Information Package / Course Catalogue - Adnan Menderes University

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Theory of Integral Equations

Course Code	: MTK540
Course Type	: Area Elective
Couse Group	: Second Cycle (Master's Degree)
Education Language	: Turkish
Work Placement	: N/A

Theory	: 3
Prt.	: 0
Credit	: 3
Lab	: 0
ECTS	: 8

Objectives of the Course

This course aims to acquaint students with the basic knowledge of integral equations. Students will be familiar with classification of equations Volterra and Fredholm method of solutions. They may easily understand the features of topics used at the area of information other courses. They will be able to make applications related to physics, and other sciences.

Course Content

Introduction to define and classify of integral equations, Volterra and Fredholm integral equations, integral equations systems

Name of Lecturer(s)

Learning Outcomes

1.	To be able to define, classify and find of Integral Equations
2.	To be able to find relation between integral equations and differantial equations .To be able to solve Integral equations with separable kernels and to solve using general solution of them
3.	To be able to solve successive approximation to integral equations and apply to volterra andFredholm
4.	To be able to make applications related to physics, and other sciences.
5.	To be able to use mathematical concepts in solving certain types of problems

Recommended or Required Reading

1.	Ram P. KANWAL (1971) Lineer integral denklemler (Linear Integral Equations), Academic Press, 1. New York and London.
2.	Villiam Vernon LOVITT (1950) Lineer integral denklemler (Linear Integral Equations), Dower publications, New York
3.	Yavuz AKSOY (1983) İntegral Denklemler (Integral Equations), Yıldız üniversitesi yayınları

Weekly Detailed Course Contents

Week 1 - Theoretical

Introduction, Classification of integral equations

Week 3 - Theoretical

Method of successive approximation

Week 4 - Theoretical

Fredholm integral equations

Week 5 - Theoretical

Volterra integral equations

Week 6 - Theoretical

Linear system of Volterra integral equations

Week 7 - Theoretical

Nonlinear Volterra integral equations of the second kind

Week 8 - Theoretical

Fredholm integral equations with degenerate kernel

Week 9 - Theoretical

Fredholm theorem for integral equations, Midterm Exam

Week 10 - Theoretical

Fredholm theorem for integral equations

Week 11 - Theoretical

Eigenvalues of the kernel of an integral equations

Week 12 - Theoretical

Integral equations with continuous kernel

Week 13 - Theoretical

Singular Volterra integral equations

Week 14 - Theoretical

Singular Volterra integral equations

Week 15 - Final Exam

FINAL EXAM

Assessment Methods and Criteria

Type of Assessment	Count	Percent
Midterm Examination	1	%30
Final Examination	1	%70

Workload Calculation

Activities	Count	Preparation	Time	Total Work Load (hours)
Lecture - Theory	14	0	3	42
Individual Work	14	0	4	56
Midterm Examination	1	42	3	45
Final Examination	1	54	3	57
TOTAL WORKLOAD (hours)				200

Contribution of Learning Outcomes to Programme Outcomes

	PÇ-1	PÇ-2	PÇ-3	PÇ-4	PÇ-5	PÇ-6	PÇ-7	PÇ-8	PÇ-9	PÇ-10	PÇ-11	PÇ-12	PÇ-13	PÇ-14	PÇ-15
OÇ-1	3		4	2	3	4	4	2	3	4	2	2	2	3
OÇ-2	4			2	4	4	4	3	4	4	3	4	3	3
OÇ-3	2		4	2	5	4	4	2	4	4	4	3	3	3
OÇ-4	3		4	3	4	4	4	2	4	4	4	3	4	4
OÇ-5	3		4	3		4	4		4	4	4		4	4

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