Information Of Programmes

INSTITUTE OF SCIENCE / MAT589 - MATHEMATICS

Code: MAT589

Course Title: ADVANCED INTEGRAL TRANSFORMS I

Theoretical+Practice: 3+0

ECTS: 6

Year/Semester of Study

1 / Fall 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 Forurier and Laplace 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 Fourier and Inverse Fourier 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 Laplace and Inverse Laplace 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
Fourier Transform, Inverse Fourier Transform, Laplace Transform, Inverse Laplace Transform, Convolution
Weekly Course Content
Week	Subject	Learning Activities and Teaching Methods
1	Basic definitions about Integral transforms	Oral expression,discussion, question-answer
2	General informations about Fourier series	Oral expression,discussion, question-answer
3	Introduction to the Fourier transforms	Oral expression,discussion, question-answer
4	Basic properties of Fourier transforms	Oral expression,discussion, question-answer
5	Algebraic properties of the convolution	Oral expression,discussion, question-answer
6	Solving ordinary differential equations with the help of Fourier transforms	Oral expression,discussion, question-answer
7	Solving ordinary differential equations with the help of Fourier transforms	Oral expression,discussion, question-answer
8	mid-term exam
9	Basic definitions and properties about Laplace transforms	Oral expression,discussion, question-answer
10	Definition and rules of inverse Laplace transforms	Oral expression,discussion, question-answer
11	Properties and general applications of inverse Laplace transforms	Oral expression,discussion, question-answer
12	Advanced inverse Laplace transforms	Oral expression,discussion, question-answer
13	Advanced inverse Laplace transforms	Oral expression,discussion, question-answer
14	Applications of inverse Laplace transforms to differential equations	Oral expression,discussion, question-answer
15	Applications of inverse Laplace transforms to differential equations	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
[1] 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