COURSE SYLLABUS
PARTIAL DIFFERENTIAL EQUATIONS II
| 1 |
Course Title: |
PARTIAL DIFFERENTIAL EQUATIONS II |
| 2 |
Course Code: |
MAT5412 |
| 3 |
Type of Course: |
Optional |
| 4 |
Level of Course: |
Third 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: |
Doç. Dr. Emrullah Yaşar,
Yrd. Doç. Dr. Setenay Doğan
Yrd. Doç. Dr. Nisa Çelik |
| 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: |
To provide the necessary infrastructure to do research in high level in partial differential equations |
| 20 |
Contribution of the Course to Professional Development |
Gaining analytical thinking skills and providing the necessary background in applied mathematics |
| 21 |
Learning Outcomes: |
| 1 |
Knows Laplace, heat and wave equations and the boundary value, initial value, initial-boundary value problems defined for these equations.;
|
| 2 |
Knows the method of spherical means, Hadamard Descend method and Duhamel Principle;
|
| 3 |
knows existence and uniqueness theorems;
|
|
| Week |
Theoretical |
Practical |
| 1 |
The solution of Laplace's equation, Green's identities |
|
| 2 |
Some properties of harmonic functions, the fundamental solution |
|
| 3 |
Types of boundary-value problems. |
|
| 4 |
Solution of interior Dirichlet problem. Green's function. |
|
| 5 |
the solution of interior Neumann problem. Neumann function. |
|
| 6 |
Poisson's integral formula and the results. |
|
| 7 |
Initial value problem for the wave equation. |
|
| 8 |
the method of spherical means. |
|
| 9 |
Hadamard Descend method. |
|
| 10 |
Duhamel Principle. |
|
| 11 |
Initial value problem for heat equation. |
|
| 12 |
Initial-boundary value problem for heat equation. |
|
| 13 |
Maximum and minimum principle. |
|
| 14 |
Existence and uniqueness theorems. |
|
| 23 |
Textbooks, References and/or Other Materials: |
1. M. Çağlıyan, Okay Çelebi, Kısmi Diferensiyel Denklemler, Vipaş, 2002.
2. İbrahim Ethem Anar, Kısmi diferensiyel denklemler, Palme Yayıncılık, 2005.
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| 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
|
0
|
0
|
3
|
0
|
4
|
0
|
0
|
0
|
4
|
4
|
|
LO2
|
0
|
0
|
3
|
0
|
3
|
0
|
0
|
0
|
5
|
4
|
|
LO3
|
0
|
0
|
3
|
0
|
4
|
0
|
0
|
0
|
4
|
4
|
|
| LO: Learning Objectives |
PQ: Program Qualifications |
| Contribution Level: |
1 Very Low |
2 Low |
3 Medium |
4 High |
5 Very High |
