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Course Information
Course Unit Title : Functional Analysis II
Course Unit Code : MAT408
Type of Course Unit : Compulsory
Level of Course Unit : First Cycle
Year of Study : 4
Semester : 8.Semester
Number of ECTS Credits Allocated : 6,00
Name of Lecturer(s) : ---
Course Assistants : ---
Learning Outcomes of The Course Unit : Inner product spaces, Hilbert spaces, Orthonormal sequences and sets
Legendre , Hermite and Laguerre Polynominals
Representation of fuctionals on Hilbert spaces
Fundamental Theorems for Normed and Banach spaces
Mode of Delivery : Face-To-Face
Prerequisities and Co-requisities Courses : Unavailable
Recommended Optional Programme Components : Unavailable
Course Contents : Inner product spaces: Hilbert spaces, inner product space , Hilbert space and properties of inner product spaces.
Orthonormality: Orthogonal complements and direct sums , series related to orthonormal sequences and sets, total orthonormal sets and sequences.
Operators: Legendre , Hermite and Laguerre, polynominals, representation of fuctionals on Hilbert spaces, Hilbert-adjoint operator, self ?adjoint operator , unitary and normal operators.
Hahn-Banach Theorem: Fundamental theorems for normed and Banach spaces, Zorn`s Lemma , Hahn-Banach theorem, Hahn-Banach theorem for complex vector spaces and normed spaces, adjoint operator, reflexive spaces, Category theorem, uniform boundedness theorem , strong and weak convergence , open mapping and closed graph theorems, Banach fixed point theorem.

Languages of Instruction : Turkish-English
Course Goals : Inner product spaces, Hilbert spaces, Orthonormal sequences and sets
Legendre , Hermite and Laguerre Polynominals
Representation of fuctionals on Hilbert spaces
Fundamental Theorems for Normed and Banach 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 15 15  
Finals :
1 15 15  
Workload Hour (30) :
30  
Total Work Charge / Hour :
188  
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 Inner product space, Hilbert space
 
2 Hilbert space and properties of inner product spaces
 
3 Orthogonal complements and direct sums
 
4 Series related to orthonormal sequences and sets
 
5 Total orthonormal sets and sequences
 
6 Representation of fuctionals on Hilbert spaces
 
7 Hilbert-adjoint operators
 
8 Self?adjoint, unitary and normal operators
 
9 Hahn-Banach theorem
 
10 Adjoint operators
 
11 Category theorem and Uniform boundedness theorem
 
12 Strong and weak convergence
 
13 Open mapping and closed graph theorems
 
14 Banach fixed point theorem