Ders Bilgileri

#### Ders Tanımı

Ders Kodu Yarıyıl T+U Saat Kredi AKTS
QUALITATIVE THEORY OF DIFFERANTIAL EQUATIONS MAT 624 0 3 + 0 3 6
Ön Koşul Dersleri No. No.
 Dersin Dili Türkçe Dersin Seviyesi Doktora Dersin Türü SECMELI Dersin Koordinatörü Prof.Dr. ŞEVKET GÜR Dersi Verenler 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, Long Time Behavior of the Solutions, Continuous Dependence of the Solutions
 Dersin Öğrenme Çıktıları Öğretim Yöntemleri Ölçme Yöntemleri 1 - He/She Knows the classical inequalities. 1 - 2 - 4 - 15 - A - C - F - 2 - He/She Knows Sobolev spaces. 1 - 2 - 4 - 15 - A - C - F - 3 - He/She Learns the concept of stability. 1 - 2 - 4 - 15 - A - C - F - 4 - He/She Examine the long time behavior of solutions. 1 - 2 - 4 - 15 - A - C - F - 5 - He/She Examine the continuous dependence of solutions. 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 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.
[2] Topics in Functional Analysis and Applications, S.Kesevan, John Wiley, 1989.
[3] Exact Controllability and Stabilization, V.Komornik, John Wiley, 1994

Ders Kaynakları

[4] Diferansiyel Denklemler Teorisi, Prof.Dr.Elman Hasanov, Prof.Dr.Gökhan Uzgören, Prof.Dr.Alinur Büyükaksoy, Papatya Yayıncılık, Mart 2002.
[5] Current Articles.

#### 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 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
3 Student completes the missing or limited knowledge by using the scientific methods. X
4 Student freely poses a problem of his/her field, develops a solution method, solves the problem, and evaluates the result. X
5 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
6 Student finds a solution to the unforeseen complex problems in his/her studies by developing new approaches. X
7 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.
8 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
9 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
10 Student knows enough foreign language to do a collaborative work with the scientists studying on the same field as him/her abroad. X
11 Student follows the necessary technological developments in his/her field, and s/he uses them. X
12 Student looks out for the scientific and ethic values while gathering, interpreting and publishing data. 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 15 15
Assignment 1 15 15
Final examination 1 15 15
Toplam İş Yükü 141
Toplam İş Yükü /25(s) 5.64
Dersin AKTS Kredisi 5.64
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