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COURSE SYLLABUS
ELLIPTIK PARTIAL DIFFERANTIAL EQUATIONS
1 Course Title: ELLIPTIK PARTIAL DIFFERANTIAL EQUATIONS
2 Course Code: MAT5414
3 Type of Course: Optional
4 Level of Course: Second Cycle
5 Year of Study: 1
6 Semester: 2
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
0(224)29 41765
18 Website:
19 Objective of the Course: 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
PQ1 PQ2 PQ3 PQ4 PQ5 PQ6 PQ7 PQ8 PQ9 PQ10
LO1 3 0 0 4 0 5 0 0 0 0
LO2 0 0 0 0 0 0 0 0 0 0
LO3 0 0 0 0 0 0 0 0 0 0
LO4 0 0 0 0 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
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