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
MAT20120121310	ANALYSİS - III	Compulsory	2	3	7

Level of Course Unit

First Cycle

Objectives of the Course

To give convergence theorem for the number and function sequences and series, to examine generalized integral and functions of several variables.

Name of Lecturer(s)

Doç. Dr. Erhan SET

Learning Outcomes

1	Students who successfully complete this course will develop the right thinking and the ability to interpret and will gain basic knowledge about mathematics.

Mode of Delivery

Formal Education

Prerequisites and co-requisities

The first courses, Analysis I and II must be completed, successively

Recommended Optional Programme Components

Course Contents

Pointwise and uniform convergence of function sequences, uniform convergence and integration, uniform convergence and differentiation, uniform convergence of function series. Radius and interval of convergence of power series, derivatives and integrals of power series, Taylor polynomials and series. Generalized integrals, convergence criteria for the first and second kind of generalized integrals, Gamma and Beta functions. Vector-valued functions, limit, continuity, derivatives and integrals of vector valued functions, space curves and lengths. Functions of several variables and their domains, graphs, limit and continuity of two variables functions. Partial derivatives, chain rule, total differential, directional derivative.

Weekly Detailed Course Contents

Week	Theoretical	Practice	Laboratory
1	Pointwise and uniform convergence of function sequences
2	Uuniform convergence and integration
3	Uniform convergence and differentiation
4	Uniform convergence of function series
5	Radius and interval of convergence of power series
6	Derivatives and integrals of power series
7	Taylor polynomials and series
8	Midterm exam
9	Generalized integrals, convergence criteria for the first and second kind of generalized integrals
10	Gamma and Beta functions
11	Vector-valued functions, limit, continuity, derivatives and integrals of vector valued functions
12	Space curves and lengths
13	Functions of several variables and their domains
14	Graphs, limit and continuity of two variables functions
15	Partial derivatives, chain rule, total differential, directional derivative
16	Final exam

Recommended or Required Reading

Analiz II, Mustafa BALCI Yüksek Matematik Cilt II, Ahmet KARADENİZ Yüksek Matematik Cilt II, Hüseyin HALİLOV Ömer AKIN, Matematik Analiz ve Analitik Geometri (cilt 1-2), Palme Yayıncılık, 2001

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)

Workload Calculation

Activities	Number	Time (hours)	Total Work Load (hours)
Midterm Examination	1	1.5	1.5
Final Examination	1	1.5	1.5
Attending Lectures	14	6	84
Self Study	14	4	56
Individual Study for Homework Problems	14	2.5	35
Individual Study for Mid term Examination	2	6	12
Individual Study for Final Examination	3	8	24
TOTAL WORKLOAD (hours)			214.0

Contribution of Learning Outcomes to Programme Outcomes

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

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