Nevşehir Hacı Bektaş Veli University Course Catalogue
|
|||||
| 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 | SEYDİ BATTAL GAZİ KARAKOÇ (sbgkarakoc@nevsehir.edu.tr) | ||||
| Name of Lecturer(s) | SEYDİ BATTAL GAZİ KARAKOÇ, | ||||
| Language of Instruction | Turkish | ||||
| Work Placement(s) | None | ||||
| Objectives of the Course | |||||
| The aim of the course is to give a general definition and theorems on main principles of Ordinary Differential Equation. | |||||
| Learning Outcomes | PO | MME | |
| The students who succeeded in this course: | |||
| LO-1 | Classify Differential Equations, investigate Existence of Differential Equations |
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-6 Following the developments in science and technology and gain self-renewing ability. |
Examination Performance Project |
| LO-2 | Knows the Solution Methods of First Order Linear Differential Equations. Knows Solution Methods of First Order Higher Order Equations. Solves Constant Coefficient Linear Differential Equations. |
PO-2 Ability to assimilate mathematic related concepts and associate these concepts with each other. 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-6 Following the developments in science and technology and gain self-renewing ability. PO-13 Ability to use mathematical knowledge in technology. PO-15 To apply mathematical principles to real world problems. 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 |
| PO: Programme Outcomes MME:Method of measurement & Evaluation |
|||
| Course Contents | ||
| First Order Differantial Equations, Second Order Linear Equations, Higher Order Linear Equations, Series Solutions of Second Order Linear Equations | ||
| Weekly Course Content | ||
| Week | Subject | Learning Activities and Teaching Methods |
| 1 | Basic Definitions Classification of Differential Equations Creating Differential Equations Initial and Boundary Value Problems Existence and Uniqueness Theorems for Initial and Boundary Value Problems | Oral Represention, Questioning-Answering, Problem solving |
| 2 | Existence and Uniqueness Theorems Separable Equations for Initial and Boundary Value Problems | Oral Represention, Questioning-Answering, Problem solving |
| 3 | Exact Differential Equations Equations That Can Be Constructed into Exact Differential Equations | Oral Represention, Questioning-Answering, Problem solving |
| 4 | First Order Linear Differential Equations Homogeneous Equations | Oral Represention, Questioning-Answering, Problem solving |
| 5 | Bernoulli Differential Equation Riccati Differential Equation | Oral Represention, Questioning-Answering, Problem solving |
| 6 | 1st Order Higher Order Equations Shape of the Equation | Oral Represention, Questioning-Answering, Problem solving |
| 7 | Differential Equations That Can Be Solved By Derivative | Oral Represention, Questioning-Answering, Problem solving |
| 8 | mid-term exam | |
| 9 | Contrary Solution p-discriminant | Oral Represention, Questioning-Answering, Problem solving |
| 10 | Envelope C-discriminant | Oral Represention, Questioning-Answering, Problem solving |
| 11 | Clairaut Differential Equation Lagrange Differential Equation | Oral Represention, Questioning-Answering, Problem solving |
| 12 | n. Order Linear Differential Equations Theory Differential Operator Basic Theorems for Solutions of Linear Differential Equations | Oral Represention, Questioning-Answering, Problem solving |
| 13 | Homogeneous Linear Differential Equations Inhomogeneous Linear Differential Equations | Oral Represention, Questioning-Answering, Problem solving |
| 14 | 2nd Order Homogeneous Linear Differential Equations with Constant Coefficients | Oral Represention, Questioning-Answering, Problem solving |
| 15 | n. Order Homogeneous Linear Differential Equations with Constant Coefficients | Oral Represention, Questioning-Answering, Problem solving |
| 16 | final exam | |
| Recommend Course Book / Supplementary Book/Reading | ||
| 1 | Elementary Differantial Equations, William E.Boyce, Richard C.Diprima | |
| 2 | Diferensiyel Denklemler ve Sınır Değer Problemleri, Ö. Akın, Palme yayınları | |
| 3 | Adi Diferensiyel Denklemler, Mehmet Çağlıyan, Nisa Çelik, Setenay Doğan | |
| 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 | 3 | 14 | 42 |
| b) Search in internet/Library | 2 | 7 | 14 |
| c) Performance Project | 2 | 8 | 16 |
| 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 | 3 | 8 | 24 |
| mid-term exam | 2 | 1 | 2 |
| Own study for final exam | 3 | 15 | 45 |
| final exam | 2 | 1 | 2 |
| 0 | |||
| 0 | |||
| Total work load; | 187 | ||