1	Course Title:	INTEGRAL EQUATIONS
2	Course Code:	MAT4032
3	Type of Course:	Optional
4	Level of Course:	First Cycle
5	Year of Study:	4
6	Semester:	8
7	ECTS Credits Allocated:	6
8	Theoretical (hour/week):	3
9	Practice (hour/week) :	0
10	Laboratory (hour/week) :	0
11	Prerequisites:	None
12	Recommended optional programme components:	None
13	Language:	Turkish
14	Mode of Delivery:	Face to face
15	Course Coordinator:	Dr. Ögr. Üyesi NISA ÇELİK
16	Course Lecturers:	Yrd.Doç.Dr.Setenay DOĞAN Yrd.Doç.Dr.Nisa ÇELİK Yrd.Doç.Dr.Sezai HIZLIYEL Yrd.Doç.Dr.Emrullah YAŞAR
17	Contactinformation of the Course Coordinator:	caglayan@uludag.edu.tr 0 224 2941752 U.Ü. Fen Edebiyat Fak. Mat.Böl. Görükle Yerleşkesi, Nilüfer BURSA
18	Website:
19	Objective of the Course:	To introduce the concept of integral equation and give some applications
20	Contribution of the Course to Professional Development

21

Learning Outcomes:

1 Learns the modelling of some events as an integral equations; 2 Understands the relationship between integral and differential equations.; 3 Learns to get solutions of some integral equations.;

22	Course Content:

Week	Theoretical	Practical
1	Preliminary information. Definition, classification, Fredholm and Volterra equations, the concept.of solution
2	Fredholm integral equation of second kind with dejenerate kernel. Reducing to system of algebric equations, obtaining of the solution in case is not an eigenvalue. Resolvent kernel. Exercises.
3	Homegenous Fredholm equation, eigenvalues and eigenfunctions. Exercises.
4	Adjoint homegeneous and inhomegeneous Fredholm equations. Existance of the solutions in case is an eigenvalue
5	Successive substitutions method, the applications of the method to Fredholm and Volterra equations.
6	Iterated kernels and resolvent kernels. Neumann series. Exercises.
7	Method of successive appoximations. Applications of the method to Fredholm and Volterra equations. Exercises.
8	Midterm exam, general review
9	Classical Fredholm theory in case an arbitrary kernel.
10	Obtainig of the solutions in case lambda is not an eigenvalue.
11	Existence of solutions in case lambda is an eigenvalue
12	Integral equations with symmetric kernel.
13	Reduction of initial and boundary problems to integral equations.
14	General exercises.

23	Textbooks, References and/or Other Materials:	Linear İntegral Equations William Vernon Lovitt
24	Assesment

TERM LEARNING ACTIVITIES	NUMBER	PERCENT
Midterm Exam	1	40
Quiz	0	0
Homeworks, Performances	0	0
Final Exam	1	60
Total	2	100
Contribution of Term (Year) Learning Activities to Success Grade		40
Contribution of Final Exam to Success Grade		60
Total		100
Measurement and Evaluation Techniques Used in the Course
Information

25

ECTS / WORK LOAD TABLE

Activites	NUMBER	TIME [Hour]	Total WorkLoad [Hour]
Theoretical	14	3	42
Practicals/Labs	0	0	0
Self Study and Preparation	14	4	56
Homeworks, Performances	0	4	56
Projects	0	0	0
Field Studies	0	0	0
Midtermexams	1	12	12
Others	0	0	0
Final Exams	1	14	14
Total WorkLoad			180
Total workload/ 30 hr			6
ECTS Credit of the Course			6

26	CONTRIBUTION OF LEARNING OUTCOMES TO PROGRAMME QUALIFICATIONS
PQ1 PQ2 PQ3 PQ4 PQ5 PQ6 PQ7 PQ8 PQ9 PQ10 LO1 2 3 1 2 4 1 4 4 3 1 LO2 3 2 1 2 4 1 3 4 2 1 LO3 2 3 1 2 5 1 3 4 2 1

LO: Learning Objectives

PQ: Program Qualifications

Contribution Level:

1 Very Low

2 Low

3 Medium

4 High

5 Very High