Course Name Code Semester T+U Hours Credit ECTS
Introduction To Inverse Problems MAT 535 0 3 + 0 3 6
Precondition Courses Partial differential equations
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 Research assistants
Course Category
Course Objective To introduce and analyze the inverse problems arise in the applied sciences.
Course Content Introduction, examples of some inverse problems, ill-posed problems, uniqueness and stability problems, inverse problems for parabolic equations, inverse problems for hyperbolic equations
# Course Learning Outcomes Teaching Methods Assessment Methods
1 He/She defines the inverse problems. Lecture, Drilland Practice, Self Study, Problem Solving, Testing, Homework, Performance Task,
2 He/She has information about ill-posed problems. Lecture, Drilland Practice, Self Study, Problem Solving, Testing, Homework, Performance Task,
3 He/She learns some methods to solve the inverse problems . Lecture, Drilland Practice, Self Study, Problem Solving, Testing, Homework, Performance Task,
4 He/She has knowledge about stability and uniquesness of problem. Lecture, Drilland Practice, Self Study, Problem Solving, Testing, Homework, Performance Task,
5 He/She develops a method for solving parabolic equation. Lecture, Drilland Practice, Self Study, Problem Solving, Testing, Homework, Performance Task,
6 He/She develops a method for solving hyperbolic equation. Lecture, Drilland Practice, Self Study, Problem Solving, Testing, Homework, Performance Task,
7 He/ she applies this methods to some problems. Lecture, Drilland Practice, Self Study, Problem Solving, Testing, Homework, Performance Task,
Week Course Topics Preliminary Preparation
1 Fundamental concepts
2 What is the inverse problem, examples
3 Ill-posed problems
4 Existence-uniqueness
5 Stability problems
6 Stability problems
7 Inverse problems for parabolic equations
8 Inverse problems for parabolic equations
9 Inverse problems for parabolic equations
10 Midterm
11 Inverse problems for hyperbolic equations
12 Inverse problems for hyperbolic equations
13 Inverse problems for hyperbolic equations
14 Some applications
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.
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.
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
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 10 10
Assignment 1 30 30
Final examination 1 10 10
Total Workload 146
Total Workload / 25 (Hours) 5.84
dersAKTSKredisi 6