

Course Information
Course Unit Title 
: 
Green Functions and Boundary Value Problems 
Course Unit Code 
: 
01MAK6140 
Type of Course Unit 
: 
Optional 
Level of Course Unit

: 
Second Cycle 
Year of Study

: 
Preb 
Semester

: 
255.Semester 
Number of ECTS Credits Allocated

: 
6,00 
Name of Lecturer(s) 
: 


Course Assistants 
: 

Learning Outcomes of The Course Unit 
: 
1) Developing mathematical models of the physical systems and obtaining general solutions . 2) To bring some explanation by using Green Functions about solutions of the encountered boundary value problems. 3) Using various Linear operators 4) To understand DiracDelta functions and Sequence 5) Derivatives of generalized functions 6) Solutions of ordinary differential equations 7) Solutions of partial differential equations

Mode of Delivery 
: 
FaceToFace

Prerequisities and Corequisities Courses 
: 
Unavailable

Recommended Optional Programme Components 
: 
Unavailable

Course Contents 
: 
Mathematical models of physical systems, Linear operators, General solution metrhods, Classification of partial differential equations, Green functions, Eigenfunctions, SturmLiouville Problems

Languages of Instruction 
: 
Turkish

Course Goals 
: 
1) To teach setting up mathematical model for physical systems 2) To recognize boundary value problems 3) To give up concept of linear opertor 4) To recognize the Dirac  Delta functions and sequency 5) To teach obtaining of derivatives of generalized functions 6) Solutions of ordinary differential equations by using Green functions 7) Solutions of partial differential equations by using Green functionsv

Course Aims 
: 
Solutions of ordinary and partial differential equations by using Green Functions

WorkPlacement 



Recommended or Required Reading
Textbook

: 


Additional Resources

: 
Nagle, R.K., Saff, E.B., Snider, A.D., "Fundemantals of Differential Eqautions and Boundary Value Problems", Addison Wesley,2004.
Haberman, R. "Appl. Partial Diff. Eqs. With Fourier Series and Boundary Value Problems", Prentice Hall,2004.
Stakgold, Ivar. "Green's Functions and Boundary Value Problems", 2nd Edition, WileyInterscience. 1997.
Arfken,George B., Weber,Hans J. "Mathematical Methods for Physicists", Academic Pres.2000.

Material Sharing
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Planned Learning Activities and Teaching Methods
Lectures, Practical Courses, Presentation, Seminar, Project, Laboratory Applications (if necessary)


ECTS / Table Of Workload (Number of ECTS credits allocated)
Student workload surveys utilized to determine ECTS credits.

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Workload Hour (30)

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Assessment Methods and Criteria
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Visa

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Weekly Detailed Course Content
Week

Topics

1

Ordinary and partial differential equations, Remembering to the initial and boundary value problems, Concepts of linear and nonlinear operators


Study Materials: To study sources concerning with course

2

Functional, Formal differential operators, Formal adjoint differential operator, Differential operator, Adjoint differential operator concepts


Study Materials: To study sources concerning with course

3

Definiton of DiracDelta function and sequence


Study Materials: To study sources concerning with course

4

Generalized functions and its derivatives


Study Materials: To study sources concerning with course

5

Integral representation of Delta Functions


Study Materials: To study sources concerning with course

6

Sample Applications


Study Materials: To study sources concerning with course

7

Solutions of ordinary differential equations by Green Functions


Study Materials: To study sources concerning with course

8

Deflection problem of a loading cable


Study Materials: To study sources concerning with course

9

Infinite beam problem on elastic foundation


Study Materials: To study sources concerning with course

10

Orthopgonality of functions


Study Materials: To study sources concerning with course

11

Application of Green functions to the partial differential equations


Study Materials: To study sources concerning with course

12

Fredholm and Volterra integral equations


Study Materials: To study sources concerning with course

13

SturmLiouville boundaryvalue problems


Study Materials: To study sources concerning with course

14

Eigenfunctions method


Study Materials: To study sources concerning with course

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