BAHÇEŞEHİR UNIVERSITY BİLGİ PAKETİ / DERS KATALOĞU
| MATHEMATICS (TURKISH, PHD) | |||||
| PhD | TR-NQF-HE: Level 8 | QF-EHEA: Third Cycle | EQF-LLL: Level 8 | ||
Course Introduction and Application Information
| Course Code | Course Name | Semester | Theoretical | Practical | Credit | ECTS |
| MAT6015 | Special Functions | Fall | 3 | 0 | 3 | 8 |
| This catalog is for information purposes. Course status is determined by the relevant department at the beginning of semester. |
Basic information
| Language of instruction: | Turkish |
| Type of course: | Departmental Elective |
| Course Level: | |
| Mode of Delivery: | Face to face |
| Course Coordinator : | Assoc. Prof. ERSİN ÖZUĞURLU |
| Recommended Optional Program Components: | None |
| Course Objectives: | To introduce students functions of the legendre, hermite, bessel, laguerre that are important in mathematics. |
Learning Outcomes
|
The students who have succeeded in this course; 1) He/She Recognizes and solves hypergeometric equation 2) He/She Recognizes and solves Bessel equation 3) He/She Recognizes and solves Legendre equation 4) He/She Recognizes and solves Hermite equation 5) He/She Recognizes and solves Laguerre equation 6) He/She has knowledge about solutions without solving the equation 7) He/She Establishes a connection inside special functions |
Course Content
| The Hypergeometric Functions, The Bessel Functions, The Hermite Functions, The Legendre Functions, The Laguerre Functions. |
Weekly Detailed Course Contents
| Week | Subject | Related Preparation |
| 1) | Hypergeometric Differential Equation. | |
| 2) | The Hypergeometric Functions. | |
| 3) | Bessel Differential Equation. | |
| 4) | Generating Function of Bessel Polynomial. | |
| 5) | Legendre Differential Equation. | |
| 6) | Generating Function of Legendre Polynomial. | |
| 7) | Recurrence Relations. | |
| 8) | Hermite Differential Equation. | |
| 9) | Generating Function of Hermite Polinomial and Recurrence Relations. | |
| 10) | Generating Function of Hermite Polinomial and Recurrence Relations (continued) | |
| 11) | The Legendre Functions. | |
| 12) | Generating Functions and Recurrence Relations. | |
| 13) | The Laguerre Functions. | |
| 14) | Laguerre Functions (continued) |
Sources
| Course Notes / Textbooks: | Special Functions, Earl. D. Rainville, 1971, Chelsea Pub Co. |
| References: | Special Functions, George E. Andrews, Richard Askey, Ranjan Roy, 2001, Cambridge University Press. Hypergeometric Functions and Their Applications, James B. Seaborn, 1991, Springer. |
Evaluation System
| Semester Requirements | Number of Activities | Level of Contribution |
| Presentation | 1 | % 20 |
| Midterms | 1 | % 30 |
| Final | 1 | % 50 |
| Total | % 100 | |
| PERCENTAGE OF SEMESTER WORK | % 50 | |
| PERCENTAGE OF FINAL WORK | % 50 | |
| Total | % 100 | |
ECTS / Workload Table
| Activities | Number of Activities | Duration (Hours) | Workload |
| Course Hours | 14 | 3 | 42 |
| Study Hours Out of Class | 14 | 5 | 70 |
| Presentations / Seminar | 1 | 40 | 40 |
| Midterms | 1 | 20 | 20 |
| Final | 1 | 28 | 28 |
| Total Workload | 200 | ||
Contribution of Learning Outcomes to Programme Outcomes
| No Effect | 1 Lowest | 2 Low | 3 Average | 4 High | 5 Highest |
| Program Outcomes | Level of Contribution |