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
FMA619	REAL ANALYSIS I	Compulsory	1	1	6

Level of Course Unit

Second Cycle

Objectives of the Course

• to provide the basic real analysis information

Name of Lecturer(s)

Yrd. Doç. Dr. Erdal ÜNLÜYOL

Learning Outcomes

1	To have the ability and knowledge of the advanced level of related to the field and use it in real learning environments

Mode of Delivery

Formal Education

Prerequisites and co-requisities

None

Recommended Optional Programme Components

None

Course Contents

• Algebras • Sigma algebras • Outer measure of a set and the measurable sets • Lebesque measure • Vital’s covering theorem • Measurable functions • Baire classes • Egorov's theorem • Lebesque integral of bounded and unbounded measurable functionsandcomparison with the Riemannian integral • Monotone functions • Bounded variation functions and their derivatives • Absolute continuity • Lebesque integrals • Lp spaces • Convergence concepts in Lp

Weekly Detailed Course Contents

Week	Theoretical	Practice	Laboratory
1	Algebras, sigma algebras
2	Outer measure of a set and the measurable sets
3	Lebesque measure
4	Vital’s covering theorem
5	Measurable functions
6	Measurable functions
7	Baire classes
8	Midterm exam
9	Egorov's theorem
10	Arrays of functions and convergence in measure
11	Lebesque integral of bounded and unbounded measurable functions and comparison with the Riemannian integral
12	Monotone functions
13	Bounded variation functions and their derivatives
14	Absolute continuity
15	Absolute continuity
16	Final exam

Recommended or Required Reading

C.D. Aliprantis, O. Burkinshaw (1990), Principles of Real Analysis, Academic Pres inc. Second edition. Other References H. L. Royden (1986), Real Analysis, Macmillan publishing., inc. New York, second edition D. L. Cohn (1980), Measure Theory, Birkhauser, Boston.

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
Yarıyıl (Yıl) İçi Etkinlikleri		40
Yarıyıl (Yıl) Sonu Etkinlikleri		60
SUM		100

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	1	1
Attending Lectures	14	6	84
Problem Solving	10	2	20
Self Study	14	4	56
Individual Study for Mid term Examination	8	4	32
Individual Study for Final Examination	6	4	24
TOTAL WORKLOAD (hours)			221

Contribution of Learning Outcomes to Programme Outcomes

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

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