| Ders Adı | Kodu | Yarıyıl | T+U Saat | Kredi | AKTS |
|---|---|---|---|---|---|
| Introduction To Partial Differential Equation Theo | MAT 510 | 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. METİN YAMAN |
| Dersi Verenler | Prof.Dr. METİN YAMAN, |
| Dersin Yardımcıları | |
| Dersin Kategorisi | Alanına Uygun Öğretim |
| Dersin Amacı | It’s aiming to solve partial differential equations arising in engineering and science. |
| Dersin İçeriği | Sobolev spaces, sobolev inequality, fonction spaces, second order eliptik equations, second order evolution equations, |
| # | Ders Öğrenme Çıktıları | Öğretim Yöntemleri | Ölçme Yöntemleri |
|---|---|---|---|
| 1 | He/She recognizes sobolev spaces. | Lecture, Drilland Practice, Self Study, Problem Solving, | Testing, Homework, Performance Task, |
| 2 | He/She defines concept of weak derivative. | Lecture, Drilland Practice, Self Study, Problem Solving, | Testing, Homework, Performance Task, |
| 3 | He/She investigates existence of weak and classical solutions. | Lecture, Drilland Practice, Self Study, Problem Solving, | Testing, Homework, Performance Task, |
| 4 | He/She learns evolution equations. | Lecture, Drilland Practice, Self Study, Problem Solving, | Testing, Homework, Performance Task, |
| 5 | He/She comprehends parabolic and hyperbolic equations. | Lecture, Drilland Practice, Self Study, Problem Solving, | Testing, Homework, Performance Task, |
| 6 | He/She applies these to some examples. | Lecture, Drilland Practice, Self Study, Problem Solving, | Testing, Homework, Performance Task, |
| Hafta | Ders Konuları | Ön Hazırlık |
|---|---|---|
| 1 | Introduction to PDE | |
| 2 | Clasiccal solution, weak solution | |
| 3 | Sobolev spaces | |
| 4 | Sobolev inequalities | |
| 5 | Function spaces, spaces, spaces with time | |
| 6 | Second order eliptik equation | |
| 7 | Existence of weak solution, Lax-Milgram theorem | |
| 8 | Regularity, maximum principle | |
| 9 | Linear evolution equation | |
| 10 | Second order parabolic equation | |
| 11 | Midterm | |
| 12 | Weak solution and maximum principle | |
| 13 | Second order hyperbolic equation | |
| 14 | Existence of weak solution |
| Kaynaklar | |
|---|---|
| Ders Notu | |
| Ders Kaynakları | |
| Sıra | Program Çıktıları | Katkı Düzeyi | |||||
|---|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | |||
| 2 | Student follows the current journals in his/her field and puts forward problems. | ||||||
| 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. | ||||||
| 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. | 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 | |||||
| 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. | 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 | |||||
| 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. Ödev | 50 |
| 2. 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 | 10 | 10 |
| Assignment | 1 | 30 | 30 |
| Final examination | 1 | 10 | 10 |
| Toplam İş Yükü | 146 | ||
| Toplam İş Yükü / 25 (Saat) | 5,84 | ||
| Dersin AKTS Kredisi | 6 | ||