Nevşehir Hacı Bektaş Veli University Course Catalogue
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| Year/Semester of Study | 4 / Spring Semester | ||||
| Level of Course | 1st 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 | SURE KÖME (sure.kome@nevsehir.edu.tr) | ||||
| Name of Lecturer(s) | |||||
| Language of Instruction | Turkish | ||||
| Work Placement(s) | None | ||||
| Objectives of the Course | |||||
| The purpose of this course is to teach the basic concepts, solution methods and applications of integral equations and to enable students to develop solution techniques. | |||||
| Learning Outcomes | PO | MME | |
| The students who succeeded in this course: | |||
| LO-1 | Can convert differential equations to integral equations and integral equations to differential equations. |
PO-1 Have the ability to conceptualize the events and facts related to the field of mathematics such as Analysis, Geometry and Algebra with the help of the scientific methods and techniques and can define these concepts. PO-2 Have the knowledge to critize, analyze, and evaluate the correctness, reliability, and validity of mathematical data. |
Examination |
| LO-2 | Can obtain the solutions of some integral equations. |
PO-1 Have the ability to conceptualize the events and facts related to the field of mathematics such as Analysis, Geometry and Algebra with the help of the scientific methods and techniques and can define these concepts. PO-2 Have the knowledge to critize, analyze, and evaluate the correctness, reliability, and validity of mathematical data. |
Examination |
| LO-3 | Can recognize Fredholm integral equations. |
PO-1 Have the ability to conceptualize the events and facts related to the field of mathematics such as Analysis, Geometry and Algebra with the help of the scientific methods and techniques and can define these concepts. PO-2 Have the knowledge to critize, analyze, and evaluate the correctness, reliability, and validity of mathematical data. |
Examination |
| LO-4 | Can recognize Volterra integral equations. |
PO-1 Have the ability to conceptualize the events and facts related to the field of mathematics such as Analysis, Geometry and Algebra with the help of the scientific methods and techniques and can define these concepts. PO-2 Have the knowledge to critize, analyze, and evaluate the correctness, reliability, and validity of mathematical data. |
Examination |
| PO: Programme Outcomes MME:Method of measurement & Evaluation |
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| Course Contents | ||
| Fredholm equations, Volterra integral equations, Applications of integral equations to ordinary differential equations. | ||
| Weekly Course Content | ||
| Week | Subject | Learning Activities and Teaching Methods |
| 1 | Basic informations about the integral equtions | Oral expression, discussion, question-answer |
| 2 | Solution of integral equations | Oral expression, discussion, question-answer |
| 3 | Transformation of Linear Differential Equations into Volterra Integral Equations | Oral expression, discussion, question-answer |
| 4 | Transformation of the Volterra integral equation into a linear differential equation | Oral expression, discussion, question-answer |
| 5 | Introduction to Fredholm Integral Equations | Oral expression, discussion, question-answer |
| 6 | Degenerate kernel Fredholm integral equations | Oral expression, discussion, question-answer |
| 7 | Hammerstein-type integral equations | Oral expression, discussion, question-answer |
| 8 | mid-term exam | |
| 9 | Eigenvalues and Eigenfunctions of Fredholm Integral Equations | Oral expression, discussion, question-answer |
| 10 | The relationship between the kernel and the resolvent | Oral expression, discussion, question-answer |
| 11 | Iterative kernels | Oral expression, discussion, question-answer |
| 12 | Succesive approximation method for solving Fredholm integral equations | Oral expression, discussion, question-answer |
| 13 | Introduction to Volterra Integral Equations | Oral expression, discussion, question-answer |
| 14 | Solving Volterra integral equations with the help of the resolvent | Oral expression, discussion, question-answer |
| 15 | Succesive approximation method for solving Volterra integral equations | Oral expression, discussion, question-answer |
| 16 | final exam | |
| Recommend Course Book / Supplementary Book/Reading | ||
| 1 | Kevser Özden Köklü, İntegral Denklemler, Papatya Yayıncılık, 2018. | |
| Required Course instruments and materials | ||
| 1) Textbook -Kevser Ozden Koklu, Integral Denklemler, Papatya Yayincilik, 2018. 2) Lecture Notes | ||
| 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) | 4 | 14 | 56 |
| Outside Class | |||
| a) Reading | 0 | ||
| b) Search in internet/Library | 0 | ||
| 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 | 10 | 2 | 20 |
| mid-term exam | 2 | 1 | 2 |
| Own study for final exam | 15 | 2 | 30 |
| final exam | 2 | 1 | 2 |
| Individual study before class | 5 | 14 | 70 |
| 0 | |||
| Total work load; | 180 | ||