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
MAT516	APPLICABLE FUNCTIONAL ANALYSIS II	Elective	1	2	6

Level of Course Unit

Second Cycle

Objectives of the Course

With the help of inner product spaces and Hilbert spaces discrete approach to student

Name of Lecturer(s)

Prof. Dr. Mammad Mustafayev

Learning Outcomes

1	Defining Dual spaces and the Adjoint operators.
2	Learning compactness in normed spaces and compact operators
3	Learning inner product space rigidity and vertical projection operator
4	Explaining method of sequential approaches
5	Defining the conversion principle of shrinking
6	The ability to prove being and uniqueness theorem to integral equations
7	To ability Fredholm and Volterra integral equations expression

Mode of Delivery

Formal Education

Prerequisites and co-requisities

None

Recommended Optional Programme Components

None

Course Contents

Hahn-Banach theorem and optimization problems, Variational principles and weak convergence, Principles of linear functional analysis, Theorems about non-explicit operators, Fredholm operators, Abstract approximations

Weekly Detailed Course Contents

Week	Theoretical	Practice	Laboratory
1	Dual spaces and Adjoint operators
2	Theorem of Hanh-Banach
3	Compactness in Normed spaces and the compact operators
4	Compactness in Normed spaces and the compact operators
5	Inner product space rigidity and vertical projection operator
6	Inner product space rigidity and vertical projection operator
7	The method of sequential approaches
8	The method of sequential approaches
9	Midterm exam
10	Narrowing conversion principle
11	Narrowing conversion principle
12	Being and uniqueness theorem for ıntegral equations
13	Being and uniqueness theorem for ıntegral equations
14	Fredholm and Volterra integral equations
15	Fredholm and Volterra integral equations
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 Press, (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	7	56
Individual Study for Mid term Examination	8	7	56
Individual Study for Final Examination	8	7	56
TOTAL WORKLOAD (hours)			190

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