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
FMA616	REAL FUNCTIONS OF SEVERAL VARIABLES II	Compulsory	1	2	6

Level of Course Unit

Second Cycle

Objectives of the Course

• to gain the basic information necessary in the field of Theory of Functions of Several Variables

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

• Analytic Functions in En • Taylor Series • Local Extremes • İntegrals in En • Moments • Centers of gravity • Spherical Coordinates in En • n-dimensional sphere Volume and Surface domain • Differentiable Functions and Derivatives • Differential Operators • Implicit Function and Inverse Function Theorems • Homeomorphism and diffeomorphism

Weekly Detailed Course Contents

Week	Theoretical	Practice	Laboratory
1	Analytic Functions in Rn
2	Taylor Series
3	Local Extremes
4	Integrals in Rn
5	Moments, centers of gravity
6	Spherical Coordinates in Rn
7	n-dimensional sphere Volume and Surface domain
8	Midterm exam
9	Differentiable Functions and Derivatives
10	Differentiable Functions and Derivatives
11	Differential Operators
12	Implicit Function and Inverse Function Theorems
13	Implicit Function and Inverse Function Theorems
14	Homeomorphism and diffeomorphism
15	Homeomorphism and diffeomorphism
16	Final exam

Recommended or Required Reading

Webb, J. R. L., (1991), Functions of Several Real Variables, Chichester, west sussec, England. Other References Moskowitz, Martin and Paliogiannis, Fotions, Functions of Several Real Variables

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	2	2
Attending Lectures	14	6	84
Problem Solving	10	5	50
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)			252

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