1	Course Title:	BOUNDARY-VALUE PROBLEMS
2	Course Code:	MAT4062
3	Type of Course:	Optional
4	Level of Course:	First Cycle
5	Year of Study:	4
6	Semester:	8
7	ECTS Credits Allocated:	6
8	Theoretical (hour/week):	3
9	Practice (hour/week) :	0
10	Laboratory (hour/week) :	0
11	Prerequisites:	None
12	Recommended optional programme components:	None
13	Language:	Turkish
14	Mode of Delivery:	Face to face
15	Course Coordinator:	Prof. Dr. SEZAYİ HIZLIYEL
16	Course Lecturers:
17	Contactinformation of the Course Coordinator:	hizliyel@uludag.edu.tr Tel:(0224)2941765 Uludağ Ünv. Fen Ed. Fakültesi Matematik Bölümü Görükle Yerleşkesi 16059 Bursa-Türkiye
18	Website:
19	Objective of the Course:	The aim of this course is give methods to solve mathematical problems that arise in areas of application such as physics and engineering.
20	Contribution of the Course to Professional Development

21

Learning Outcomes:

1 To understand boundary value and initial value problems that may arise in Engineering and physics; 2 Classifies almost linear second order partial differential equations; 3 knows İnitial value and Cauchy problems defined for general hyperbolic equations and solves; 4 knows defined boundary value problems for elliptic equation and solves; 5 Knows the general properties of Green and Neumann functions; 6 Knows the initial and boundary value problems defined for the heat equation and solves; 7 Knows of separation of variables method and the heat, wave and Laplace equation applies;

22	Course Content:

Week	Theoretical	Practical
1	The classification of the second order partial differantial equation with two independent variables
2	Homogeneous and inhomogeneous initial value problem for the wave equation
3	The Cauchy problem for general hyperbolic equations, Green's identity
4	Riemann's method, the symmetric of Rieman function
5	the general solution to Laplace's equation, Green's identities, the fundamental solution, boundary value problems
6	The solution of the Interior Dirichlet problem, some properties of Green's functions for the Green's function and Green's function for some regions
7	Poisson's formula and the results
8	Repeating courses and midterm exam
9	The solution of the Interior Neumann problem, and Neumann functions
10	Initial value problem for heat equation
11	Initial and boundary value problem for heat equation
12	the method of separation of variables , Fourier series expansion
13	Application of heat and wave equation
14	Application of the Laplace equation

23	Textbooks, References and/or Other Materials:	Prof.Dr. Mehmet ÇAĞLIYAN, Okay Çelebi Kısmi Diferensiyel Denklemler, Vipaş Bursa 2002.
24	Assesment

TERM LEARNING ACTIVITIES	NUMBER	PERCENT
Midterm Exam	1	40
Quiz	0	0
Homeworks, Performances	0	0
Final Exam	1	60
Total	2	100
Contribution of Term (Year) Learning Activities to Success Grade		40
Contribution of Final Exam to Success Grade		60
Total		100
Measurement and Evaluation Techniques Used in the Course
Information

25

ECTS / WORK LOAD TABLE

Activites	NUMBER	TIME [Hour]	Total WorkLoad [Hour]
Theoretical	14	3	42
Practicals/Labs	0	0	0
Self Study and Preparation	14	3	42
Homeworks, Performances	0	10	40
Projects	0	0	0
Field Studies	0	0	0
Midtermexams	1	18	18
Others	1	14	14
Final Exams	1	20	20
Total WorkLoad			176
Total workload/ 30 hr			5,87
ECTS Credit of the Course			6

26	CONTRIBUTION OF LEARNING OUTCOMES TO PROGRAMME QUALIFICATIONS
PQ1 PQ2 PQ3 PQ4 PQ5 PQ6 PQ7 PQ8 PQ9 PQ10 LO1 4 4 0 5 0 0 4 0 4 0 LO2 4 4 0 4 0 0 0 0 0 0 LO3 4 4 0 4 0 0 0 0 0 0 LO4 4 4 0 4 0 0 0 0 0 0 LO5 4 4 0 4 0 0 0 0 0 0 LO6 4 4 0 4 0 0 0 0 0 0 LO7 4 4 0 4 0 0 0 0 0 0

LO: Learning Objectives

PQ: Program Qualifications

Contribution Level:

1 Very Low

2 Low

3 Medium

4 High

5 Very High