| Course Title | Code | Semester | L+U Hour | Credits | ECTS |
|---|---|---|---|---|---|
| Extensions in Multivariate Polynomials II | MAT641 | 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 | 1.Improving, deepening, statistically analyzing and commenting on the knowledge in the same or a different field to expertise level based on undergraduate qualifications. 2.Diagnosing interdisciplinary interaction related to the field. 3.Running a study demanding expertise independently in the field. 4.Critically evaluating the expertise level knowledge and skills acquired in the field, and redirecting learning |
| Course Content | 1 Introduction to q-series 2 q-Integral 3 q-Binom Theorem 4 q-Binom Theorem 5 q-Gamma Function 6 q-Beta Function 7 q-Analogue of Hypergeometric Series 8 q-Analogues of some special polynomials 9 q-Analogues of some special polynomials 10 Construction of q-Lagrange Polynomials 11 q-Lagrange Polynomials for Bilinear and Bilateral Generating Functions 12 Recurrence Relations of q-Lagrange Polynomials 13 q-Analogues of some special polynomials in several variables 14 q-Analogues of some special polynomials in several variables |
| Learning Outcomes |
- The concept of q-series, The concept of q-integral and to get their applications, To get q-Binom theorem and its proof, To applicate q-Binom theorem, To get q-Gamma function, To get q-Beta function, To get q-analogues of Hypergeometric series, To get q-analogues of some special polynomials in one variable, To find q-Lagrange polynomials in several variables and to get their properties, To construct some another multivariable polynomials and to get their properties |
| Week | Topics | Learning Methods |
|---|---|---|
| 1. Week | Introduction to q-series | |
| 2. Week | q-Integral | |
| 3. Week | q-Binom Theorem | |
| 4. Week | q-Binom Theorem | |
| 5. Week | q-Gamma Function | |
| 6. Week | q-Beta Function | |
| 7. Week | q-Analogue of Hypergeometric Series | |
| 8. Week | Mid-term Exam | |
| 9. Week | q-Analogues of some special polynomials | |
| 10. Week | q-Analogues of some special polynomials | |
| 11. Week | Construction of q-Lagrange Polynomials | |
| 12. Week | q-Lagrange Polynomials for Bilinear and Bilateral Generating Functions | |
| 13. Week | Recurrence Relations of q-Lagrange Polynomials | |
| 14. Week | q-Analogues of some special polynomials in several variables |
| Andrews, G.E., Askey, R. and Roy, R. ,Special Functions. Cambridge University Pres, 1999. |
| Program Requirements | Contribution Level | DK1 | Measurement Method |
|---|---|---|---|
| PY1 | 10 | 10 | 40,60 |
| PY2 | 10 | 10 | 40 |
| PY3 | 10 | 10 | 40,60 |
| PY4 | 10 | 10 | 40,60 |
| PY5 | 10 | 10 | 40,60 |
| PY6 | 10 | 10 | - |
| PY7 | 10 | 10 | 40,60 |
| PY8 | 10 | 10 | 40,60 |
| PY9 | 10 | 10 | 40,60 |
| PY10 | 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 | ||
