GAZI UNIVERSITY INFORMATION PACKAGE - 2019 ACADEMIC YEAR

COURSE DESCRIPTION
FUNCTIONAL ANALYSIS II/MAT4004
Course Title: FUNCTIONAL ANALYSIS II
Credits 4 ECTS 6
Semester 8 Compulsory/Elective Elective
COURSE INFO
 -- LANGUAGE OF INSTRUCTION
  Turkish
 -- NAME OF LECTURER(S)
  Assist. Prof. Dr. Kadir KANAT
 -- WEB SITE(S) OF LECTURER(S)
  
 -- EMAIL(S) OF LECTURER(S)
  kadirkanat@gazi.edu.tr
 -- LEARNING OUTCOMES OF THE COURSE UNIT
Linear and non-linear operators comprehend the difference operator.
Learns the classifications bounded,continuous, compact operators
Understands the solution of operator equations.
Integral equations, differential equations, algebraic equations, etc.. The solution to all their comments with the same understanding.
Using the properties of Hilbert space operators to grasp the advantages of this space.
Learns the concepts of spectrum and solvent operators
Cauchy-Schwarz inequality, the concept of orthogonality orthonormal sets and prove theorems about them.
Prove some theorems about approximation theory in Hilbert spaces
 -- MODE OF DELIVERY
  The mode of delivery of this course is Face to face
 -- PREREQUISITES AND CO-REQUISITES
  There is no prerequisite or co-requisite for this course.
 -- RECOMMENDED OPTIONAL PROGRAMME COMPONENTS
  Bu dersle ilişkili önerilen başka dersler bulunmamaktadır..
 --COURSE CONTENT
1. Week  Hilbert space, orthogonal and orthonormal sequences and sentences
2. Week  Hilbert space, orthogonal and orthonormal sequences and sentences
3. Week  Functional representation in Hilbert spaces, Hilbert adjoint, self-adjoint, unitary and normal operators
4. Week  Functional representation in Hilbert spaces, Hilbert adjoint, self-adjoint, unitary and normal operators
5. Week  Functional representation in Hilbert spaces, Hilbert adjoint, self-adjoint, unitary and normal operators
6. Week  Zorn's lemma, the Hahn-Banach theorem and some results
7. Week  Zorn's lemma, the Hahn-Banach theorem and some results
8. Week  Midterm Exam
9. Week  Adjoint operator, reflexive spaces, category theorem
10. Week  Adjoint operator, reflexive spaces, category theorem
11. Week  Uniform boundedness theorem, strong and weak convergence
12. Week  unctional convergence of sequences of operators, open mapping theorem
13. Week  unctional convergence of sequences of operators, open mapping theorem
14. Week  Closed linear operators, closed graph theorem.
15. Week  Closed linear operators, closed graph theorem.
16. Week  Final Exam
 -- RECOMMENDED OR REQUIRED READING
  “Fonksiyonel Analiz” Mustafa Bayraktar, Erzurum, 1996 “Fonksiyonel Analiz” Binali Musayev ve Murat Alp, Balcı yayınları
 -- PLANNED LEARNING ACTIVITIES AND TEACHING METHODS
  Anlatım, Soru-Yanıt, Gösterme, Uygulama - Alıştırma
 -- WORK PLACEMENT(S)
  Not Applicable
 -- ASSESSMENT METHODS AND CRITERIA
 
Quantity
Percentage
 Mid-terms
1
40
 Assignment
0
0
 Exercises
0
0
 Projects
0
0
 Practice
0
0
 Quiz
0
0
 Contribution of In-term Studies to Overall Grade  
40
 Contribution of Final Examination to Overall Grade  
60
 -- WORKLOAD
 Efficiency  Total Week Count  Weekly Duration (in hour)  Total Workload in Semester
 Theoretical Study Hours of Course Per Week
14
4
56
 Practising Hours of Course Per Week
0
 Reading
0
 Searching in Internet and Library
14
3
42
 Designing and Applying Materials
0
 Preparing Reports
0
 Preparing Presentation
0
 Presentation
0
 Mid-Term and Studying for Mid-Term
5
5
25
 Final and Studying for Final
7
5
35
 Other
0
 TOTAL WORKLOAD: 
158
 TOTAL WORKLOAD / 25: 
6.32
 ECTS: 
6
 -- COURSE'S CONTRIBUTION TO PROGRAM
NO
 PROGRAM LEARNING OUTCOMES
1
2
3
4
5
1To train individuals who are contemporary, entrepreneur and have unique and aesthetic values, self-confidence and capable of independent decision-making.X
2To train individuals who are equipped with enough mathematicsX
3To teach mathematical thinking methods in order to improve the ability to express mathematics both orally and in writing,X
4To train individuals who are knowledgeable about the history of mathematics and the production of scientific knowledge and can follow developments in these disciplines.X
5To provide necessary equipments to take positions such areas as banking, finance, econometrics, and actuarial,X
6To acquire ability to solve problems encountered in real life by means of mathematical modeling using mathematical methods,X
7To provide ability to do necessary resource researches in the areas of mathematics and to use accessed information,X
8To give appropriate training in such areas as in computer programming and creating algorithms in order to take parts in developing IT sector,X
9To gain substructure to be able to study at graduate level.X
10The skill to have professional and ethical responsibilityX