GAZI UNIVERSITY INFORMATION PACKAGE - 2019 ACADEMIC YEAR

COURSE DESCRIPTION
FUNCTIONAL ANALYSIS I/MAT4003
Course Title: FUNCTIONAL ANALYSIS I
Credits 4 ECTS 6
Semester 7 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
Learns metric spaces, convergence, Cauchy sequence, completeness concepts, learns to completion of a metric space, separable metric space
Learns vector spaces, normed vector spaces, inner product and Hilbert spaces with basic features
Completion of a normed space, with full and complete knowledge about the non-normed spaces.
Learn the concept of linear operators, limitations,continuity.
Proves Hanh-Banach theorem and understand the results
Learns Banach theorem Steinhauss .
Learns open mapping and closed graph theorems and applications to


 -- 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
  There is no recommended optional programme component for this course.
 --COURSE CONTENT
1. Week  Metric spaces, continuous transformations
2. Week  Topological spaces, separable spaces
3. Week  Convergence in metric spaces
4. Week  Completeness, complation of metric spaces
5. Week  Normed linear spaces
6. Week  Function spaces
7. Week  Banach spaces
8. Week  Finite dimensional normed spaces
9. Week  Midterm Exam
10. Week  Equivalent norms, compactness
11. Week  Linear operators, limitations, continuity
12. Week  Expansion of linear operators, linear functionals and dual spaces
13. Week  Hanh-Banach theorem and its consequences
14. Week  Banach Steinhauss Theorem
15. Week  Open mapping and closed graph theorems and applications
16. Week  Final Exam
 -- RECOMMENDED OR REQUIRED READING
   “Fonksiyonel Analiz” Mustafa Bayraktar, Erzurum, 1996 “Fonksiyonel Analiz” Binali Musayev ve Murat Alp, Balcı yayınları, 200
 -- PLANNED LEARNING ACTIVITIES AND TEACHING METHODS
  Lecture, Question & Answer, Demonstration, Drill - Practise
 -- 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