Course Name Code Semester T+U Hours Credit ECTS
Boundary Value Problems MAT 554 0 3 + 0 3 6
 Precondition Courses ADVANCED DIFFERENTIAL EQUATIONS I, II Recommended Optional Courses Course Language Turkish Course Level yuksek_lisans Course Type Optional Course Coordinator Doç.Dr. YALÇIN YILMAZ Course Lecturers Doç.Dr. YALÇIN YILMAZ, Course Assistants Course Category Course Objective Comprehension of mathematical models of phsyical systems, Introduction of mathematical essences of problems arising in some engineering branches. Course Content Mathematical models of phsyical systems, general solution methods, Classification of PDE’s, Green function, Systems of eigenfunction, Sturm-Liouville Problems, Energy Methods, Lyapunov’s Direct Method, Continuous Dependence of Solutions .
# Course Learning Outcomes Teaching Methods Assessment Methods
1 He/She develops mathematical models of the physical systems to obtain general solution methods. Lecture, Drilland Practice, Problem Solving, Testing, Homework,
2 He/She solves encountered boundary value problems by separation of variables. Problem Solving, Lecture, Drilland Practice, Testing, Homework,
3 He/She finds eigenvalues and eigenfunctions of the given boundary value problems. Lecture, Drilland Practice, Problem Solving, Testing, Homework,
4 He/She obtains Green function of the given boundary value problems. Lecture, Drilland Practice, Problem Solving, Testing, Homework,
5 He/She restates existence of solutions of the given Sturm-Liouville Problem. Lecture, Drilland Practice, Problem Solving, Testing, Homework,
6 He/She identifies continous dependence of the solutions of the given boundary value problem. Lecture, Drilland Practice, Problem Solving, Testing, Homework,
Week Course Topics Preliminary Preparation
1 Mathematical models of phsyical systems
2 Classification of PDE’s
3 general solution methods
4 Eigenfunction Problems
5 Regular Sturm-Liouville equations
6 Solution by Eigenfunction expansion
7 Green’s Functions
8 Singular Sturm-Liouville Boundary Value Problems
9 Midterm exam
10 Ossilation and Comparison Theory
11 Energy Methods
12 Lyapunov’s Direct Method
13 Lyapunov Stability
14 Continuous Dependence of Solutions
Resources
Course Notes
Course Resources
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. 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.
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. 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. Ara Sınav 100
Total 100
1. Yıl İçinin Başarıya 50
1. Final 50
Total 100