Introduction To Sobolev Spaces
Mathematics
Institute of Natural and Applied Sciences
Third Cycle (Doctorate Degree)
| Course Unit Title | Course Unit Code | Type of Course Unit | Level of Course Unit | Year of Study | Semester | ECTS Credits |
|---|---|---|---|---|---|---|
| Introduction To Sobolev Spaces | MAT619 | Elective | Doctorate degree | 1 | Spring | 8 |
Name of Lecturer(s)
Prof. Dr. Zahir MURADOĞLU
Associate Prof. Dr. Arzu COŞKUN
Learning Outcomes of the Course Unit
1) Explaining the basic definitions of the Sobolev spaces
2) Clarifying compactness theorem (Arzela Ascoli)
3) Using the information about boundary values of functions in Sobolev spaces called Trace theorem.
4) Distinguishing about the dual spaces of Sobolev spaces, the so-called "negative" spaces.
5) Doing density theorems, coordinating transformations, extension theorems and embedding theorems
Program Competencies-Learning Outcomes Relation
| Program Competencies | ||||||||
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | ||
| Learning Outcomes | ||||||||
| 1 | No relation | No relation | No relation | No relation | No relation | No relation | No relation | |
| 2 | No relation | No relation | No relation | No relation | No relation | No relation | No relation | |
| 3 | No relation | No relation | No relation | No relation | No relation | No relation | No relation | |
| 4 | No relation | No relation | No relation | No relation | No relation | No relation | No relation | |
| 5 | No relation | No relation | No relation | No relation | No relation | No relation | No relation | |
Mode of Delivery
Face to Face
Prerequisites and Co-Requisites
None
Recommended Optional Programme Components
Variational Methods
Course Contents
Candidates are provided with in-depth knowledge on the standart topic from real and functional analysis of Lebesgue spaces Lp, of which Sobolev spaces are special subspaces and for completeness, proofs , all the basic properties of Sobolev spaces of positive integral order and culminate in the very important Sobolev imbedding theorem and the corresponding compact imbedding theorem.
Recommended or Required Reading
Planned Learning Activities and Teaching Methods
Assessment Methods and Criteria
Language of Instruction
Turkish
Work Placement(s)
Not Required