Information Of Programmes

INSTITUTE OF SCIENCE / MAT590 - MATHEMATICS

Code: MAT590

Course Title: ADVANCED INTEGRAL TRANSFORMS II

Theoretical+Practice: 3+0

ECTS: 6

Year/Semester of Study

1 / Spring Semester

Level of Course

2nd Cycle Degree Programme

Type of Course

Optional

Department

MATHEMATICS

Pre-requisities and Co-requisites

None

Mode of Delivery

Face to Face

Teaching Period

14 Weeks

Name of Lecturer

SURE KÖME (sure.kome@nevsehir.edu.tr)

Name of Lecturer(s)

Language of Instruction

Turkish

Work Placement(s)

None

Objectives of the Course

The purpose of this course is for the student to have detailed information about Mellin and Hankel transformations, which have an important place in the theory of integral transformations.

Learning Outcomes		PO	MME
The students who succeeded in this course:
LO-1	Recognizes the concepts of Mellin and Inverse Mellin transforms.	PO-1 Fundamental theorems of about some sub-theories of Analysis, Applied Mathematics, Geometry, and Algebra can apply to new problems. PO-2 Ability to assimilate mathematic related concepts and associate these concepts with each other.	Examination Term Paper
LO-2	Recognizes the concepts of Hankel and Inverse Hankel transforms.	PO-1 Fundamental theorems of about some sub-theories of Analysis, Applied Mathematics, Geometry, and Algebra can apply to new problems. PO-2 Ability to assimilate mathematic related concepts and associate these concepts with each other.	Examination Term Paper
PO: Programme Outcomes MME:Method of measurement & Evaluation

Course Contents
Mellin Transform, Inverse Mellin Transform, Hankel Transform, Inverse Hankel Transform, Convolution
Weekly Course Content
Week	Subject	Learning Activities and Teaching Methods
1	Basic definitions about Integral transforms	Oral expression, discussion, question-answer
2	Basic definitions about Integral transforms	Oral expression, discussion, question-answer
3	Introduction to the Mellin transforms	Oral expression, discussion, question-answer
4	Basic properties of Mellin transforms	Oral expression, discussion, question-answer
5	Algebraic properties of the convolution	Oral expression, discussion, question-answer
6	Applications of Mellin transforms	Oral expression, discussion, question-answer
7	Applications of Mellin transforms	Oral expression, discussion, question-answer
8	mid-term exam
9	Basic definitions and properties about Hankel transforms	Oral expression, discussion, question-answer
10	Basic definitions and properties about Hankel transforms	Oral expression, discussion, question-answer
11	Applications of Hankel transforms	Oral expression, discussion, question-answer
12	Applications of Hankel transforms	Oral expression, discussion, question-answer
13	Definitions and rules of inverse Hankel transforms	Oral expression, discussion, question-answer
14	General applications and properties of inverse Hankel transforms	Oral expression, discussion, question-answer
15	General applications and properties of inverse Hankel transforms	Oral expression, discussion, question-answer
16	final exam
Recommend Course Book / Supplementary Book/Reading
1	Spiegel, Murray R. Laplace transforms. New York: McGraw-Hill, 1965.
2	Yaşar, İrfan Baki. İntegral Dönüşümleri ve Uygulamaları. Siyasal Kitabevi, 2003.
Required Course instruments and materials
Spiegel, Murray R. Laplace transforms. New York: McGraw-Hill, 1965.

Assessment Methods
Type of Assessment	Week	Hours	Weight(%)
mid-term exam	8	2	40
Other assessment methods
1.Oral Examination
2.Quiz
3.Laboratory exam
4.Presentation
5.Report
6.Workshop
7.Performance Project
8.Term Paper
9.Project
final exam	16	2	60

Student Work Load
Type of Work	Weekly Hours	Number of Weeks	Work Load
Weekly Course Hours (Theoretical+Practice)	3	14	42
Outside Class
a) Reading	5	14	70
b) Search in internet/Library	2	14	28
c) Performance Project			0
d) Prepare a workshop/Presentation/Report			0
e) Term paper/Project			0
Oral Examination			0
Quiz			0
Laboratory exam			0
Own study for mid-term exam	4	4	16
mid-term exam	2	1	2
Own study for final exam	5	4	20
final exam	2	1	2
			0
			0
Total work load;			180