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| MATL7462 | Continued Fractions for Special Functions | 3+0+0 | ECTS:7.5 | | Year / Semester | Fall Semester | | Level of Course | Third Cycle | | Status | Elective | | Department | DEPARTMENT of MATHEMATICS | | Prerequisites and co-requisites | None | | Mode of Delivery | | | Contact Hours | 14 weeks - 3 hours of lectures per week | | Lecturer | Doç. Dr. Ali Hikmet DEĞER | | Co-Lecturer | None | | Language of instruction | Turkish | | Professional practise ( internship ) | None | | | | The aim of the course: | | The aim of this course is to analyse the connections of special type functions with continued fractions. |
| Programme Outcomes | CTPO | TOA | | Upon successful completion of the course, the students will be able to : | | | | PO - 1 : | recognize continued fractions. | 3,8 | 1, | | PO - 2 : | relate continued fractions to special functions. | 3,8 | 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 | | |
| Basic concepts, Continued fraction representations of functions, Convergence criterion, Pade approximations, Moment theory and orthogonal functions, Continued fraction construction, Cutting error bounds, Continued fraction evaluation, Mathematical constants, Elementary functions, Gamma function and related functions, Error function and related integrals, Exponential integrals and related functions, Hyper geometric functions, Combining hyper geometric functions, Bessel functions, Probability functions, Basic hyper geometric functions. |
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| Course Syllabus | | Week | Subject | Related Notes / Files | | Week 1 | Basic concepts, Symbols and notations, Recurrence relations, Continued fraction concept. | | | Week 2 | Some features of continued fractions, Continued fraction families. | | | Week 3 | Convergence criteria, Uniform convergence, Periodic and limit periodic continued fractions. | | | Week 4 | Pade approaches, Basic properties, Convergence of Pade approaches. | | | Week 5 | Moment theory and orthogonal functions, Construction of solutions. | | | Week 6 | Constructing continued fractions, Continued fraction types. | | | Week 7 | Cutting error boundaries, Parabola's theorems, Change selection. | | | Week 8 | Continued fractional evaluation, Evaluation of approaches. | | | Week 9 | Mid-term exam. | | | Week 10 | Mathematical constants, Uniform continued fractions, Euler numbers, Natural logarithm. | | | Week 11 | Elementary functions, Exponential functions, Hyperbolic functions, Power functions. | | | Week 12 | Gamma function and related functions, Binet function. | | | Week 13 | Error function and related integrals, Exponential integrals and related functions, Hypergeometric functions. | | | Week 14 | Coupled hypergeometric functions, Bessel functions, Modified Bessel functions. | | | Week 15 | Probability functions, Repeated integrals, Basic hypergeometric functions. | | | Week 16 | Final exam. | | | |
| 1 | Cuyt, A., Petersen, V.B., Verdonk, B., Waadeland, H., Jones, W.B.,2008, Handbook of Continued Fractions for Special Functions, SpringerScience+Business Media B.V., Netherlands. | | | |
| 1 | Jones , W. B., Thron, W.J., 1980, Continued Fractions Analytic Theory and Applications, Encyclopedia of Mathematics and It?s Applications, Volume 11, Addison-Wesley Publishing Company, London. | | | |
| Method of Assessment | | Type of assessment | Week No | Date | Duration (hours) | Weight (%) | | Mid-term exam | 9 | 15/03/2024 | 2 | 30 | | Quiz | 12 | 15/04/2024 | 1 | 20 | | End-of-term exam | 16 | 06/06/2024 | 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 | | Arasınav için hazırlık | 6 | 1 | 6 | | Arasınav | 2 | 1 | 2 | | Dönem sonu sınavı için hazırlık | 10 | 1 | 10 | | Dönem sonu sınavı | 2 | 1 | 2 | | Total work load | | | 202 |
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