Course Name Code Semester T+U Hours Credit ECTS
Special Topics On Partial Differantial Equations MAT 566 0 3 + 0 3 6
 Precondition Courses

Students are assumed to be familiar with Ordinary differential equations and partial differential equations.

Recommended Optional Courses Course Language Turkish Course Level yuksek_lisans Course Type Optional Course Coordinator Prof.Dr. ÖMER FARUK GÖZÜKIZIL Course Lecturers Course Assistants Course Category Course Objective To Understand the applications of Partial Differantial Equations in engineering and other applied sciences. Course Content Classification of the partial differantial equation for second order and more. Some solution methods of second order differential equations. Green functions. Some hyperbolic methods. Compare of hyperbolic methos with the method of separated variables.
# Course Learning Outcomes Teaching Methods Assessment Methods
1 He/she understands the applications of Partial Differantial Equations in engineering and other applied sciences. Lecture, Drilland Practice, Problem Solving, Testing, Homework,
2 He/she establishs differantial equation of an engineering problem. Lecture, Drilland Practice, Problem Solving, Testing, Homework,
3 He/she linferences to Partial Differantial Equations. Lecture, Drilland Practice, Problem Solving, Testing, Homework,
4 He/she compares to the different solution methods. Lecture, Drilland Practice, Problem Solving, Testing, Homework,
Week Course Topics Preliminary Preparation
1 Classification of the partial differantial equations.
2 Hyperbolic , parabolic and elliptic types.
3 Separable variables methods.
4 Green functions.
5 The green functions of some partial equations.
6 The hyperbolic method.
7 Sin-cos expansions.
8 To solve partial equations by using sin-cos expansions.
9 Midterm
10 Tanh and cotanh methods.
11 To solve partial equations by using sin-cos expansions.
12 Extended sin-cos methods.
13 Extended Tanh and cotanh methods.
14 Comparing to the hyperbolic expansions and separable variables methods.
Resources
Course Notes
Course Resources

1. Elements of Partial Differential Equations , McGraw-Hill , 1957.
2.Nonlinear Partial Differential Equations for Scientist and Engineers,
Debnath L., Boston , 1997.
3. Kısmi diferansiyel denklemeler , ÇAĞLIYAN M. , ÇELEBİ A.O., Bursa , 2002.
4. Partial Differential Equations: Methods and Applications , Wazwaz A.M.,
Netherlands , 2002.

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. 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
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. 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
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 70
1. Ödev 30
Total 100
1. Yıl İçinin Başarıya 50
1. Final 50
Total 100