Ders Bilgileri

#### Ders Tanımı

Ders Kodu Yarıyıl T+U Saat Kredi AKTS
ADNANCED DIFFERENTIAL EQUATIONS II MAT 557 0 3 + 0 3 6
Ön Koşul Dersleri No. No.
 Dersin Dili Türkçe Dersin Seviyesi Yüksek Lisans Dersin Türü SECMELI Dersin Koordinatörü Prof.Dr. ŞEVKET GÜR Dersi Verenler Dersin Yardımcıları Dersin Kategorisi Alanına Uygun Öğretim Dersin Amacı To provide advanced information about the theory of linear and nonlinear equations. Dersin İçeriği Lipschitz continuity, The Existence and uniqueness theorem, The Green function, Elemantary inequalities,.
 Dersin Öğrenme Çıktıları Öğretim Yöntemleri Ölçme Yöntemleri 1 - He/She Learns the concept of Lipschitz continuity. 1 - 2 - 4 - 15 - A - C - F - 2 - He/She Solves the equation using Picard´s method. 1 - 2 - 4 - 15 - A - C - F - 3 - He/She Learns the existence and uniqueness theorem. 1 - 2 - 4 - 15 - A - C - F - 4 - He/She Recognizes the boundary value problems. 1 - 2 - 4 - 15 - A - C - F - 5 - He/She Learns the Green´s function. 1 - 2 - 4 - 15 - A - C - F - 6 - He/She Recognizes and implements elemantary inequalities 1 - 2 - 4 - 15 - A - C - F -
 Öğretim Yöntemleri: 1:Lecture 2:Question-Answer 4:Drilland Practice 15:Problem Solving Ölçme Yöntemleri: A:Testing C:Homework F:Performance Task

#### Ders Akışı

Hafta Konular ÖnHazırlık
1 Lipschitz continuity.
2 Lipschitz continuity.
3 The method of successive approximations.
4 The Existence and uniqueness theorem
5 The Existence and uniqueness theorem
6 Boundary value problems.
7 Boundary value problems.
8 The Green Functions.
9 Midterm.
10 The Green Functions.
11 Elemantary Inequalities (Cauchy, Young)
12 Elemantary Inequalities (Hölder, Minkowski)
13 Elemantary Inequalities (Gronwall (differential and İntegral form))
14 Elemantary Inequalities (İnterpolation)

#### Kaynaklar

Ders Notu

[1] Differential Equations, Shepley L. Ross.

Ders Kaynakları

[2] Solutions of Partial Dif. Equations,Dean G. Duffy
[3] Elemantary Differential Equations, Rainville P.
[4] Adi diferansiyel denklemler, Prof.Dr.Mehmet Çağlıyan, Y.Doç.Dr.Nisa Çelik, Y.Doç.Dr.Setenay Doğan, Dora yayınları.

#### Dersin Program Çıktılarına Katkısı

No Program Öğrenme Çıktıları KatkıDüzeyi
1 2 3 4 5
1 Develop strategic, political and practice plans and evaluate the results by taking into account the quality process in his/her area of expertise 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
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

YARIYIL İÇİ ÇALIŞMALARI SIRA KATKI YÜZDESİ
AraSinav 1 75
Odev 1 25
Toplam 100
Yıliçinin Başarıya Oranı 50
Finalin Başarıya Oranı 50
Toplam 100

#### AKTS - İş Yükü

Etkinlik Sayısı Süresi(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 30 30
Assignment 1 25 25
Final examination 1 10 10
Toplam İş Yükü 161
Toplam İş Yükü /25(s) 6.44
Dersin AKTS Kredisi 6.44
; ;