Course Name Code Semester T+U Hours Credit ECTS
Adnanced Differential Equations II MAT 557 0 3 + 0 3 6
Precondition Courses <p>No.</p>
Recommended Optional Courses <p>No.</p>
Course Language Turkish
Course Level yuksek_lisans
Course Type Optional
Course Coordinator Prof.Dr. ŞEVKET GÜR
Course Lecturers Prof.Dr. ŞEVKET GÜR,
Course Assistants
Course Category Field Proper Education
Course Objective

To provide advanced information about the theory of linear and nonlinear equations.

Course Content

Lipschitz continuity, The Existence and uniqueness theorem, The Green function, Elemantary inequalities,.

# Course Learning Outcomes Teaching Methods Assessment Methods
1 He/She Learns the concept of Lipschitz continuity. Lecture, Question-Answer, Drilland Practice, Problem Solving, Testing, Homework, Performance Task,
2 He/She Solves the equation using Picard´s method. Lecture, Question-Answer, Drilland Practice, Problem Solving, Testing, Homework, Performance Task,
3 He/She Learns the existence and uniqueness theorem. Lecture, Question-Answer, Drilland Practice, Problem Solving, Testing, Homework, Performance Task,
4 He/She Recognizes the boundary value problems. Lecture, Question-Answer, Drilland Practice, Problem Solving, Testing, Homework, Performance Task,
5 He/She Learns the Green´s function. Lecture, Question-Answer, Drilland Practice, Problem Solving, Testing, Homework, Performance Task,
6 He/She Recognizes and implements elemantary inequalities Lecture, Question-Answer, Drilland Practice, Problem Solving, Testing, Homework, Performance Task,
Week Course Topics Preliminary Preparation
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)
Resources
Course Notes <p>[1] Differential Equations, Shepley L. Ross.</p>
Course Resources

[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.

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
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
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 30 30
Assignment 1 25 25
Final examination 1 10 10
Total Workload 161
Total Workload / 25 (Hours) 6.44
dersAKTSKredisi 6