Course Information
SemesterCourse Unit CodeCourse Unit TitleL+PCreditNumber of ECTS Credits

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 Study numerical methods for the solution of linear integral equation of the second kind.
Course Content Compact operator. The Fredholm alternative. Degenerate kernel methods. Projection methods. The Nyström method. Global approximation methods on smooth surfaces.
Solution of integral equations on the unit sphere.
Course Methods and Techniques
Prerequisites and co-requisities None
Course Coordinator None
Name of Lecturers Olha Ivanyshyn Yaman
Assistants None
Work Placement(s) No

Recommended or Required Reading
Resources Delves, L.M., and Mohamed, J.L.: Computational Methods for Integral Equations. Cambridge Univ. Press, Cambridge 1985.
Hackbusch, W.: Integral Equations: Theory and Numerical Treatment. Birkhäuser-Verlag, Basel 1994
Kress, R.: Linear integral equations. Springer, 2014
Atkinson, K.E.: The Numerical Solution of Integral Equations of the Second Kind. Cambridge Univ. Press, Cambridge 1997.

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 % 40
Quizzes 0 % 0
Homeworks 5 % 20
Other activities 0 % 0
Laboratory works 0 % 0
Projects 0 % 0
Final examination 1 % 40
% 100

ECTS Allocated Based on Student Workload
Activities Quantity Duration Total Work Load
Weekly Course Time 1 20 20
Outside Activities About Course (Attendance, Presentation, Midterm exam,Final exam, Quiz etc.) 2 20 40
Application (Homework, Reading, Self Study etc.) 3 20 60
Exams and Exam Preparations 3 20 60
Total Work Load   Number of ECTS Credits 6 180

Course Learning Outcomes: Upon the successful completion of this course, students will be able to:
NoLearning Outcomes
1 To be able to classify integral equations according to their properties and to decide whether they are uniquely solvable
2 To be able to apply numerical solution techniques for integral equations over a curve
3 To be able to solve numerically integral equations on the unit sphere

Weekly Detailed Course Contents
WeekTopicsStudy MaterialsMaterials
1 Compact integral operators
2 Fredholm alternative theorem
3 Degenerate kernel methods
4 Interpolatory degenerate kernel approximation
5 Collocation methods
6 Galerkin’s method
7 Iterated projection methods
8 Condition numbers for the projection methods
9 The Nyström method for continuous kernels
10 Product integration methods
11 Discrete projection solution
12 Global approximation methods on smooth surfaces
13 Numerical integration on the sphere
14 Solution of integral equations on the unit sphere

Contribution of Learning Outcomes to Programme Outcomes
P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 P11 P12 P13 P14
C1 2 2
C2 4 3
C3 3

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