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
MAT515	APPLICABLE FUNCTIONAL ANALYSIS	Elective	1	1	6

Level of Course Unit

Second Cycle

Objectives of the Course

Generalizing of mathematical analysis, a specific type of linear algebra and geometry and methods infinite-dimensional space.

Name of Lecturer(s)

Prof. Dr. Mammad Mustafayev

Learning Outcomes

1	Defining concept of metric space
2	To explain concepts of convergence, continuity, cauchy sequence, and exactness
3	Defining the entire spaces and metric spaces
4	Learning properties of normed space and linear spaces
5	Learning definition of Banach space
6	Learning definitions of inner product and Hilbert spaces
7	Learning the basic terms of the theory of operator.

Mode of Delivery

Formal Education

Prerequisites and co-requisities

None

Recommended Optional Programme Components

None

Course Contents

Banach space and fixed point theorem, Orthogonality in Hilbert space and Dirichlet principle, Generalized Fourier series in Hilbert space, Characteristic numbers and vectors of linear compact symmetric operators, Eigen conjugate operators

Weekly Detailed Course Contents

Week	Theoretical	Practice	Laboratory
1	Metric spaces
2	Metric spaces
3	Convergence and continuity
4	Cauchy sequences and exactness
5	Entire spaces, compactness in metric spaces
6	Linear spaces
7	Normed spaces
8	Normed spaces
9	Midterm Exam
10	Banach spaces
11	Banach spaces
12	Inner product spaces and Hilbert spaces
13	Inner product spaces and Hilbert spaces
14	Basic terms of operator theory
15	Basic terms of operator theory
16	Final exam

Recommended or Required Reading

Musayev B., Alp M., Fonksiyonel Analiz, Bole Yayınları, Ankara, (2002) Erwin Kreyszig, Introductory functional analysis with applications, John Wiley and Sons. Inc., (1978) I. J. Maddox, Elements of Functional Analysis, Cambridge University Pres, (1988)

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	6	3	18
Individual Study for Homework Problems	8	6	48
Individual Study for Mid term Examination	8	7	56
Individual Study for Final Examination	8	7	56
TOTAL WORKLOAD (hours)			182

Contribution of Learning Outcomes to Programme Outcomes

LO1

LO2

LO3

LO4

LO5

LO6

LO7

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