

:


Finals

:


Workload Hour (30)

:


Total Work Charge / Hour

:


Course's ECTS Credit

:



Assessment Methods and Criteria
Studies During Halfterm

: 

Visa

: 

Quiz

: 

Homework

: 

Attendance

: 

Application

: 

Lab

: 

Project

: 

Workshop

: 

Seminary

: 

Field study

: 




TOTAL

: 

The ratio of the term to success

: 

The ratio of final to success

: 

TOTAL

: 


Weekly Detailed Course Content
Week

Topics

1

Metric spaces, examples of metric spaces



2

Inequalities, Hölder and Minkowski inequalities for sums



3

Convergence, Cauchy sequence, completeness



4

Examples related to completeness proofs, completion of metric space



5

Vector spaces



6

Normed spaces, examples



7

Banach spaces, examples



8

Finite dimensional normed spaces and subspaces



9

Compactness and finite dimension



10

Linear operators



11

Linear functionals



12

Linear operators and functionals on finite dimensional spaces



13

Bounded and continuous linear operators and functionals



14

Spaces of operators and dual spaces



























































































