Course Name Code Semester T+U Hours Credit ECTS
Qualitative Theory Of Differantial Equations MAT 624 0 3 + 0 3 6
Precondition Courses <p>No.</p>
Recommended Optional Courses <p>No.</p>
Course Language Turkish
Course Level Doctorate Degree
Course Type Optional
Course Coordinator Prof.Dr. ŞEVKET GÜR
Course Lecturers Prof.Dr. ŞEVKET GÜR,
Course Assistants
Course Category Field Proper Education
Course Objective

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.

Course Content

Classical İnequalities, Stationary points, Liapunov Stability,
Long Time Behavior of the Solutions, Continuous Dependence of the Solutions

# Course Learning Outcomes Teaching Methods Assessment Methods
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,
Week Course Topics Preliminary Preparation
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
Resources
Course Notes <p>[1] Asymptotic Behavior of Dissipative Systems, Jack K. Hale, American Mathematical Society,1988.<br /> [2] Topics in Functional Analysis and Applications, S.Kesevan, John Wiley, 1989.<br /> [3] Exact Controllability and Stabilization, V.Komornik, John Wiley, 1994</p>
Course Resources

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

Order Program Outcomes Level of Contribution
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
Evaluation System
Semester Studies Contribution Rate
1. Ödev 100
Total 100
1. Yıl İçinin Başarıya 40
1. Final 60
Total 100
ECTS - Workload Activity Quantity Time (Hours) Total Workload (Hours)
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
Total Workload 141
Total Workload / 25 (Hours) 5.64
dersAKTSKredisi 6