Course Name Code Semester T+U Hours Credit ECTS
Introduction To Partial Differential Equation Theo MAT 510 0 3 + 0 3 6
 Precondition Courses Recommended Optional Courses Course Language Turkish Course Level yuksek_lisans Course Type Optional Course Coordinator Prof.Dr. METİN YAMAN Course Lecturers Prof.Dr. METİN YAMAN, Course Assistants Course Category Field Proper Education Course Objective It’s aiming to solve partial differential equations arising in engineering and science. Course Content Sobolev spaces, sobolev inequality, fonction spaces, second order eliptik equations, second order evolution equations,
# Course Learning Outcomes Teaching Methods Assessment Methods
1 He/She recognizes sobolev spaces. Lecture, Drilland Practice, Self Study, Problem Solving, Testing, Homework, Performance Task,
2 He/She defines concept of weak derivative. Lecture, Drilland Practice, Self Study, Problem Solving, Testing, Homework, Performance Task,
3 He/She investigates existence of weak and classical solutions. Lecture, Drilland Practice, Self Study, Problem Solving, Testing, Homework, Performance Task,
4 He/She learns evolution equations. Lecture, Drilland Practice, Self Study, Problem Solving, Testing, Homework, Performance Task,
5 He/She comprehends parabolic and hyperbolic equations. Lecture, Drilland Practice, Self Study, Problem Solving, Testing, Homework, Performance Task,
6 He/She applies these to some examples. Lecture, Drilland Practice, Self Study, Problem Solving, Testing, Homework, Performance Task,
Week Course Topics Preliminary Preparation
1 Introduction to PDE
2 Clasiccal solution, weak solution
3 Sobolev spaces
4 Sobolev inequalities
5 Function spaces, spaces, spaces with time
6 Second order eliptik equation
7 Existence of weak solution, Lax-Milgram theorem
8 Regularity, maximum principle
9 Linear evolution equation
10 Second order parabolic equation
11 Midterm
12 Weak solution and maximum principle
13 Second order hyperbolic equation
14 Existence of weak solution
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.
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.
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.
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. Ödev 50
2. Ödev 50
Total 100
1. Yıl İçinin Başarıya 50
1. Final 50
Total 100