| Course Title | Code | Semester | L+U Hour | Credits | ECTS |
|---|---|---|---|---|---|
| Mathematical Analysis I | MAT505 | 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 |
Mehmet Zeki SARIKAYA |
| Assistants | |
| Goals | To give the knowledge of advanced calculus |
| Course Content | Completeness properties of IR, Topological structure of IRn, Convergence sequences in IRn, compact and connected sets, Continuous functions and uniform continuity, uniform convergence, Stone-Weierstrass Theorems, Multivariate differantial calculus, Curves in IRn, directional derivatives and differantial, Derivative definition and matrix representation, Differentiable transformations, The chain rule, Multivariate mean-value theorem, Taylor theorem, Higher order derivatives, Maximums and minimums, Inverse Function Theorem, Closed Function Theorem and Conditional extremums |
| Learning Outcomes |
| Week | Topics | Learning Methods |
|---|---|---|
| 1. Week | Completeness properties of IR | |
| 2. Week | Topological structure of IRn | |
| 3. Week | Convergence sequences in IRn, compact and connected sets | |
| 4. Week | Continuous functions and uniform continuity ,uniform convergence | |
| 5. Week | Stone-Weierstrass Theorems | |
| 6. Week | Multivariable differential calculus | |
| 7. Week | Curves in IRn, directional derivatives and differantial | |
| 8. Week | Midterm | |
| 9. Week | Definition of derivative and its matrix representation, Differentiable transformations, the chain rule | |
| 10. Week | Mean value theorem for multivariate functions | |
| 11. Week | Taylor theorem | |
| 12. Week | Higher order derivatives, Maximums and minimums | |
| 13. Week | Inverse Function Theorem | |
| 14. Week | Closed Function Theorem and Conditional extremums |
| 1.Mathematical Analysis, A. Browder, Springer-Verlag, 1996 |
| 2.Advanced Calculus of Several Variables, C.H.Edwards, Dover Publications, 1973 |
| Program Requirements | Contribution Level | Measurement Method |
|---|---|---|
| PY1 | 5 | 60 |
| PY2 | 4 | 40 |
| PY3 | 4 | 60 |
| PY4 | 2 | 40 |
| PY5 | 4 | 40 |
| PY6 | 5 | 60 |
| PY7 | 5 | 40,60 |
| PY8 | 4 | 60 |
| PY9 | 4 | 60 |
| PY10 | 4 | 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 | ||
