Course Information


Course Information
Course Title Code Semester L+U Hour Credits ECTS
REAL ANALYSIS 801500715190 3 + 0 3.0 8.0

Prerequisites None

Language of Instruction Turkish
Course Level Graduate Degree
Course Type Compulsory
Mode of delivery Oral and writing presentation, question and answer, discussion.
Course Coordinator
Instructors
Assistants
Goals This lecture deals with Infinite sets, The properties of the sets, limit points, measurable sets, measure of sets, measurable functions, properties of measurable functions, sequence of functions and convergence in measure, Lebesgue integral of a bounded function, square-summable functions
Course Content Infinite sets, The properties of the sets, limit points, measurable sets, measure of sets, measurable functions, properties of measurable functions, sequence of functions and convergence in measure, Lebesgue integral of a bounded function, square-summable functions
Learning Outcomes 1) Describes limit points, infinite sets and the properties of the sets
2) Explains measurable sets, measure of sets, measurable functions, properties of measurable functions, sequence of functions and convergence in measure
3) Has a knowledge about Lebesgue integral of a bounded function, square-summable functions

Weekly Topics (Content)
Week Topics Teaching and Learning Methods and Techniques Study Materials
1. Week Infinite sets Lecture

 Presentation (Including Preparation Time)
2. Week The properties of the sets Lecture

 Presentation (Including Preparation Time)
3. Week limit points Lecture

 Presentation (Including Preparation Time)
4. Week measurable sets Lecture

 Presentation (Including Preparation Time)
5. Week measurable functions and properties of measurable functions Lecture

 Presentation (Including Preparation Time)
6. Week sequence of functions and convergence in measure Lecture

 Presentation (Including Preparation Time)
7. Week Midterm Exam

8. Week Lebesgue integral of a bounded function Lecture

 Presentation (Including Preparation Time)
9. Week summable functions Lecture

 Presentation (Including Preparation Time)
10. Week square-summable functions Lecture

 Presentation (Including Preparation Time)
11. Week Lp spaces Lecture

 Presentation (Including Preparation Time)
12. Week lp spaces Lecture

 Presentation (Including Preparation Time)
13. Week mean convergence Lecture

 Presentation (Including Preparation Time)
14. Week final exam


Sources Used in This Course
Recommended Sources
Reel Analizin Prensipleri, C .D. Aliprantis, O. Burkinshaw
Reel Değerli Fonksiyonlar Teorisi, I. P. Natanson, E. Hewitt

Relations with Education Attainment Program Course Competencies
Program RequirementsContribution LevelDK1DK2DK3
PY15000
PY25000
PY35000
PY45000
PY45000
PY45000
PY45000
PY45000
PY45000
PY45000
PY45000
PY45000
PY45000
PY45000
PY45000
PY45000
PY45000
PY45000
PY45000
PY45000

*DK = Course's Contrubution.
0 1 2 3 4 5
Level of contribution None Very Low Low Fair High Very High
.

ECTS credits and course workload
Event Quantity Duration (Hour) Total Workload (Hour)
Course Duration (Total weeks*Hours per week) 14 3
Work Hour outside Classroom (Preparation, strengthening) 14 4
Homework 6 3
Presentation (Including Preparation Time) 14 2
Midterm Exam 1 1
Time to prepare for Midterm Exam 1 30
Final Exam 1 1
Time to prepare for Final Exam 1 30
Total Workload
Total Workload / 30 (s)
ECTS Credit of the Course
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Course Information
  • Course Information
  • Weekly Topics (Content)
  • Sources Used in This Course
  • Relations with Education Attainment Program Course Competencies
  • ECTS credits and course workload