| Course Title | Code | Semester | L+U Hour | Credits | ECTS |
|---|---|---|---|---|---|
| Elliptic Functions | MAT635 | 3 + 0 | 3.0 | 8.0 |
| Prerequisites | None |
| Language of Instruction | Turkish |
| Course Level | Graduate |
| Course Type | |
| Mode of delivery | verbal |
| Course Coordinator |
Prof. Dr. Mehmet Zeki SARIKAYA Res. Assist. Burcu FEDAKAR |
| Instructor(s) | |
| Assistants | |
| Goals | Teaching high level of mathematics to doctoral students. |
| Course Content | Historical introduction,Preliminary concepts and general discussion of periodic functions,The general theory of elliptic functions,Weierstrass’s elliptic functions,Weierstrass’s associated functions,Application of the Weierstrassian functions to the problems of geometry and mechanics,The theta functions,The Jacobi’s elliptic functions,Applications of the Jacobi’s elliptic functions,The theory of elliptic integrals ,Applications of the elliptic integrals,The hyperelliptic and abelian integrals,The automorphic and elliptic modular functions, |
| Learning Outcomes |
- Students will learn theoretical concepts in mathematics. - Students will learn how to read academical journals. |
| Week | Topics | Learning Methods |
|---|---|---|
| 1. Week | Historical introduction | |
| 2. Week | Preliminary concepts and general discussion of periodic functions | |
| 3. Week | The general theory of elliptic functions | |
| 4. Week | Weierstrass’s elliptic functions | |
| 5. Week | Weierstrass’s associated functions | |
| 6. Week | Application of the Weierstrassian functions to the problems of geometry and mechanics | |
| 7. Week | The theta functions | |
| 8. Week | Midterm | |
| 9. Week | The Jacobi’s elliptic functions | |
| 10. Week | Applications of the Jacobi’s elliptic functions | |
| 11. Week | The theory of elliptic integrals | |
| 12. Week | Applications of the elliptic integrals | |
| 13. Week | The hyperelliptic and abelian integrals | |
| 14. Week | The automorphic and elliptic modular functions |
| Elements of functions Mahadev Dutta Lokenath Debnath |
| Program Requirements | Contribution Level | DK1 | DK2 | Measurement Method |
|---|---|---|---|---|
| PY1 | 5 | 5 | 5 | 40 |
| PY2 | 5 | 5 | 5 | 40 |
| PY3 | 4 | 4 | 4 | 60 |
| PY4 | 5 | 5 | 5 | 60 |
| PY5 | 5 | 5 | 5 | 40 |
| PY6 | 5 | 5 | 5 | 60 |
| PY7 | 5 | 5 | 5 | 40 |
| PY8 | 4 | 4 | 4 | 60 |
| PY9 | 5 | 5 | 5 | 60 |
| PY10 | 4 | 4 | 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 | ||
