GAZI UNIVERSITY INFORMATION PACKAGE - 2019 ACADEMIC YEAR

COURSE DESCRIPTION
FUNCTIONAL ANALYSIS II/5041305
Course Title: FUNCTIONAL ANALYSIS II
Credits 3 ECTS 7.5
Course Semester 1 Type of The Course Elective
COURSE INFORMATION
 -- (CATALOG CONTENT)
 -- (TEXTBOOK)
 -- (SUPPLEMENTARY TEXTBOOK)
 -- (PREREQUISITES AND CO-REQUISITES)
 -- LANGUAGE OF INSTRUCTION
  Turkish
 -- COURSE OBJECTIVES
 -- COURSE LEARNING OUTCOMES
Appreciate how functional analysis uses and unifies ideas from vector spaces, the theory of metrics, and complex analysis
Apply ideas from the theory of Hilbert spaces to other areas, including Fourier series, the theory of Fredholm operators
Understand the advantages of Hilbert spaces for operators by using the properties of Hilbert spaces
Recognize adjoint operators, simetric operators and self-adjoint operators, unitary operator
Learn the notions of resolvant and spectrum of an operator
Understand the fundamentals of spectral theory
Understand the solution of an operator equation
Learn the classifications such as the concepts for an operator of being bounded, continuous and compact
Evaluate the solutions of integral equations, differential equations and algebraic equations
Recognize the Banach algebras
 -- MODE OF DELIVERY
  The mode of delivery of this course is face to face
 --WEEKLY SCHEDULE
1. Week  Inner product spaces, orthogonality, orthogonal complement
2. Week  Hilbert spaces
3. Week  Fourier series
4. Week  The adjoint of an operator
5. Week  Normal, selfadjoint and uniter operators
6. Week  Normal, selfadjoint and uniter operators
7. Week  The spectrum of an operator
8. Week  Positive operators and projections
9. Week  Compact operators on Banach and Hilbert spaces
10. Week  The spectral theory of compact operators on Hilbert spaces
11. Week  Selfadjoint compact operators
12. Week  Fredholm integral equations
13. Week  Volterra integral equations
14. Week  Banach algebras, disc algebras, ideals, and quotient algebras
15. Week  
16. Week  
 -- TEACHING and LEARNING METHODS
 -- ASSESSMENT CRITERIA
 
Quantity
Total Weighting (%)
 Midterm Exams
1
30
 Assignment
5
20
 Application
0
0
 Projects
0
0
 Practice
0
0
 Quiz
0
0
 Percent of In-term Studies  
50
 Percentage of Final Exam to Total Score  
50
 -- WORKLOAD
 Activity  Total Number of Weeks  Duration (weekly hour)  Total Period Work Load
 Weekly Theoretical Course Hours
14
3
42
 Weekly Tutorial Hours
14
0
0
 Reading Tasks
10
8
80
 Searching in Internet and Library
8
4
32
 Material Design and Implementation
4
2
8
 Report Preparing
0
0
0
 Preparing a Presentation
0
0
0
 Presentation
0
0
0
 Midterm Exam and Preperation for Midterm Exam
1
10
10
 Final Exam and Preperation for Final Exam
1
16
16
 Other (should be emphasized)
0
0
0
 TOTAL WORKLOAD: 
188
 TOTAL WORKLOAD / 25: 
7.52
 Course Credit (ECTS): 
7.5
 -- COURSE'S CONTRIBUTION TO PROGRAM
NO
 PROGRAM LEARNING OUTCOMES
1
2
3
4
5
1To be able to develop their knowledge of theory and applications at master degree depending on the competencies acquired in undergraduate level.X
2To be able to recognize different problems encountered in mathematics and to be able to make studies for their solutions.X
3To be able to formulate new solutions with scientific methods mostly based on analysis and synthesis.X
4To be able to carry out his/her works either independently or in groups within a project considering his/her knowledge on the field he/she works in a critical approach.X
5To be able to continue his/her works considering social, scientific and ethical values.X
6To be able to follow scientific and social developments related to his/her field.X
7To be able to carry out his/her works within the framework of quality management, workplace safety and environmental awareness and to be able to present systematically his/her works using various methods like written, oral or visual.X
8To be able to use methods of accessing knowledge effectively in accordance with ethical values.X
9To be able to use knowledge in other disciplines by combining it with mathematical information.X
10To be able to make activities in the awareness of need for lifelong learning.X
11To be able to make connections between mathematical and social concepts and produce solutions with scientific methods.X
12To be able to use his/her mathematical knowledge in technology.X
 -- NAME OF LECTURER(S)
   (Prof. Bahri TURAN , Assoc.Prof. Cüneyt ÇEVİK )
 -- WEB SITE(S) OF LECTURER(S)
   (websitem.gazi.edu.tr/site/bturan , websitem.gazi.edu.tr/site/ccevik)
 -- EMAIL(S) OF LECTURER(S)
   (bturan@gazi.edu.tr , ccevik@gazi.edu.tr)