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
MAT567	FOURİER ANALİZİ	Elective	1	2	6

Level of Course Unit

Second Cycle

Objectives of the Course

To introduce to the student applications of Laplace transformation.

Name of Lecturer(s)

Doç.Dr.Abdullah SÖNMEZOĞLU

Learning Outcomes

1	To understand Laplace transformation
2	To apply Laplace transformation
3	Understanding between the relations of the Laplace transform with the inverse Laplace

Mode of Delivery

Formal Education

Prerequisites and co-requisities

None

Recommended Optional Programme Components

None

Course Contents

A brief outline of Lp spaces, density theorems in Lp spaces, Stone-Weierstrass density theorem, Fourier series, the relationship between differentiability and shrinkage of Fourier coefficients, Cesaro sum, Fejer kernel and convergent units, Fourier series absolute and point, uniform, L2- norm, L1-norm convergence, Fourier transform, L1 theory: convolution, convergent units, Schwartz space, L2 theory: Plancherel's theorem, Lp theory: Riesz-Thorin and Marcinkiewicz interpolation theorems, Young convolution theorem, Hausdorff-Young theorem, Band-bound theorem and Paley-Wiener spaces, Classical sampling theorem

Weekly Detailed Course Contents

Week	Theoretical	Practice	Laboratory
1	Definition of Laplace transformation
2	Existence and uniqueness of the Laplace transformation
3	Laplace transforms of some functions
4	first-shift feature and its applications
5	second -shift feature and its applications
6	The properties of linear of Laplace transformation
7	Heaviside theorem
8	Midterm exam
9	Laplace transformation of derivatives
10	Laplace transformation of integrals
11	Product funcion with t
12	Split function with t
13	Laplace transformation of periodic functions
14	İnverse Laplace transformation and its applications
15	İnverse Laplace transformation and its applications
16	Final exam

Recommended or Required Reading

Differential equations and their applications, Prof.Dr.İrfan Baki Yasar, political bookstore, Ankara, 2005. Differantial equations, Dennis G. Zill, Michael R. Cullen, PWS Publishing Company, Boston, 1993.

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	1	1
Makeup Examination	1	12	12
Attending Lectures	14	3	42
Problem Solving	14	2	28
Self Study	14	2	28
Individual Study for Mid term Examination	14	2	28
Individual Study for Final Examination	14	2	28
TOTAL WORKLOAD (hours)			168

Contribution of Learning Outcomes to Programme Outcomes

LO1

LO2

LO3

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