Course Name Code Semester T+U Hours Credit ECTS
Numerical Methods For Differential Equations MAT 565 0 3 + 0 3 6
 Precondition Courses Recommended Optional Courses Course Language Turkish Course Level yuksek_lisans Course Type Optional Course Coordinator Doç.Dr. MUSTAFA ERÖZ Course Lecturers Course Assistants Course Category Course Objective Since most problems arise in applied mathematics and engineering have no analytical solutions, the theory of numerical solutions of these problems is investigated. The complexity of these equations which represent the natural phenomenon bring us to study the approximate solutions. Course Content Existence and uniqueness of the solutoin of differential equations, Tayloer series method, Runge-Kutta methods, Multistep methods, System of equations, Boundary-value problems, Shooting methods, Finite difference methods, Collocation, Linear differential equations, Stiff equations, Introduction to numerical solution of partial differential equations.
# Course Learning Outcomes Teaching Methods Assessment Methods
1 Students will have explained the need of a numerical solution of a differential equation. Lecture, Question-Answer, Drilland Practice, Testing, Homework,
2 Students will have constructed the numerical solutions of differential equations Lecture, Question-Answer, Drilland Practice, Testing, Homework,
3 Students will have constructed the numerical solutions of differential equations of higher order and systems. Lecture, Question-Answer, Drilland Practice, Testing, Homework,
4 Students will have composed an alghorithm for the numerical solutions of DEs. Lecture, Question-Answer, Drilland Practice, Testing, Homework,
5 Students will have demonstrated how to reach more accurate numerical solutions. Lecture, Question-Answer, Drilland Practice, Testing, Homework,
6 Students will have summarized the numerical solutions of PDEs. Lecture, Question-Answer, Drilland Practice, Testing, Homework,
Week Course Topics Preliminary Preparation
1 The existence and the uniquness of the solutions of differential equations
2 Taylor series method
3 Runge-Kutta methods
4 Multistep methods
5 Equations and systems of higher order
6 Boundary value problems
7 Shooting methods
8 Finite difference method
9 Collocation
10 Linear differential equations
11 Stiff equations
12 Introduction to numerical solution of PDEs
13 Parabolic equations: Explicit and implicit methods
14 Finite difference method for PDEs
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
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. Ara Sınav 50
1. Ödev 50
Total 100
1. Yıl İçinin Başarıya 50
1. Final 50
Total 100