Nevşehir Hacı Bektaş Veli University Course Catalogue

Information Of Programmes

INSTITUTE OF SCIENCE / MAT668 - MATHEMATICS (DOCTORATE DEGREE)

Code: MAT668 Course Title: BOUNDARY VALUE PROBLEMS II Theoretical+Practice: 3+0 ECTS: 6
Year/Semester of Study 1 / Spring Semester
Level of Course 3rd Cycle Degree Programme
Type of Course Optional
Department MATHEMATICS (DOCTORATE DEGREE)
Pre-requisities and Co-requisites None
Mode of Delivery Face to Face
Teaching Period 14 Weeks
Name of Lecturer SEYDİ BATTAL GAZİ KARAKOÇ (sbgkarakoc@nevsehir.edu.tr)
Name of Lecturer(s)
Language of Instruction Turkish
Work Placement(s) None
Objectives of the Course
The aim of this course is to introduce basic methods of solution of boundary value problems including boundary conditions.

Learning Outcomes PO MME
The students who succeeded in this course:
LO-1 PO-3 Students will be dominated by current issues in mathematics.
PO-14 Ability to use the approaches and knowledge of other disciplines in Mathematics.
PO-15 Be able to set up and develope a solution method for a problem in mathematics independently, be able to solve and evaluate the results and to apply them if necessary.
 		Examination
PO: Programme Outcomes
MME:Method of measurement & Evaluation

Course Contents
Liouville problems, Regular Strum-Liouville problems, Eigenfunction expansion method, Green function method, Singular Strum-Liouville problems, Bessel functions, and Bessel functions. Legendre Polynomials, Boundary-Value Problems in Cylindrical Coordinates, Boundary-Value Problems in Spherical Coordinates
Weekly Course Content
Week Subject Learning Activities and Teaching Methods
1 Standard Equations of Mathematical Physics with Mathematical Models of Physical Problems Oral Represention, Problem solving method.
2 The existence and uniqueness of solutions of boundary-value problems Oral Represention, Problem solving method.
3 Fourier series and Fourier transformations Oral Represention, Problem solving method.
4 Applications of Fourier transformations Oral Represention, Problem solving method.
5 Strum-Liouville eigenvalue problems Oral Represention, Problem solving method.
6 Regular Strum-Liouville problems Oral Represention, Problem solving method.
7 Periodic Strum-Liouville problems Oral Represention, Problem solving method.
8 mid-term exam
9 Nonhomogeneous boundary value problems and Fredholm Alternative Oral Represention, Problem solving method.
10 Eigenfunction expansion method Oral Represention, Problem solving method.
11 Green function method Oral Represention, Problem solving method.
12 Singular Strum-Liouville problems Oral Represention, Problem solving method.
13 Bessel functions and Legendre polynomials Oral Represention, Problem solving method.
14 Boundary-value problems in cylindrical coordinates Oral Represention, Problem solving method.
15 Boundary-value problems in spherical coordinates Oral Represention, Problem solving method.
16 final exam
Recommend Course Book / Supplementary Book/Reading
1 Numerical Solution of Partial Differential Equations Leon LAPIDUS and George F. PINDER. Numerical Solution of Partial Differential Equations: Finite Difference Methods G. D. Smith, Gordon D. Smith Numerical Solution of Partial Differential Equations K. W
Required Course instruments and materials

Assessment Methods
Type of Assessment Week Hours Weight(%)
mid-term exam 8 2 40
Other assessment methods
1.Oral Examination
2.Quiz
3.Laboratory exam
4.Presentation
5.Report
6.Workshop
7.Performance Project
8.Term Paper
9.Project
final exam 16 2 60

Student Work Load
Type of Work Weekly Hours Number of Weeks Work Load
Weekly Course Hours (Theoretical+Practice) 3 14 42
Outside Class
       a) Reading 5 14 70
       b) Search in internet/Library 2 14 28
       c) Performance Project 0
       d) Prepare a workshop/Presentation/Report 0
       e) Term paper/Project 0
Oral Examination 0
Quiz 0
Laboratory exam 0
Own study for mid-term exam 4 4 16
mid-term exam 2 1 2
Own study for final exam 5 4 20
final exam 2 1 2
0
0
Total work load; 180