Elliptic partial differential equations provide the necessary infrastructure to do advanced research
20
Contribution of the Course to Professional Development
Gaining analytical thinking skills and providing the necessary background in applied mathematics
21
Learning Outcomes:
1
know Singularities functions, the fundamental solution and represent formulas;
2
knows Green's function .;
3
Knows the properties of maximum, minimum, and mean value;
4
Dirichlet problem and knows the existence and uniqueness theorem;
22
Course Content:
Week
Theoretical
Practical
1
Preliminaries (classification of two-variable equations (elliptic, parabolic and hyperbolic types), harmonic functions of two variables, the fundamental solution and representations obtained with the help of the fundamental solution, the mean value, maximum, minimum principle), the Dirichlet problem for a circle
2
Classification of second order equations with n independent variables and the necessity of classification
3
n-dimensional Laplace equation and Green's identities
4
Singularities functions, fundamental solution, formulas representing
5
Dirichlet problem in hypersphere , existence and uniqueness theorem
6
Green function, Poisson's formula and the results
7
mean value, and Maximum, minimum properties
8
the mean value properties for equation ?_3 u+k^2 u=f
9
Dirichlet problem for the more generally the regions and the existence and uniqueness theorem
10
Conformal transformation method
11
Integral equation method
12
Finite difference method
13
Dirichlet principle
14
Sub-harmonic functions
23
Textbooks, References and/or Other Materials:
M. Çağlıyan, Okay Çelebi, Kısmi Diferensiyel Denklemler, Vipaş, 2002.
24
Assesment
TERM LEARNING ACTIVITIES
NUMBER
PERCENT
Midterm Exam
0
0
Quiz
0
0
Homeworks, Performances
0
0
Final Exam
1
100
Total
1
100
Contribution of Term (Year) Learning Activities to Success Grade
0
Contribution of Final Exam to Success Grade
100
Total
100
Measurement and Evaluation Techniques Used in the Course
Success is evaluated with 1 YYSS in accordance with the content of 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
7
98
Homeworks, Performances
0
5
20
Projects
0
0
0
Field Studies
0
0
0
Midtermexams
0
0
0
Others
0
0
0
Final Exams
1
20
20
Total WorkLoad
180
Total workload/ 30 hr
6
ECTS Credit of the Course
6
26
CONTRIBUTION OF LEARNING OUTCOMES TO PROGRAMME QUALIFICATIONS
