Nevşehir Hacı Bektaş Veli University Course Catalogue
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| Year/Semester of Study | 1 / Fall 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 | SEYDİ BATTAL GAZİ KARAKOÇ (sbgkarakoc@nevsehir.edu.tr) | ||||
| Name of Lecturer(s) | |||||
| Language of Instruction | Turkish | ||||
| Work Placement(s) | None | ||||
| Objectives of the Course | |||||
| The aim of this course is to introduce the basic methods of solution of boundary value problems including differential equations and boundary conditions. | |||||
| Learning Outcomes | PO | MME | |
| The students who succeeded in this course: | |||
| PO: Programme Outcomes MME:Method of measurement & Evaluation |
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| Course Contents | ||
| First order ordinary differential equations, Cauchy-Euler method, Existence and uniqueness theorem, Differential inequalities, Integral equations, Picard method and existence theorem, Complex valued equations, Linear differantial equations, Second order differantial equations, Boundary value problems, Eigenvalue problems. | ||
| Weekly Course Content | ||
| Week | Subject | Learning Activities and Teaching Methods |
| 1 | First order ordinary differential equations | |
| 2 | The Cauchy-Euler method and proof of Existence and uniqueness theorem. | |
| 3 | Differential inequalities | |
| 4 | Integral equations | |
| 5 | Systems and high order ordinary differential equations | |
| 6 | Picard method and existence theory | |
| 7 | Complex valued equations | |
| 8 | mid-term exam | |
| 9 | Linear differential equations | |
| 10 | Second order differential equations | |
| 11 | Wroskian identity | |
| 12 | Boundary value problems | |
| 13 | Eigenvalue problems | |
| 14 | Eigenvalue problems | |
| 15 | The number of solutions of a boundary value problem | |
| 16 | final exam | |
| Recommend Course Book / Supplementary Book/Reading | ||
| 1 | Numerical Solution of Partial Differential Equations Leon LAPIDUS and George F. PINDER. Numerical Solution of Partial Differential Equations: Finite Difference Methods G. D. Smith, Gordon D. Smith Numerical Solution of Partial Differential Equations K. W | |
| 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 | 5 | 14 | 70 |
| 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 | 4 | 4 | 16 |
| mid-term exam | 2 | 1 | 2 |
| Own study for final exam | 5 | 4 | 20 |
| final exam | 2 | 1 | 2 |
| 0 | |||
| 0 | |||
| Total work load; | 180 | ||