Mathematical Analysis II
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 |
|---|---|---|---|---|---|---|
| Mathematical Analysis II | MAT626 | Compulsory | Doctorate degree | 1 | Fall | 8 |
Name of Lecturer(s)
Prof. Dr. Halis AYGÜN
Prof. Dr. Abdülkadir AYGÜNOĞLU
Prof. Dr. Serap BULUT
Prof. Dr. Ali DEMİR
Associate Prof. Dr. Arzu AKGÜL
Learning Outcomes of the Course Unit
1) Explain the relations between Lebesque and Riemann integrals by learning Lebesque integration.
2) Explain how to extend the one dimensional analysis to n-dimensional analysis.
3) State the compact operators and their fundamental properties.
4) Explain the conjeguate operators and theiir fundamental properties.
5) State the analysis of an n-dimensional space.
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
Not Required
Course Contents
This course provides candidates with profound knowledge on lack of Riemann integration and lebesque integraion, fundamental properties of Lebesque integration, comparing of Riemann and Lebesque integration, compactness and compactness in IR, compactness in metric spaces, finite dimensionality and compactness, weak compactness, the sequence and convergence of compact operators, compactness of conjuguate operators.
Recommended or Required Reading
Planned Learning Activities and Teaching Methods
Assessment Methods and Criteria
Contribution of Midterm Examination to Course Grade |
40% |
|---|---|
Contribution of Final Examination to Course Grade |
60% |
Total |
100% |
Language of Instruction
Other
Work Placement(s)
Not Required