Ders Adı Kodu Yarıyıl T+U Saat Kredi AKTS
Introductıon To Inverse Problems MAT 535 0 3 + 0 3 6
Ön Koşul Dersleri Partial differential equations
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 Research assistants
Dersin Kategorisi Diğer
Dersin Amacı To introduce and analyze the inverse problems arise in the applied sciences.
Dersin İçeriği Introduction, examples of some inverse problems, ill-posed problems, uniqueness and stability problems, inverse problems for parabolic equations, inverse problems for hyperbolic equations
# Ders Öğrenme Çıktıları Öğretim Yöntemleri Ölçme Yöntemleri
1 He/She defines the inverse problems. Lecture, Drilland Practice, Self Study, Problem Solving, Testing, Homework, Performance Task,
2 He/She has information about ill-posed problems. Lecture, Drilland Practice, Self Study, Problem Solving, Testing, Homework, Performance Task,
3 He/She learns some methods to solve the inverse problems . Lecture, Drilland Practice, Self Study, Problem Solving, Testing, Homework, Performance Task,
4 He/She has knowledge about stability and uniquesness of problem. Lecture, Drilland Practice, Self Study, Problem Solving, Testing, Homework, Performance Task,
5 He/She develops a method for solving parabolic equation. Lecture, Drilland Practice, Self Study, Problem Solving, Testing, Homework, Performance Task,
6 He/She develops a method for solving hyperbolic equation. Lecture, Drilland Practice, Self Study, Problem Solving, Testing, Homework, Performance Task,
7 He/ she applies this methods to some problems. Lecture, Drilland Practice, Self Study, Problem Solving, Testing, Homework, Performance Task,
Hafta Ders Konuları Ön Hazırlık
1 Fundamental concepts
2 What is the inverse problem, examples
3 Ill-posed problems
4 Existence-uniqueness
5 Stability problems
6 Stability problems
7 Inverse problems for parabolic equations
8 Inverse problems for parabolic equations
9 Inverse problems for parabolic equations
10 Midterm
11 Inverse problems for hyperbolic equations
12 Inverse problems for hyperbolic equations
13 Inverse problems for hyperbolic equations
14 Some applications
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. 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.
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. 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.
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 70
1. Ödev 30
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