GAZI UNIVERSITY INFORMATION PACKAGE - 2019 ACADEMIC YEAR

COURSE DESCRIPTION
REAL ANALYSIS II/MAT- 406
Course Title: REAL ANALYSIS II
Credits 3 ECTS 5
Semester 8 Compulsory/Elective Elective
COURSE INFO
 -- LANGUAGE OF INSTRUCTION
   Turkish
 -- NAME OF LECTURER(S)
  Prof. Nurhayat İSPİR
 -- WEB SITE(S) OF LECTURER(S)
  websitem.gazi.edu.tr/site/nispir
 -- EMAIL(S) OF LECTURER(S)
  nispir@gazi.edu.tr
 -- LEARNING OUTCOMES OF THE COURSE UNIT
explanation and practicability the concept of integrable and Lebesgue integral
explanation and practicability the concept of Lp sapces and convergence in Lp
Understanding the properties of measure spaces and space of integrable functions
explanation and practicability the concept of monotone, absoluate and bounded variation functions
Solvable the problems on the integrals
 -- 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   Measure space ve integrable functions
2. Week  Measure space ve integrable functions
3. Week  Lp and L_infinity spaces
4. Week  L_infinity space and solution of problems
5. Week  Converge in Lp , pointwise and uniform convergence
6. Week  Converge in Lp and measurement convergence
7. Week   Solution of problems
8. Week  Mid term exam
9. Week   Integral of monotone functions
10. Week  Bounded variation functions
11. Week  Problems related by bounded variation functions
12. Week  Derivative of indefine integral
13. Week  Absolute continiuity
14. Week  Decomposition of measures
15. Week  Problems
16. Week  Final exam
 -- RECOMMENDED OR REQUIRED READING
  Mustafa Balcı "Reel analiz" Ali Dönmez “Reel analiz" E. M. Stein and R. Shakarchi, Real Analysis: Measure Theory, Integration, and Hilbert Spaces, Prentice Lectures in Analysis III, Princeton University Press, 2005. M. Capinski and e. Kopp, Measure, Integral, and Probability, 2nd Edition, Springer, 2004.
 -- PLANNED LEARNING ACTIVITIES AND TEACHING METHODS
  Lecture, Question & Answer, Demonstration, Drill - Practise
 -- WORK PLACEMENT(S)
  None
 -- ASSESSMENT METHODS AND CRITERIA
 
Quantity
Percentage
 Mid-terms
1
25
 Assignment
1
15
 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
3
42
 Practising Hours of Course Per Week
5
5
25
 Reading
5
5
25
 Searching in Internet and Library
0
 Designing and Applying Materials
0
 Preparing Reports
0
 Preparing Presentation
0
 Presentation
0
 Mid-Term and Studying for Mid-Term
1
12
12
 Final and Studying for Final
1
15
15
 Other
5
3
15
 TOTAL WORKLOAD: 
134
 TOTAL WORKLOAD / 25: 
5.36
 ECTS: 
5
 -- 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 give good education in the program fields as algebra, geometry, applied mathematics, topology and analysis in order to be equipped with enough mathematics.X
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
10To enable the student to gain the ability of relating mathematics with the other sciences.X