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 Introduction to Dirac’s delta and Green’s functions with application to BVP.
Course Content Dirac’s delta function. Generalized functions and properties. ODE and PDE with delta potential. Green’s functions for ODE. Green’s functions for wave, heat and Laplace equations. Klein-Gordon and Helmholz equations. Boundary value problems
Course Methods and Techniques
Prerequisites and co-requisities None
Course Coordinator None
Name of Lecturers Prof.Dr. Oktay Pashaev
Fatih Erman
Assistants None
Work Placement(s) No

Recommended or Required Reading
Resources Green’s Functions with applications by D. G. Duffy, Chapman, 2001.

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 % 50
Quizzes 0 % 0
Homeworks 0 % 0
Other activities 0 % 0
Laboratory works 0 % 0
Projects 0 % 0
Final examination 1 % 50
% 100

ECTS Allocated Based on Student Workload
Activities Quantity Duration Total Work Load
Weekly Course Time 1 36 36
Outside Activities About Course (Attendance, Presentation, Midterm exam,Final exam, Quiz etc.) 1 27 27
Exams and Exam Preparations 1 81 81
Total Work Load   Number of ECTS Credits 5 144

Course Learning Outcomes: Upon the successful completion of this course, students will be able to:
NoLearning Outcomes
1 To understand how Green's functions contibute to solve boundary value problems.
2 To be able to solve typical problems associated with this theory.

Weekly Detailed Course Contents
WeekTopicsStudy MaterialsMaterials
1 The Dirac Delta function . Definition and properties
2 Delta sequences and sequential approach
3 Generalized functions and properties
4 ODE and PDE with delta potential
5 1st Midterm
6 Green’s functions and properties
7 Green’s functions for ODE
8 IVP and BVP
9 Green’s function for wave equation
10 2nd Midterm
11 Green’s function for heat equatipon. Green’s function for Laplace equation
12 Green’s function for Helmholz equation
13 Green’s function for Klein-Gordon equation
14 Scattering theory applications

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

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