Ders Adı | Kodu | Yarıyıl | T+U Saat | Kredi | AKTS |
---|---|---|---|---|---|
Boundary Value Problems | MAT 554 | 0 | 3 + 0 | 3 | 6 |
Ön Koşul Dersleri | ADVANCED DIFFERENTIAL EQUATIONS I, II |
Önerilen Seçmeli Dersler | |
Dersin Dili | Türkçe |
Dersin Seviyesi | YUKSEK_LISANS |
Dersin Türü | Seçmeli |
Dersin Koordinatörü | Doç.Dr. YALÇIN YILMAZ |
Dersi Verenler | Doç.Dr. YALÇIN YILMAZ, |
Dersin Yardımcıları | |
Dersin Kategorisi | Diğer |
Dersin Amacı | Comprehension of mathematical models of phsyical systems, Introduction of mathematical essences of problems arising in some engineering branches. |
Dersin İçeriği | Mathematical models of phsyical systems, general solution methods, Classification of PDE’s, Green function, Systems of eigenfunction, Sturm-Liouville Problems, Energy Methods, Lyapunov’s Direct Method, Continuous Dependence of Solutions . |
# | Ders Öğrenme Çıktıları | Öğretim Yöntemleri | Ölçme Yöntemleri |
---|---|---|---|
1 | He/She develops mathematical models of the physical systems to obtain general solution methods. | Lecture, Drilland Practice, Problem Solving, | Testing, Homework, |
2 | He/She solves encountered boundary value problems by separation of variables. | Problem Solving, Lecture, Drilland Practice, | Testing, Homework, |
3 | He/She finds eigenvalues and eigenfunctions of the given boundary value problems. | Lecture, Drilland Practice, Problem Solving, | Testing, Homework, |
4 | He/She obtains Green function of the given boundary value problems. | Lecture, Drilland Practice, Problem Solving, | Testing, Homework, |
5 | He/She restates existence of solutions of the given Sturm-Liouville Problem. | Lecture, Drilland Practice, Problem Solving, | Testing, Homework, |
6 | He/She identifies continous dependence of the solutions of the given boundary value problem. | Lecture, Drilland Practice, Problem Solving, | Testing, Homework, |
Hafta | Ders Konuları | Ön Hazırlık |
---|---|---|
1 | Mathematical models of phsyical systems | |
2 | Classification of PDE’s | |
3 | general solution methods | |
4 | Eigenfunction Problems | |
5 | Regular Sturm-Liouville equations | |
6 | Solution by Eigenfunction expansion | |
7 | Green’s Functions | |
8 | Singular Sturm-Liouville Boundary Value Problems | |
9 | Midterm exam | |
10 | Ossilation and Comparison Theory | |
11 | Energy Methods | |
12 | Lyapunov’s Direct Method | |
13 | Lyapunov Stability | |
14 | Continuous Dependence of Solutions |
Kaynaklar | |
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Ders Notu | |
Ders Kaynakları |
Sıra | Program Çıktıları | Katkı Düzeyi | |||||
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1 | 2 | 3 | 4 | 5 | |||
2 | Student follows the current journals in his/her field and puts forward problems. | X | |||||
2 | Student follows the current journals in his/her field and puts forward problems. | X | |||||
3 | Student understands the relations between the disciplines pertaining to the undergraduate programs of Mathematics | X | |||||
3 | Student understands the relations between the disciplines pertaining to the undergraduate programs of Mathematics | X | |||||
4 | Student gets new knowledge by relating the already acquired experience and knowledge with the subject-matters out of his/her field. | X | |||||
4 | Student gets new knowledge by relating the already acquired experience and knowledge with the subject-matters out of his/her field. | X | |||||
5 | Student uses different proof methods to come to a solution by analyzing the problems encountered. | X | |||||
5 | Student uses different proof methods to come to a solution by analyzing the problems encountered. | X | |||||
6 | Student determines the problems to be solved within his/her field and if necessary takes the lead. | X | |||||
6 | Student determines the problems to be solved within his/her field and if necessary takes the lead. | X | |||||
7 | Student conveys, in team work, his/her knowledge in the studies done in different disciplines by applying the dynamics pertaining to his/her own field. | X | |||||
7 | Student conveys, in team work, his/her knowledge in the studies done in different disciplines by applying the dynamics pertaining to his/her own field. | ||||||
8 | Student critically evaluates the knowledge got at the bachelor´s degree level, makes up the missing knowledge and focuses on the current subject-matters | ||||||
8 | Student critically evaluates the knowledge got at the bachelor´s degree level, makes up the missing knowledge and focuses on the current subject-matters | X | |||||
9 | Student knows a foreign language to communicate orally and in writing and uses the foreign language in a way that he/she can have a command of the Maths terminology and can do a source research. | X | |||||
9 | Student knows a foreign language to communicate orally and in writing and uses the foreign language in a way that he/she can have a command of the Maths terminology and can do a source research. | ||||||
10 | Student improves himself/herself at a level of expertness in Mathematics or in the fields of application by improving the knowledge got at the bachelor´s degree level. | ||||||
10 | Student improves himself/herself at a level of expertness in Mathematics or in the fields of application by improving the knowledge got at the bachelor´s degree level. | X | |||||
10 | Student improves himself/herself at a level of expertness in Mathematics or in the fields of application by improving the knowledge got at the bachelor´s degree level. | X | |||||
11 | Student considers the scientific and cultural ethical values in the phases of gathering and conveying data or writing articles. | X |
Değerlendirme Sistemi | |
---|---|
Yarıyıl Çalışmaları | Katkı Oranı |
1. Ara Sınav | 100 |
Toplam | 100 |
1. Yıl İçinin Başarıya | 50 |
1. Final | 50 |
Toplam | 100 |
AKTS - İş Yükü Etkinlik | Sayı | Süre (Saat) | Toplam İş Yükü (Saat) |
---|---|---|---|
Course Duration (Including the exam week: 16x Total course hours) | 16 | 3 | 48 |
Hours for off-the-classroom study (Pre-study, practice) | 16 | 3 | 48 |
Mid-terms | 1 | 20 | 20 |
Assignment | 1 | 30 | 30 |
Final examination | 1 | 10 | 10 |
Toplam İş Yükü | 156 | ||
Toplam İş Yükü / 25 (Saat) | 6,24 | ||
Dersin AKTS Kredisi | 6 |