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Course Information
Course Unit Title : Green Functions and Boundary Value Problems
Course Unit Code : 01IMM5149
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 Dirac-Delta functions and Sequence
5) Derivatives of generalized functions
6) Solutions of ordinary differential equations
7) Solutions of partial differential equations
Mode of Delivery : Face-To-Face
Prerequisities and Co-requisities 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, Eigen-functions, Sturm-Liouville 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 functions
Course Aims : Solutions of ordinary and partial differential equations by using Green Functions
WorkPlacement   Not Available
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, Wiley-Interscience. 1997.

Arfken,George B., Weber,Hans J. "Mathematical Methods for Physicists", Academic Pres.2000.
Material Sharing
Documents :
Assignments :
Exams :
Additional Material :
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.
Activity :
Number Duration Total  
Course Duration (Excluding Exam Week) :
14 4 56  
Time Of Studying Out Of Class :
14 5 70  
Homeworks :
4 6 24  
Presentation :
0 0 0  
Project :
0 0 0  
Lab Study :
0 0 0  
Field Study :
0 0 0  
Visas :
1 8 8  
Finals :
1 16 16  
Workload Hour (30) :
30  
Total Work Charge / Hour :
174  
Course's ECTS Credit :
6      
Assessment Methods and Criteria
Studies During Halfterm :
Number Co-Effient
Visa :
1 50
Quiz :
1 20
Homework :
4 20
Attendance :
1 10
Application :
0 0
Lab :
0 0
Project :
0 0
Workshop :
0 0
Seminary :
0 0
Field study :
0 0
   
TOTAL :
100
The ratio of the term to success :
40
The ratio of final to success :
60
TOTAL :
100
Weekly Detailed Course Content
Week Topics  
1 Ordinary and partial differential equations, Remembering to the initial and boundary value problems, Concepts of linear and non-linear 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 Dirac-Delta 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 Sturm-Liouville boundary-value problems
  Study Materials: To study sources concerning with course
14 Eigen-functions method
  Study Materials: To study sources concerning with course
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