| Ders Adı | Kodu | Yarıyıl | T+U Saat | Kredi | AKTS |
|---|---|---|---|---|---|
| Qualıtatıve Theory Of Dıfferantıal Equatıons | MAT 624 | 0 | 3 + 0 | 3 | 6 |
| Ön Koşul Dersleri | No. |
| Önerilen Seçmeli Dersler | No. |
| Dersin Dili | Türkçe |
| Dersin Seviyesi | Doktora |
| Dersin Türü | Seçmeli |
| Dersin Koordinatörü | Prof.Dr. ŞEVKET GÜR |
| Dersi Verenler | Prof.Dr. ŞEVKET GÜR, |
| Dersin Yardımcıları | |
| Dersin Kategorisi | Alanına Uygun Öğretim |
| Dersin Amacı | It is always not possible to find solutions of differential equations.It is important to have knowledge about the behavior of solutions without solving a differential equation. So it is important to be taught in this course. |
| Dersin İçeriği | Classical İnequalities, Stationary points, Liapunov Stability, |
| # | Ders Öğrenme Çıktıları | Öğretim Yöntemleri | Ölçme Yöntemleri |
|---|---|---|---|
| 1 | He/She Knows the classical inequalities. | Lecture, Question-Answer, Drilland Practice, Problem Solving, | Testing, Homework, Performance Task, |
| 2 | He/She Knows Sobolev spaces. | Lecture, Question-Answer, Drilland Practice, Problem Solving, | Testing, Homework, Performance Task, |
| 3 | He/She Learns the concept of stability. | Lecture, Question-Answer, Drilland Practice, Problem Solving, | Testing, Homework, Performance Task, |
| 4 | He/She Examine the long time behavior of solutions. | Lecture, Question-Answer, Drilland Practice, Problem Solving, | Testing, Homework, Performance Task, |
| 5 | He/She Examine the continuous dependence of solutions. | Lecture, Question-Answer, Drilland Practice, Problem Solving, | Testing, Homework, Performance Task, |
| Hafta | Ders Konuları | Ön Hazırlık |
|---|---|---|
| 1 | Basic Concepts of Stability Theory | |
| 2 | Basic Concepts of Stability Theory | |
| 3 | Sobolev Space ( Definition and Basic Properties ) | |
| 4 | Sobolev Space ( Embedding Theorems ) | |
| 5 | Liapunov stability | |
| 6 | Liapunov stability | |
| 7 | Long Time Behavior of Nonlinear Hyperbolic Equations | |
| 8 | Long Time Behavior of Nonlinear Hyperbolic Equations | |
| 9 | Midterm | |
| 10 | Structural Stability for Nonlinear Wave Equations | |
| 11 | Structural Stability for Nonlinear Wave Equations | |
| 12 | Continuous Dependence of Solutions for Nonlinear Equations | |
| 13 | Continuous Dependence of Solutions for Nonlinear Equations | |
| 14 | Continuous Dependence of Solutions for Nonlinear Equations |
| Kaynaklar | |
|---|---|
| Ders Notu | [1] Asymptotic Behavior of Dissipative Systems, Jack K. Hale, American Mathematical Society,1988. |
| Ders Kaynakları | [4] Diferansiyel Denklemler Teorisi, Prof.Dr.Elman Hasanov, Prof.Dr.Gökhan Uzgören, Prof.Dr.Alinur Büyükaksoy, Papatya Yayıncılık, Mart 2002. |
| 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 | X | |||||
| 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. | ||||||
| 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. Ödev | 100 |
| Toplam | 100 |
| 1. Yıl İçinin Başarıya | 40 |
| 1. Final | 60 |
| 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 | 15 | 15 |
| Assignment | 1 | 15 | 15 |
| Final examination | 1 | 15 | 15 |
| Toplam İş Yükü | 141 | ||
| Toplam İş Yükü / 25 (Saat) | 5,64 | ||
| Dersin AKTS Kredisi | 6 | ||