Nevşehir Hacı Bektaş Veli University Course Catalogue
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| Year/Semester of Study | 1 / Spring Semester | ||||
| Level of Course | 3rd Cycle Degree Programme | ||||
| Type of Course | Optional | ||||
| Department | MATHEMATICS (DOCTORATE DEGREE) | ||||
| 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 | |||||
| To comprehend numerical methods for partial differential equations and to solve equations with these methods. | |||||
| Learning Outcomes | PO | MME | |
| The students who succeeded in this course: | |||
| LO-1 |
PO-1 Students can design an original issue and explore new, different and / or comprehend complex issues. PO-2 Students will understand all aspects of mathematics and deepen the knowledge level that can innovate in this field. PO-3 Students will be dominated by current issues in mathematics. PO-10 Ability to transfer ideas and suggestions, related to topics about his/her field of interest, written and verball. PO-15 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 Term Paper |
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| PO: Programme Outcomes MME:Method of measurement & Evaluation |
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| Course Contents | ||
| Parabolic, elliptic and hyperbolic partial differential equations, finite element method, finite volume method and analytical methods. | ||
| Weekly Course Content | ||
| Week | Subject | Learning Activities and Teaching Methods |
| 1 | Classification, Finite Difference representation. | Oral presentation, Group Work, Question Answer. |
| 2 | Parabolic PDE: Explicit and implicit schemes. Compatibility,Stability and Convergence. | Oral presentation, Group Work, Question Answer. |
| 3 | Parabolic PDE: Explicit and implicit schemes. Compatibility,Stability and Convergence. | Oral presentation, Group Work, Question Answer. |
| 4 | Elliptic PDE:Solution of Laplace/Poisson PDE ADI and SOR schemes, | Oral presentation, Group Work, Question Answer. |
| 5 | Elliptic PDE:Solution of Laplace/Poisson PDEADI and SOR schemes, | Oral presentation, Group Work, Question Answer. |
| 6 | Hyperbolic equations: Finite difference schemes, Method of characteristics. | Oral presentation, Group Work, Question Answer. |
| 7 | Hyperbolic equations: Finite difference schemes, Method of characteristics. | Oral presentation, Group Work, Question Answer. |
| 8 | mid-term exam | |
| 9 | Finite element method. | Oral presentation, Group Work, Question Answer. |
| 10 | Finite element method. | Oral presentation, Group Work, Question Answer. |
| 11 | Finite volume method. | Oral presentation, Group Work, Question Answer. |
| 12 | Finite volume method. | Oral presentation, Group Work, Question Answer. |
| 13 | Tanh method. | Oral presentation, Group Work, Question Answer. |
| 14 | Auxilary equation method | Oral presentation, Group Work, Question Answer. |
| 15 | Sub-equation method. | Oral presentation, Group Work, Question Answer. |
| 16 | final exam | |
| Recommend Course Book / Supplementary Book/Reading | ||
| 1 | The Numerical Solution of Ordinary and Partial Differential Equations, Granville Sewell, John Wiley & Sons, 2005. | |
| 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 | ||