Course Name Code Semester T+U Hours Credit ECTS
Adnanced Differential Equations I MAT 546 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

Theory of Linear Differential Equations, Higher order Nonlinear Differential Equations.

# Course Learning Outcomes Teaching Methods Assessment Methods
1 He/She Recognizes the differential operators. Lecture, Question-Answer, Drilland Practice, Problem Solving, Testing, Homework, Performance Task,
2 He/She Know the basic theorems of linear differential equations. Lecture, Question-Answer, Drilland Practice, Problem Solving, Testing, Homework, Performance Task,
3 He/She Knows homogeneous differential equations. Lecture, Question-Answer, Drilland Practice, Problem Solving, Testing, Homework, Performance Task,
4 He/She Knows nonhomogeneous differential equations. Lecture, Question-Answer, Drilland Practice, Problem Solving, Testing, Homework, Performance Task,
5 He/She Learns definitions of Adjoint and self adjoint operators. Lecture, Question-Answer, Drilland Practice, Problem Solving, Testing, Homework, Performance Task,
6 He/She Recognizes the non-linear equations. Lecture, Question-Answer, Drilland Practice, Problem Solving, Testing, Homework, Performance Task,
7 He/She Knows the methods of solution of nonlinear equations. Lecture, Discussion, Drilland Practice, Problem Solving, Testing, Homework, Performance Task,
Week Course Topics Preliminary Preparation
1 Basic definitions and concepts.
2 Basic definitions and concepts.
3 Differential operator.
4 Basic theory of linear differential equations.
5 Algebra of linear differential operators.
6 Algebra of linear differential operators.
7 Basic theorems about solutions of linear differential equations.
8 Basic theorems about solutions of linear differential equations.
9 Midterm.
10 Further properties homogeneous linear differential equation.
11 Further properties homogeneous linear differential equation.
12 Methods of solution of nonlinear equations.
13 Methods of solution of nonlinear equations.
14 Methods of solution of nonlinear equations.
Resources
Course Notes <p>[1] Differential Equations, Shepley L. Ross</p>
Course Resources

[2] 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
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. X
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.
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
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.
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.
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.
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. Ara Sınav 75
1. Ödev 25
Total 100
1. Yıl İçinin Başarıya 50
1. Final 50
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