Nevşehir Hacı Bektaş Veli University Course Catalogue
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| Year/Semester of Study | 1 / Fall Semester | ||||
| Level of Course | 2nd Cycle Degree Programme | ||||
| Type of Course | Optional | ||||
| Department | MATHEMATICS | ||||
| Pre-requisities and Co-requisites | None | ||||
| Mode of Delivery | Face to Face | ||||
| Teaching Period | 14 Weeks | ||||
| Name of Lecturer | MEHMET ŞENOL (msenol@nevsehir.edu.tr) | ||||
| Name of Lecturer(s) | |||||
| Language of Instruction | Turkish | ||||
| Work Placement(s) | None | ||||
| Objectives of the Course | |||||
| Comprehension of the general structure of differential equations of fractional order and analytical and numerical solutions of such equations. | |||||
| Learning Outcomes | PO | MME | |
| The students who succeeded in this course: | |||
| LO-1 |
PO-1 Fundamental theorems of about some sub-theories of Analysis, Applied Mathematics, Geometry, and Algebra can apply to new problems. PO-3 Mathematics, natural sciences and their branches in these areas and related issues has sufficient infrastructure solutions for the problems of theoretical and practical uses of mathematics. PO-10 Be able to organize events, for the development of critical and creative thinking and problem solving skills, by using appropriate methods and techniques. PO-16 Ability to use the approaches and knowledge of other disciplines in Mathematics. PO-17 Be able to set up and develope a solution method for a problem in mathematics independently, be able to solve and evaluate the results and to apply them if necessary. |
Examination Performance Project |
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| PO: Programme Outcomes MME:Method of measurement & Evaluation |
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| Course Contents | ||
| Fractional derivative and integral concepts. Analytical and numerical solutions of fractional differential equations. | ||
| Weekly Course Content | ||
| Week | Subject | Learning Activities and Teaching Methods |
| 1 | Concept and history of fractional analysis. | Oral presentation, Group Work, Question Answer. |
| 2 | Gamma function, Beta function and Mittag-Leffler function in Fractional Analysis | Oral presentation, Group Work, Question Answer. |
| 3 | Riemann-Liouville fractional integral, derivatives and properties. | Oral presentation, Group Work, Question Answer. |
| 4 | Grünwald-Letnikov fractional derivative and properties. | Oral presentation, Group Work, Question Answer. |
| 5 | Caputo fractional derivative and properties. | Oral presentation, Group Work, Question Answer. |
| 6 | Comparison of fractional derivative approaches. | Oral presentation, Group Work, Question Answer. |
| 7 | Calculation of fractional derivatives with Laplace transformations. | Oral presentation, Group Work, Question Answer. |
| 8 | mid-term exam | |
| 9 | Fractional order differential equations. | Oral presentation, Group Work, Question Answer. |
| 10 | The existence and uniqueness of solutions. | Oral presentation, Group Work, Question Answer. |
| 11 | Fractional Green functions. | Oral presentation, Group Work, Question Answer. |
| 12 | Physical problems defined by fractional differential equations. | Oral presentation, Group Work, Question Answer. |
| 13 | Numerical solutions for fractional derivatives and integrals. | Oral presentation, Group Work, Question Answer. |
| 14 | Numerical solutions of differential equations in fractional order. | Oral presentation, Group Work, Question Answer. |
| 15 | MATHEMATICA applications of differential equation solutions in fractional order. | Oral presentation, Group Work, Question Answer. |
| 16 | final exam | |
| Recommend Course Book / Supplementary Book/Reading | ||
| 1 | K. S. Miller, B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations, John Wiley & Sons, Inc., 1993. | |
| 2 | I. Podlubny, Fractional Differential Equations, Academic Pres, 1999 | |
| 3 | K. B. Oldham and J. Spanier, The Fractional Calculus, Academic Press, 1974. | |
| Required Course instruments and materials | ||
| Assessment Methods | |||
| Type of Assessment | Week | Hours | Weight(%) |
| mid-term exam | 8 | 2 | 40 |
| Other assessment methods | |||
| 1.Oral Examination | |||
| 2.Quiz | |||
| 3.Laboratory exam | |||
| 4.Presentation | |||
| 5.Report | |||
| 6.Workshop | |||
| 7.Performance Project | |||
| 8.Term Paper | |||
| 9.Project | |||
| final exam | 16 | 2 | 60 |
| Student Work Load | |||
| Type of Work | Weekly Hours | Number of Weeks | Work Load |
| Weekly Course Hours (Theoretical+Practice) | 3 | 14 | 42 |
| Outside Class | |||
| a) Reading | 6 | 14 | 84 |
| b) Search in internet/Library | 2 | 14 | 28 |
| c) Performance Project | 0 | ||
| d) Prepare a workshop/Presentation/Report | 0 | ||
| e) Term paper/Project | 0 | ||
| Oral Examination | 0 | ||
| Quiz | 0 | ||
| Laboratory exam | 0 | ||
| Own study for mid-term exam | 8 | 2 | 16 |
| mid-term exam | 2 | 1 | 2 |
| Own study for final exam | 8 | 2 | 16 |
| final exam | 2 | 1 | 2 |
| 0 | |||
| 0 | |||
| Total work load; | 190 | ||