Course Information
SemesterCourse Unit CodeCourse Unit TitleL+PCreditNumber of ECTS Credits
8MATH414INTRODUCTION TO INTEGRAL EQUATIONS3+036

Course Details
Language of Instruction English
Level of Course Unit First Cycle
Department / Program MATHEMATICS
Mode of Delivery Face to Face
Type of Course Unit Elective
Objectives of the Course The aim of the course is to introduce and show the classification of the basic concepts of integral equations, to examine the relationship between differential and integral equations, and to teach some solution techniques for integral equations. Another purpose is to create a basis for theoretical and advanced analysis studies related to integral operators.
Course Content Basic Concepts. Applications to Ordinary Differential Equations. Solution of Homogeneous Fredholm Integral Equations of the Second Kind. Fredholm Integral Equations with Separable Kernels. Integral Equations with Symmetric Kernels. Solution of Integral Equations of the Second Kind by Successive Approximation. Classical Fredholm Theory. Integral Transform Methods
Course Methods and Techniques
Prerequisites and co-requisities None
Course Coordinator None
Name of Lecturers Prof.Dr. İsmail Aslan
Assistants None
Work Placement(s) No

Recommended or Required Reading
Resources 1) Ram P. Kanwal, Linear Integral Equations, Academic Press.
2) W. V. Lovitt, Linear Integral Equations, Dover Publications.

Course Category

Planned Learning Activities and Teaching Methods
Activities are given in detail in the section of "Assessment Methods and Criteria" and "Workload Calculation"

Assessment Methods and Criteria
In-Term Studies Quantity Percentage
Midterm exams 2 % 60
Quizzes 0 % 0
Homeworks 0 % 0
Other activities 0 % 0
Laboratory works 0 % 0
Projects 0 % 0
Final examination 1 % 40
Total
3
% 100

ECTS Allocated Based on Student Workload
Activities Quantity Duration Total Work Load
Weekly Course Time 14 3 42
Outside Activities About Course (Attendance, Presentation, Midterm exam,Final exam, Quiz etc.) 12 3 36
Exams and Exam Preparations 3 10 30
Total Work Load   Number of ECTS Credits 4 108

Course Learning Outcomes: Upon the successful completion of this course, students will be able to:
NoLearning Outcomes
1 classify integral equations according to their properties
2 find transformation between integral equations and differential equations.
3 apply basic solutions techniques for integral equations


Weekly Detailed Course Contents
WeekTopicsStudy MaterialsMaterials
1 Integral Equation, Special Kinds of Kernels, Classification of Integral Equation, Iterated Kernels, Resolvent Kernel, Solution of an Integral Equation
2 Method of Conversion of an Initial Value Problem to a Volterra Integral Equation, Boundary Value Problem and its Conversion to a Fredholm Integral Equation
3 Eigenvalue and Eigenfunction, Solution of Homogeneous Fredholm Integral Equation of the Second Kind with Separable Kernel
4 Orthogonality of Two Functions, Orthogonality of Eigenfunctions
5 Solution of Fredholm Integral Equation of the Second Kind with Separable Kernel
6 Solution of Fredholm Integral Equation of the Second Kind with Separable Kernel
7 Symmetric Kernel, Regularity Condition, Inner Product of Two Functions, Orthogonal System of Functions
8 Fundamental Properties of Eigenvalues and Eigenfunctions of Symmetric Kernels, Hilbert–Schmidt Theorem, Schmidt’s Solution of Non-homogeneous Fredholm Integral Equation of the Second Kind
9 Solution of Fredholm Integral Equation of the Second Kind by Successive Substitutions, Solution of Volterra Integral Equation of the Second Kind by Successive Substitutions
10 Solution of Fredholm Integral Equation of the Second Kind by Successive Approximations: Iterative Method, Solution of Volterra Integral Equation of the Second Kind by Successive Approximations: Iterative Method
11 Fredholm’s First Theorem, Evaluating the Resolvent Kernel and Solution of Fredholm Integral Equation of the Second Kind by Using Fredholm’s First Theorem
12 Fredholm’s Second Fundamental Theorem, Fredholm’s Third Theorem
13 Singular Integral Equation, Some Important Properties of Laplace Transform, Integral Equations in Special Forms
14 Application of Laplace Transform to Find the Solutions of Volterra Integral Equation, Fourier Transforms and Their Important Properties, Application of Fourier Transform to Determine the Solution of Singular Integral Equations


Contribution of Learning Outcomes to Programme Outcomes
P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 P11 P12 P13 P14
C1 4 3 3
C2 4 3 3
C3 4 3 3

Contribution: 0: Null 1:Slight 2:Moderate 3:Significant 4:Very Significant


https://obs.iyte.edu.tr/oibs/bologna/progCourseDetails.aspx?curCourse=163227&lang=en