Ordu 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
MAT40120121310	REAL ANALYSIS	Compulsory	4	7	5

Level of Course Unit

First Cycle

Objectives of the Course

Learn to Lebesgue Integral Theory

Name of Lecturer(s)

Yrd. Doç. Dr. Erdal ÜNLÜYOL

Learning Outcomes

1	Öğrencinin doğru düşünme ve yorum yapma yeteneği gelişecek ve öğrenci matematikle ilgili temel bilgiler kazanacaktır
2	will develop the right thinking and the ability to comment and students will gain basic knowledge about mathematics

Mode of Delivery

Formal Education

Prerequisites and co-requisities

None

Recommended Optional Programme Components

None

Course Contents

Sentence sequences, the lower and upper limits and the convergence of the lower and upper limits. Sigma algebra and sigma ring. Measurable sets, measure and outer measure, Lebesgue outer measure and Lebesgue measure. Measurable functions, classes of measurable functions. Integral of simple and positive functions, integrable functions, the Lebesgue convergence and bounded convergence theorem, the Lebesgue integral and the relation between Riemann. Lp spaces and the space L_{\infty}

Weekly Detailed Course Contents

Week	Theoretical	Practice	Laboratory
1	Sentence sequences, the lower and upper limits and the convergence of the lower and upper limits
2	Sigma algebra and sigma ring
3	Measurable sets
4	Measure and outer measure, Lebesgue outer measure and Lebesgue measure
5	Measurable functions
6	Classes of measurable functions
7	Integral of simple and positive functions
8	Midterm exam
9	Integrable functions
10	The basic properties of Lebesgue integral
11	The basic properties of Lebesgue integral
12	The Lebesgue integral and the relation between Riemann
13	The Lebesgue integral and the relation between Riemann
14	Lp spaces and the space L_{\infty}
15	Lp spaces and the space L_{\infty}
16	Final exam

Recommended or Required Reading

1. R.G. BARTLE, The Elements of Intagration, Translate by METU Mathematics Foundation in 1995. Other Textbook and /or References 1 Rahim OCAK, Reel ANALYSIS, Atatürk Üniversitesi Yayınları 2002. 2 Royden H.L. Real Analysis, New York, 1968 3 Hewitt E. And Stromberg K. Real and Abstract Analysis, Berlin, 1969 4 Mustafa BALCI, Reel ANALYSIS, Balcı Yayınları, 2000.

Planned Learning Activities and Teaching Methods

Assessment Methods and Criteria

Term (or Year) Learning Activities	Quantity	Weight
SUM		0
End Of Term (or Year) Learning Activities	Quantity	Weight
SUM		0
SUM		0

Language of Instruction

Turkish

Work Placement(s)

None

Workload Calculation

Activities	Number	Time (hours)	Total Work Load (hours)
Midterm Examination	1	2	2
Final Examination	1	2	2
Makeup Examination	1	2	2
Attending Lectures	8	4	32
Problem Solving	10	4	40
Self Study	7	5	35
Individual Study for Mid term Examination	4	5	20
Individual Study for Final Examination	4	5	20
TOTAL WORKLOAD (hours)			153

Contribution of Learning Outcomes to Programme Outcomes

	PO 1	PO 2	PO 3	PO 4	PO 5	PO 6	PO 7
LO1	5	5	5	5	5	5	5
LO2

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