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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 : Face-To-Face
Prerequisities and Co-requisities 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 : Turkish-English
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 :
Number Duration Total  
Course Duration (Excluding Exam Week) :
16 4 64  
Time Of Studying Out Of Class :
16 4 64  
Homeworks :
2 15 30  
Presentation :
0 0 0  
Project :
0 0 0  
Lab Study :
0 0 0  
Field Study :
0 0 0  
Visas :
1 10 10  
Finals :
1 10 10  
Workload Hour (30) :
30  
Total Work Charge / Hour :
178  
Course's ECTS Credit :
6      
Assessment Methods and Criteria
Studies During Halfterm :
Number Co-Effient
Visa :
0 0
Quiz :
0 0
Homework :
0 0
Attendance :
0 0
Application :
0 0
Lab :
0 0
Project :
0 0
Workshop :
0 0
Seminary :
0 0
Field study :
0 0
   
TOTAL :
0
The ratio of the term to success :
0
The ratio of final to success :
0
TOTAL :
0
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