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| MATL7881 | Quantum Calculus | 3+0+0 | ECTS:7.5 | | Year / Semester | Spring Semester | | Level of Course | Third Cycle | | Status | Elective | | Department | DEPARTMENT of MATHEMATICS | | Prerequisites and co-requisites | None | | Mode of Delivery | Face to face | | Contact Hours | 14 weeks - 3 hours of lectures per week | | Lecturer | Prof. Dr. Mehmet KUNT | | Co-Lecturer | None | | Language of instruction | Turkish | | Professional practise ( internship ) | None | | | | The aim of the course: | | The aim of this course is expressing the fundemental properties of quantum derivative and quantum integral. Also, quantum Taylor's-Gauss's binomial- Heine's formulas, q-exponential-trigonometric-Gamma-Beta functions will be explain. |
| Programme Outcomes | CTPO | TOA | | Upon successful completion of the course, the students will be able to : | | | | PO - 1 : | learn quantum derivative and q-analogue of (x-a)^n | | 1 | | PO - 2 : | learn q-Taylor's, Gauss's binomial and Heine's binomial formula | | 1 | | PO - 3 : | learn q-exponential, q-trigonometric, q-Hypergeometric, q-Gamma, q-Beta functions | | 1 | | PO - 4 : | learn quantum integral | | 1 | | CTPO : Contribution to programme outcomes, TOA :Type of assessment (1: written exam, 2: Oral exam, 3: Homework assignment, 4: Laboratory exercise/exam, 5: Seminar / presentation, 6: Term paper), PO : Learning Outcome | | |
| Quantum derivative, q-analogue of (x-a)^n, q-Taylor's formula for polinomals, Gauss's binomial formula and a noncommutative binomal formula, properties of q-binomal coefficients, q-Taylor formula for formal power series and Heine's binomal formula, two Euler's identities and two q-exponential functions, q-trigonometric functions, q-Hypergeometric functions and Heine's formula, more on Heine's formula and the general binomal, q-antiderivative, Jackson integral, fundamental theorem of q-calculus and integration by parts and q-Gamma, q-Beta functions. |
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| 1 | Kac V., Cheung P., Quantum Calculus, Springer, New York, 2002. | | | |
| 1 | Annaby M.H., Mansour Z.S., q-Fractional Calculus and Equations, Springer, Heidelberg, 2012. | | | |
| Method of Assessment | | Type of assessment | Week No | Date | Duration (hours) | Weight (%) | | Mid-term exam | 9 | 06/04/2018 | 2 | 50 | | End-of-term exam | 16 | 08/06/2018 | 2 | 50 | | |
| Student Work Load and its Distribution | | Type of work | Duration (hours pw) | No of weeks / Number of activity | Hours in total per term | | Yüz yüze eğitim | 3 | 14 | 42 | | Sınıf dışı çalışma | 10 | 14 | 140 | | Laboratuar çalışması | 0 | 0 | 0 | | Arasınav için hazırlık | 6 | 1 | 6 | | Arasınav | 2 | 1 | 2 | | Uygulama | 0 | 0 | 0 | | Klinik Uygulama | 0 | 0 | 0 | | Ödev | 0 | 0 | 0 | | Proje | 0 | 0 | 0 | | Kısa sınav | 0 | 0 | 0 | | Dönem sonu sınavı için hazırlık | 10 | 1 | 10 | | Dönem sonu sınavı | 2 | 1 | 2 | | Diğer 1 | 0 | 0 | 0 | | Diğer 2 | 0 | 0 | 0 | | Total work load | | | 202 |
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