Nevşehir Hacı Bektaş Veli University Course Catalogue

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 Can recognize 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
LO-2 Can recognize 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
LO-3 Can recognize the concepts of Hilbert and Stieltjes 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
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 Introduction to the Mellin transforms Oral expression, discussion, question-answer
3 Definition and basic properties of the Mellin Transforms Oral expression, discussion, question-answer
4 Concolution Theorems for Mellin Transforms Oral expression, discussion, question-answer
5 Applications of Mellin Transforms Oral expression, discussion, question-answer
6 Inverse Mellin trasnforms Oral expression, discussion, question-answer
7 Introduction to the Hankel transforms Oral expression, discussion, question-answer
8 mid-term exam
9 Definition and basic properties of the Hankel Transforms Oral expression, discussion, question-answer
10 Applications of Hankel transforms Oral expression, discussion, question-answer
11 Inverse Hankel transforms Oral expression, discussion, question-answer
12 Definition and basic properties of the Hilbert Transforms Oral expression, discussion, question-answer
13 Applications of Hilbert transforms Oral expression, discussion, question-answer
14 Definition and basic properties of the Stieltjes Transforms Oral expression, discussion, question-answer
15 Applications of Stieltjes transforms Oral expression, discussion, question-answer
16 final exam
Recommend Course Book / Supplementary Book/Reading
1 Kevser Özden Köklü, İntegral Dönüşümler ve Uygulamaları, Papatya Yayınevi, 2018.
2 Lokenath Debnath, Dambaru Bhatta, Integral Transforms and Their Applications, CRC Press, 2015.
Required Course instruments and materials
Textbooks - Kevser Ozden Koklu, Integral Donusumler ve Uygulamalari, Papatya Yayinevi, 2018. - Lokenath Debnath, Dambaru Bhatta, Integral Transforms and Their Applications, CRC Press, 2015.

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 0
       b) Search in internet/Library 0
       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
Individual study before class 2 14 28
Individual study after class 5 14 70
Total work load; 180