Yozgat Bozok University Lifelong Learning Programme

Description of Individual Course Units

Course Unit Code	Course Unit Title	Type of Course Unit	Year of Study	Semester	Number of ECTS Credits
MAT566	REEL ANALİZ II	Elective	1	1	6

Level of Course Unit

Second Cycle

Objectives of the Course

To introduce to student concept of measure.

Name of Lecturer(s)

Doç. Dr. Abdullah SÖNMEZOĞLU

Learning Outcomes

1	To define concepts of measurable sets and functions
2	To identify and apply the concept of Lebesgue integral
3	To learn relationship between Riemann integral and Lebesgue integral

Mode of Delivery

Formal Education

Prerequisites and co-requisities

None

Recommended Optional Programme Components

None

Course Contents

Set algebra and sigma-algebras, Borel sigma-algebra on R, Pre-measure and external measure, Caratheodory criterion and measurable sets, Measure, Obtaining a pre-measure, Clusters with measure 0 and exact measure space, Lebesgue and Dirac measures on R , Example of Lebesgue non-measurable set, Measurable functions and their basic properties, Definition of Lebesgue integral and its basic properties, Convergence theorems: monotone convergence theorem, Fatou's lemma, Lebesgue convergence theorem, Convergence of function sequences almost everywhere, between convergence types bonds, generalized states of convergence theorems

Weekly Detailed Course Contents

Week	Theoretical	Practice	Laboratory
1	Clusters can not be measured
2	Measurable Functions
3	Measurable Functions
4	Riemann Integral
5	Measure the limited functions on a set of finite Lebesgue integral
6	Integral non-negative functions, general Lebesgue integral
7	Convergence in measure
8	Mid-Term Exam
9	Convergence in measure
10	Differential and Integral
11	Differential and Integral
12	Functions of bounded variation
13	Functions of bounded variation
14	Absolute Contiunity
15	Convex functions
16	Final Exam

Recommended or Required Reading

A. Dönmez, Reel Analiz, Seçkin Yayıncılık, 2001. J. Yeh, Lectures on Real Analaysis, World Scientific Publishing Company, 2001.

Planned Learning Activities and Teaching Methods

Assessment Methods and Criteria

Term (or Year) Learning Activities	Quantity	Weight
Midterm Examination	1	100
SUM		100
End Of Term (or Year) Learning Activities	Quantity	Weight
Final Examination	1	100
SUM		100
Term (or Year) Learning Activities		40
End Of Term (or Year) Learning Activities		60
SUM		100

Language of Instruction

Work Placement(s)

None

Workload Calculation

Activities	Number	Time (hours)	Total Work Load (hours)
Midterm Examination	1	2	2
Final Examination	1	2	2
Self Study	14	5	70
Individual Study for Mid term Examination	7	8	56
Individual Study for Final Examination	7	8	56
TOTAL WORKLOAD (hours)			186

Contribution of Learning Outcomes to Programme Outcomes

LO1

LO2

LO3

* Contribution Level : 1 Very low 2 Low 3 Medium 4 High 5 Very High