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
MAT570	IRAKSAK SERİLER	Elective	1	2	6

Level of Course Unit

Second Cycle

Objectives of the Course

To define the Fourier series and Fourier coefficients,to learn Fourier series representations, and other important features of this series examining the problems of convergence.

Name of Lecturer(s)

Doç. Dr. Abdullah SÖNMEZOĞLU

Learning Outcomes

1	To definite of Fourier series
2	Fourier series of a function to open a range of convergence of these series should be aware of the conditions necessary
3	Bessel's inequality, Parseval's equality and the important theorems of Riesz-Fischer theorem, known as able to understand

Mode of Delivery

Formal Education

Prerequisites and co-requisities

None

Recommended Optional Programme Components

None

Course Contents

Infinite series and infinite products (infinite series and convergence, series with positive terms, convergence criteria), series with arbitrary terms (Leibnitz criterion), absolute and conditional convergent series, Riemann's theorem, numerical calculation of series (error and remainder estimation), product of infinite series, Power series (convergence radius and region), Complex term sequences and series, Abel and Dirichlet criteria, variable term sequences, point and uniform convergence, Infinite products, Cauchy condition and absolute convergence, General warnings on divergent series, Limiting operations, C- and H-operations, A-operation, E-operation

Weekly Detailed Course Contents

Week	Theoretical	Practice	Laboratory
1	trigonometric series
2	conjugate series
3	Writing complex trigonometric series
4	represent of Fourier series
5	complex form of Fourier series
6	Trigonometric series expansions of periodic functions
7	Based on orthogonal systems, Fourier expansions
8	Midterm exam
9	Completeness of trigonometric systems in L-space
10	Uniform convergence of Fourier series
11	Bessel inequality
12	Convergence of Fourier series of L2-space
13	Connection between indoor sysrems .Closeness and completeness,
14	Riesz-Fischer theorem, the coefficients of integral evaluation of the help module.
15	Riesz-Fischer theorem, the coefficients of integral evaluation of the help module.
16	Final exam

Recommended or Required Reading

• A. Zigmund, Trigonometric Series 1–2, Cambridge Univ. Press, 1988. • N.K. Bary, Treatise on Trigonometric Series. Pergamon Press, 1964. • R.E. Edwards, Fourier series: A modern introduction Vol. 1&2 , Springer, 1979,1982. • J.-P. Kahane, Séries de Fourier Absolument Convergentes, Springer, 1970. • E.M. Stein, G. Weiss, Introduction to Fourier analysis on Euclidean spaces, Princeton Univ. Press, 1971.

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	1	1
Final Examination	1	2	2
Makeup Examination	1	24	24
Attending Lectures	14	3	42
Problem Solving	14	2	28
Self Study	14	3	42
Individual Study for Mid term Examination	14	1	14
Individual Study for Final Examination	14	1	14
TOTAL WORKLOAD (hours)			167

Contribution of Learning Outcomes to Programme Outcomes

LO1

LO2

LO3

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