| Course Title | Code | Semester | L+U Hour | Credits | ECTS |
|---|---|---|---|---|---|
| Mathematical Analysis II | MAT506 | 3 + 0 | 3.0 | 8.0 |
| Prerequisites | None |
| Language of Instruction | Turkish |
| Course Level | Graduate |
| Course Type | |
| Mode of delivery | Lecturing |
| Course Coordinator |
Prof. Dr. Mehmet Zeki SARIKAYA Res. Assist. Burcu FEDAKAR |
| Instructors |
Tuba TUNÇ |
| Assistants | |
| Goals | To give knowledge of advanced calculus |
| Course Content | Missing properties of Reimann integral and Lebesque integral, Basic properties of Lebesque integral, To limit under integral, To compare Riemann and Lebesque integrals, Introduction to concept of compactness, Compactness in IR, Compactness in metric spaces, Criterias of compactness, Finite dimensionality and compactness, Weak compactness, Sequences of compact operators and its approximation, The compactness of adjoint operators, Approximation of compact operators by means of finite dimensional continuous operators |
| Learning Outcomes |
- Students will learn theoretical concepts in mathematics. - Students will learn how to read academical journals. |
| Week | Topics | Learning Methods |
|---|---|---|
| 1. Week | Missing properties of Reimann integral and Lebesgue integral | |
| 2. Week | Basic properties of Lebesgue integral | |
| 3. Week | To limit under integral | |
| 4. Week | To compare Riemann and Lebesgue integrals | |
| 5. Week | Introduction to concept of compactness | |
| 6. Week | Compactness in IR | |
| 7. Week | Compactness in metric spaces, Compactness criterias | |
| 8. Week | Midterm | |
| 9. Week | Finite-dimensionality and compactness | |
| 10. Week | Weak compactness | |
| 11. Week | Sequences of compact operators and its approximation | |
| 12. Week | Compactness of adjoint operators | |
| 13. Week | Approximation of compact operators by means of finite dimensional continuous operators | |
| 14. Week | Approximation of compact operators by means of finite dimensional continuous operators |
| 1.Elements of Functional Analysis, Brown A.L., Page A., New York : Van Nostrand Reinhold Company, 1970 |
| 2.Theory of Linear Operators in Hilbert Space, Ahiezer N.I., Glazman I.M, New York, Ungar, 1963. |
| 3.Elements of Functional Analysis, Luisternik L.A., Sobolev V.J., New York : John Wiley & Sons, 1974 |
| Program Requirements | Contribution Level | DK1 | DK2 | Measurement Method |
|---|---|---|---|---|
| PY1 | 5 | 0 | 0 | 60 |
| PY2 | 4 | 0 | 0 | 40 |
| PY3 | 4 | 0 | 0 | 60 |
| PY4 | 2 | 0 | 0 | 60 |
| PY5 | 4 | 0 | 0 | 40 |
| PY6 | 4 | 0 | 0 | 40 |
| PY7 | 4 | 0 | 0 | 60 |
| PY8 | 4 | 0 | 0 | 60 |
| PY9 | 4 | 0 | 0 | 60 |
| PY10 | 4 | 0 | 0 | 60 |
| 0 | 1 | 2 | 3 | 4 | 5 | |
|---|---|---|---|---|---|---|
| Course's Level of contribution | None | Very Low | Low | Fair | High | Very High |
| Method of assessment/evaluation | Written exam | Oral Exams | Assignment/Project | Laboratory work | Presentation/Seminar |
| Event | Quantity | Duration (Hour) | Total Workload (Hour) |
|---|---|---|---|
| Course Hours | 1 | 3 | 3 |
| Research | 14 | 2 | 28 |
| Midterm 1 | 1 | 2 | 2 |
| Midterm 2 | 1 | 2 | 2 |
| Homework 1 | 14 | 3 | 42 |
| Homework 2 | 14 | 2 | 28 |
| Quiz 1 | 1 | 2 | 2 |
| Quiz 2 | 1 | 2 | 2 |
| Final | 1 | 2 | 2 |
| Practice | 6 | 12 | 72 |
| Classroom Activities | 14 | 1 | 14 |
| Total Workload | 197 | ||
| ECTS Credit of the Course | 8.0 | ||
