| Course Title | Code | Semester | L+U Hour | Credits | ECTS |
|---|---|---|---|---|---|
| Extensions in Multivariate Polynomials I | MAT640 | 3 + 0 | 3.0 | 8.0 |
| Prerequisites | None |
| Language of Instruction | Turkish |
| Course Level | Graduate |
| Course Type | |
| Mode of delivery | Lecturing |
| Course Coordinator |
Assoc. Prof. Dr. Nejla ÖZMEN |
| Instructors | |
| Assistants | |
| Goals | Improving, deepening, statistically analyzing and commenting on the knowledge in the same or a different field to expertise level based on undergraduate qualifications. Diagnosing interdisciplinary interaction related to the field. Running a study demanding expertise independently in the field. Critically evaluating the expertise level knowledge and skills acquired in the field, and redirecting learning |
| Course Content | 1 Gamma function, Beta function 2 Orthogonality, Generating function, Pochammer symbol 3 Hypergeometric function and Gauss differential equation 4 The Properties of Some Special Polynomials 5 Lagrange Polynomials in two variables 6 A relation between Lagrange and Jacobi Polynomials 7 Multivariable Lagrange Polynomials 8 Multilinear and Multilateral Generating Functions 9 Some Properties and Recurrence Relations including Derivative 10 Jacobi Polynomials and new relations for related some special polynomials 11 Two Main Theorem for Bilinear and Bilateral Generating Functions 12 Two Main Theorem for Bilinear and Bilateral Generating Functions 13 Some Properties and Recurrence Relations not including Derivative 14 Some Properties and Recurrence Relations not including Derivative |
| Learning Outcomes |
- The concept of Gamma and Beta functions and to get their applications, - The concept of Pochammer symbol and hypergeometric function - To solve the Gauss differential equation and to get their applications - To solve the Kummer differential equation and the concept of confluent hypergeometric function - The concept of orthogonal polynomials and generating functions - To solve some known differential equations and to get some special functions which their solutions - The concept of Legendre polynomials, to get their Rodrigues formula - To get generating function, recurrence relation of Legendre polynomials and prove orthogonality of these polynomials and to get their norm - Via methods which is used for Legendre polynomials, to get same properties of other special functions - To find the main properties of Lagrange polynomials and then to get some results for another multivariable polynomials |
| Week | Topics | Learning Methods |
|---|---|---|
| 1. Week | Gamma Function, Beta Function | |
| 2. Week | Orthogonality, Generating function, Pochammer symbol | |
| 3. Week | Hypergeometric function and Gauss differential equation | |
| 4. Week | The Properties of Some Special Polynomials | |
| 5. Week | Lagrange Polynomials in two variables | |
| 6. Week | A relation between Lagrange and Jacobi Polynomials | |
| 7. Week | Multivariable Lagrange Polynomials | |
| 8. Week | Mid-term Exam | |
| 9. Week | Multilinear and Multilateral Generating Functions | |
| 10. Week | Some Properties and Recurrence Relations including Derivative | |
| 11. Week | Jacobi Polynomials and new relations for related some special polynomials | |
| 12. Week | Two Main Theorem for Bilinear and Bilateral Generating Functions | |
| 13. Week | Two Main Theorem for Bilinear and Bilateral Generating Functions | |
| 14. Week | Some Properties and Recurrence Relations not including Derivative |
| Andrews, G.E., Askey, R. and Roy, R. ,Special Functions. Cambridge University Pres, 1999. |
| Earl D. Rainville, Special Functions. Macmillan, 1960. Andrews, G.E., Askey, R. and Roy, R. ,Special Functions. Cambridge University Pres, 1999 |
| Andrews, G.E., Askey, R. and Roy, R. ,Special Functions. Cambridge University Pres, 1999. |
| Program Requirements | Contribution Level | DK1 | DK2 | DK3 | DK4 | DK5 | DK6 | DK7 | DK8 | DK9 | DK10 | Measurement Method |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| PY1 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 40,60 |
| PY2 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 40,60 |
| PY3 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 40,60 |
| PY4 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 40,60 |
| PY5 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 40,60 |
| PY6 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 40,60 |
| PY7 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 40,60 |
| PY8 | 10 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 40,60 |
| PY9 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 40,60 |
| PY10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 40,60 |
| 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 | 14 | 3 | 42 |
| Preparation, After Class Study | 14 | 2 | 28 |
| Research | 14 | 2 | 28 |
| Other Activities | 14 | 1 | 14 |
| Midterm 1 | 1 | 2 | 2 |
| Homework 1 | 14 | 1 | 14 |
| Homework 2 | 14 | 1 | 14 |
| Final | 1 | 2 | 2 |
| Practice | 14 | 1 | 14 |
| Practice End-Of-Term | 2 | 2 | 4 |
| Classroom Activities | 14 | 3 | 42 |
| Total Workload | 204 | ||
| ECTS Credit of the Course | 8.0 | ||
