| Ders Adı | Kodu | Yarıyıl | T+U Saat | Kredi | AKTS |
|---|---|---|---|---|---|
| Nonlınear Partıal Dıfferantıal Equatıons | MAT 623 | 0 | 3 + 0 | 3 | 6 |
| Ön Koşul Dersleri | Recommended course of undergraduate education has received partial differential equations. |
| Önerilen Seçmeli Dersler | |
| Dersin Dili | Türkçe |
| Dersin Seviyesi | Doktora |
| Dersin Türü | Seçmeli |
| Dersin Koordinatörü | Prof.Dr. ÖMER FARUK GÖZÜKIZIL |
| Dersi Verenler | |
| Dersin Yardımcıları | |
| Dersin Kategorisi | Diğer |
| Dersin Amacı | It is useful for graduate students in mathematics and engeneering. |
| Dersin İçeriği | Adomian Decomposition Method , Solution of Nonlinear PDEs by Adomian Method, Solution of Nonlinear PDEs Systems by Adomian Method. Linear and Nonlinear Physical Models. The Goursat Problem. The Telegraph Equation .Schrodinger Equation. Fourth-order Parabolic Equation. The Pad´e Approximants. Solitons and Compactons. |
| # | Ders Öğrenme Çıktıları | Öğretim Yöntemleri | Ölçme Yöntemleri |
|---|---|---|---|
| 1 | To learn the details of partial differential equations. | Lecture, Question-Answer, Discussion, Drilland Practice, Motivations to Show, Group Study, Self Study, Problem Solving, | Testing, Homework, Performance Task, |
| 2 | To recognize the non-linear partial differential equations. | Lecture, Question-Answer, Discussion, Drilland Practice, Motivations to Show, Group Study, Self Study, Problem Solving, | Testing, Homework, Performance Task, |
| 3 | To learn methods of solution of nonlinear partial differential equations. | Lecture, Question-Answer, Discussion, Drilland Practice, Motivations to Show, Group Study, Self Study, Problem Solving, | Testing, Homework, Performance Task, |
| 4 | To learn the methods of numerical solution of nonlinear partial differential equations. | Lecture, Question-Answer, Discussion, Drilland Practice, Motivations to Show, Group Study, Self Study, Problem Solving, | Testing, Homework, Performance Task, |
| 5 | To learn to linear and nonlinear physical models. | Lecture, Question-Answer, Discussion, Drilland Practice, Motivations to Show, Group Study, Self Study, Problem Solving, | Testing, Homework, Performance Task, |
| 6 | To solve to the Goursat problem, telegraph equation and the Schrodinger equation. | Lecture, Question-Answer, Discussion, Drilland Practice, Motivations to Show, Group Study, Self Study, Problem Solving, | Testing, Homework, Performance Task, |
| Hafta | Ders Konuları | Ön Hazırlık |
|---|---|---|
| 1 | Adomian decomposition method. | |
| 2 | Solution of nonlinear partial differential equations by using adomian method. | |
| 3 | Solution of nonlinear partial differential equations by using adomian method. | |
| 4 | Linear and Nonlinear Physical Models. | |
| 5 | The Goursat Problem. | |
| 6 | The Telegraph Equation. | |
| 7 | Schrodinger Equation. | |
| 8 | Fourth-order Parabolic Equation. | |
| 9 | Midterm | |
| 10 | The Pad´e Approximants. | |
| 11 | The Pad´e Approximants. | |
| 12 | Solitons | |
| 13 | Solitons | |
| 14 | Compactons |
| Kaynaklar | |
|---|---|
| Ders Notu | |
| Ders Kaynakları | 1.Nonlinear Partial Differential Equations for Scientist and Engineers,Debnath L., Boston , 1997. |
| Sıra | Program Çıktıları | Katkı Düzeyi | |||||
|---|---|---|---|---|---|---|---|
| 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 | ||||||
| 1 | At a master´s degree level, student reaches new knowledge via scientific researches, the use of knowledge of the same field as him/her or of different field from him/her, and the use of knowledge based on the competence in his/her field; s/he interprets the knowledge and prospects for the fields of application. | X | |||||
| 2 | Student completes the missing or limited knowledge by using the scientific methods. | X | |||||
| 3 | Student freely poses a problem of his/her field, develops a solution method, solves the problem, and evaluates the result. | X | |||||
| 4 | Student conveys, orally or in writing, his/her studies or the current developments in his/her field to the people in or out of his/her field. | X | |||||
| 5 | Student finds a solution to the unforeseen complex problems in his/her studies by developing new approaches. | X | |||||
| 6 | At a doctorate degree level, student prepares at least one scientific article of his/her field to be published in an international indexed journal, and s/he extends its popularity. | X | |||||
| 7 | Student analyzes the works that have been published before, approaches the same subjects with different proof methods, or determines the open problems about the current subject matters. | X | |||||
| 8 | Student looks for the scientists studying on the same field as him/her, and s/he gets in touch with them for a collaborative work. | X | |||||
| 9 | Student knows enough foreign language to do a collaborative work with the scientists studying on the same field as him/her abroad. | X | |||||
| 10 | Student follows the necessary technological developments in his/her field, and s/he uses them. | X | |||||
| 11 | Student looks out for the scientific and ethic values while gathering, interpreting and publishing data. | X | |||||
| Değerlendirme Sistemi | |
|---|---|
| Yarıyıl Çalışmaları | Katkı Oranı |
| 1. Ara Sınav | 60 |
| 1. Kısa Sınav | 20 |
| 1. Ödev | 20 |
| 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 |
| Quiz | 1 | 10 | 10 |
| Assignment | 1 | 10 | 10 |
| Final examination | 1 | 15 | 15 |
| Toplam İş Yükü | 151 | ||
| Toplam İş Yükü / 25 (Saat) | 6,04 | ||
| Dersin AKTS Kredisi | 6 | ||