GAZI UNIVERSITY INFORMATION PACKAGE - 2019 ACADEMIC YEAR

COURSE DESCRIPTION
PROPERTIES OF APPROXIMATION BY SEQUENCES OF LINEAR POSITIVE OPERATOR 1/6301305
Course Title: PROPERTIES OF APPROXIMATION BY SEQUENCES OF LINEAR POSITIVE OPERATOR 1
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
Having to ability for research in approximation theory
Knowing the approximation properties of linear positive operators
Understanding the Korovkin type theorems and their applications
Obtaning the degree of approximation by modulus of continuity, second modulus of continuity and Peetre's K-functionals
Learning the concepts of Voronovskaja type asymptotic formulas and simultaneous approximation
 -- MODE OF DELIVERY
  The mode of delivery of this course is Face to face
 --WEEKLY SCHEDULE
1. Week  Weierstrass's theorem and the proof of the theorem
2. Week  Definition of linear positive operators and properties of them, Korovkin's theorems and proofs, connections of them with the Weierstrass theorems
3. Week  Korovkin's theorems in the space periodical and integrable functions on the closed intervals
4. Week  Applications of the Korovkin Theorems
5. Week  The degree of approximation by linear positive operators, modulus of continuity and their properties
6. Week  Lipschitz type functions and their properties
7. Week  Szasz and Baskakov operators and their approximation properties
8. Week  Korovkin type theorems for a sequences of linear positive operators acting in the weighted spaces of continuous functions defined on unbounded set
9. Week  The convergence properties of sequences of linear positive operators in the space of continuous functions of several variables
10. Week  Voronovskaja type asymptotic formulas
11. Week  Second modulus of continuity and Peetre K-functionals
12. Week  Divided differences, difference operator and convexity, Simultaneous approximation
13. Week  The approximation properties of a sequences of positive type operators in the space of analytic functions
14. Week  Applications and Feedback
15. Week  
16. Week  
 -- TEACHING and LEARNING METHODS
 -- ASSESSMENT CRITERIA
 
Quantity
Total Weighting (%)
 Midterm Exams
1
20
 Assignment
3
20
 Application
0
0
 Projects
0
0
 Practice
0
0
 Quiz
0
0
 Percent of In-term Studies  
40
 Percentage of Final Exam to Total Score  
60
 -- WORKLOAD
 Activity  Total Number of Weeks  Duration (weekly hour)  Total Period Work Load
 Weekly Theoretical Course Hours
14
3
42
 Weekly Tutorial Hours
0
 Reading Tasks
14
4
56
 Searching in Internet and Library
14
3
42
 Material Design and Implementation
0
 Report Preparing
0
 Preparing a Presentation
0
 Presentation
0
 Midterm Exam and Preperation for Midterm Exam
1
15
15
 Final Exam and Preperation for Final Exam
1
20
20
 Other (should be emphasized)
5
3
15
 TOTAL WORKLOAD: 
190
 TOTAL WORKLOAD / 25: 
7.6
 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. Dr. Nurhayat İSPİR , Prof.Dr. H.Gül İNCE İLARSLAN)
 -- WEB SITE(S) OF LECTURER(S)
   (websitem.gazi.edu.tr/site/nispir , websitem.gazi.edu.tr/site/ince/)
 -- EMAIL(S) OF LECTURER(S)
   (nispir@gazi.edu.tr , ince@gazi.edu.tr)