Ders Adı | Kodu | Yarıyıl | T+U Saat | Kredi | AKTS |
---|---|---|---|---|---|
Numerical Methods For Differential Equations | MAT 565 | 0 | 3 + 0 | 3 | 6 |
Ön Koşul Dersleri | |
Önerilen Seçmeli Dersler | |
Dersin Dili | Türkçe |
Dersin Seviyesi | YUKSEK_LISANS |
Dersin Türü | Seçmeli |
Dersin Koordinatörü | Prof.Dr. MUSTAFA ERÖZ |
Dersi Verenler | Prof.Dr. MUSTAFA ERÖZ, |
Dersin Yardımcıları | |
Dersin Kategorisi | Diğer |
Dersin Amacı | Since most problems arise in applied mathematics and engineering have no analytical solutions, the theory of numerical solutions of these problems is investigated. The complexity of these equations which represent the natural phenomenon bring us to study the approximate solutions. |
Dersin İçeriği | Existence and uniqueness of the solutoin of differential equations, Tayloer series method, Runge-Kutta methods, Multistep methods, System of equations, Boundary-value problems, Shooting methods, Finite difference methods, Collocation, Linear differential equations, Stiff equations, Introduction to numerical solution of partial differential equations. |
# | Ders Öğrenme Çıktıları | Öğretim Yöntemleri | Ölçme Yöntemleri |
---|---|---|---|
1 | Students will have explained the need of a numerical solution of a differential equation. | Lecture, Question-Answer, Drilland Practice, | Testing, Homework, |
2 | Students will have constructed the numerical solutions of differential equations | Lecture, Question-Answer, Drilland Practice, | Testing, Homework, |
3 | Students will have constructed the numerical solutions of differential equations of higher order and systems. | Lecture, Question-Answer, Drilland Practice, | Testing, Homework, |
4 | Students will have composed an alghorithm for the numerical solutions of DEs. | Lecture, Question-Answer, Drilland Practice, | Testing, Homework, |
5 | Students will have demonstrated how to reach more accurate numerical solutions. | Lecture, Question-Answer, Drilland Practice, | Testing, Homework, |
6 | Students will have summarized the numerical solutions of PDEs. | Lecture, Question-Answer, Drilland Practice, | Testing, Homework, |
Hafta | Ders Konuları | Ön Hazırlık |
---|---|---|
1 | The existence and the uniquness of the solutions of differential equations | |
2 | Taylor series method | |
3 | Runge-Kutta methods | |
4 | Multistep methods | |
5 | Equations and systems of higher order | |
6 | Boundary value problems | |
7 | Shooting methods | |
8 | Finite difference method | |
9 | Collocation | |
10 | Linear differential equations | |
11 | Stiff equations | |
12 | Introduction to numerical solution of PDEs | |
13 | Parabolic equations: Explicit and implicit methods | |
14 | Finite difference method for PDEs |
Kaynaklar | |
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Ders Notu | |
Ders Kaynakları |
Sıra | Program Çıktıları | Katkı Düzeyi | |||||
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1 | 2 | 3 | 4 | 5 | |||
0 | Develop strategic, political and practice plans and evaluate the results by taking into account the quality process in his/her area of expertise | ||||||
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 | |||||
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 | |||||
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 | |||||
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 | |||||
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 | |
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Yarıyıl Çalışmaları | Katkı Oranı |
1. Ara Sınav | 50 |
1. Ödev | 50 |
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 | 20 | 20 |
Final examination | 1 | 20 | 20 |
Toplam İş Yükü | 156 | ||
Toplam İş Yükü / 25 (Saat) | 6,24 | ||
Dersin AKTS Kredisi | 6 |