ECTS - Theory of Ordinary Differential Equations
Theory of Ordinary Differential Equations (MATH360) Course Detail
| Course Name | Course Code | Season | Lecture Hours | Application Hours | Lab Hours | Credit | ECTS |
|---|---|---|---|---|---|---|---|
| Theory of Ordinary Differential Equations | MATH360 | Area Elective | 3 | 0 | 0 | 3 | 6 |
| Pre-requisite Course(s) |
|---|
| (MATH262 veya MATH231) |
| Course Language | English |
|---|---|
| Course Type | Elective Courses |
| Course Level | Bachelor’s Degree (First Cycle) |
| Mode of Delivery | Face To Face |
| Learning and Teaching Strategies | Lecture, Question and Answer. |
| Course Lecturer(s) |
|
| Course Objectives | The course is designed to present other aspects of ordinary differential equations to the student who has so far seen the basic solution techniques. The emphasis is on existence-uniqueness and related questions; initial value, boundary value and eigenvalue problems are introduced within that concept. Examples and problems aim to clarify the theory. |
| Course Learning Outcomes |
The students who succeeded in this course;
|
| Course Content | First-order ordinary differential equations, the Existence and Uniqueness Theorem, systems and higher-order ordinary differential equations, linear differential equations, boundary value problems and eigenvalue problems, oscillation and comparison theorems. |
Weekly Subjects and Releated Preparation Studies
| Week | Subjects | Preparation |
|---|---|---|
| 1 | I. First Order Ordinary Differential Equations: Introduction | pp. 1-3 |
| 2 | Tangent Line Approximation, Cauchy-Euler Method | pp. 4-7 |
| 3 | The Graph Method, Direction Fields, E-U of Solutions of IVP’s | pp. 8-21 |
| 4 | II. Proof of Existence and Uniqueness (E-U) Theorem: Differential Inequalities, Integral Inequalities and Gronwall’s Lemma | pp. 22-28 |
| 5 | Integral Equations,The Uniquenness Theorem, Picard’s Method. Preparation of Existence Theorem | pp. 29-42 |
| 6 | Proof of Existence Theorem, Continuation of Solution, Dependence on Initial Value | pp. 43-61 |
| 7 | Midterm | |
| 8 | III. Systems and Higher order Ordinary Differential Equations:Introduction. The Vector Notation, Initial Value Problems | pp. 62-72 |
| 9 | The Uniqueness Theorem, Picard’s Method, The Existence Theorem | pp. 73-86 |
| 10 | Continuation of Solution, Dependence on Parameter, Complex Valued Equations | pp. 87-104 |
| 11 | IV. Linear Differential Equations: General Theory, Second Order Linear Equations and the Wronskian Identity | pp. 105-116 |
| 12 | V. Boundary Value Problems and Eigenvalue Problems:Boundary Value Problems (BVP), Examples | pp. 117-125 |
| 13 | The number of Solutions of BVP, Eigenvalue Problems | pp. 126-142 |
| 14 | VI. Oscillation and Comparison Theorems: Zeros of Solutions | pp. 143-150 |
| 15 | An Eigenvalue Problem | pp. 151-154 |
| 16 | Final Exam |
Sources
| Course Book | 1. Introduction to Theoretical Aspects of Ordinary Differential Equations, A. K. Erkip |
|---|---|
| Other Sources | 2. Differential Equations, Second Edition, by Shepley L. Ross, John |
| 3. Lectures on Differential Equations, Yılmaz Akyıldız and Ali Yazıcı. |
Evaluation System
| Requirements | Number | Percentage of Grade |
|---|---|---|
| Attendance/Participation | - | - |
| Laboratory | - | - |
| Application | - | - |
| Field Work | - | - |
| Special Course Internship | - | - |
| Quizzes/Studio Critics | - | - |
| Homework Assignments | - | - |
| Presentation | - | - |
| Project | - | - |
| Report | - | - |
| Seminar | - | - |
| Midterms Exams/Midterms Jury | 2 | 60 |
| Final Exam/Final Jury | 1 | 40 |
| Toplam | 3 | 100 |
| Percentage of Semester Work | 60 |
|---|---|
| Percentage of Final Work | 40 |
| Total | 100 |
Course Category
| Core Courses | |
|---|---|
| Major Area Courses | X |
| Supportive Courses | |
| Media and Managment Skills Courses | |
| Transferable Skill Courses |
The Relation Between Course Learning Competencies and Program Qualifications
| # | Program Qualifications / Competencies | Level of Contribution | ||||
|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | ||
| 1 | Has the ability to apply scientific knowledge gained in the undergraduate education and to expand and extend knowledge in the same or in a different area | X | ||||
| 2 | Can apply gained knowledge and problem solving abilities in inter-disciplinary research | X | ||||
| 3 | Has the ability to work independently within research area, to state the problem, to develop solution techniques, to solve the problem, to evaluate the obtained results and to apply them when necessary | X | ||||
| 4 | Takes responsibility individually and as a team member to improve systematic approaches to produce solutions in unexpected complicated situations related to the area of study | X | ||||
| 5 | Can develop strategies, implement plans and principles on the area of study and can evaluate obtained results within the framework | X | ||||
| 6 | Can develop and extend the knowledge in the area and to use them with scientific, social and ethical responsibility | X | ||||
| 7 | Has the ability to follow recent developments within the area of research, to support research with scientific arguments and data, to communicate the information on the area of expertise in a systematically by means of written report and oral/visual presentation | X | ||||
| 8 | To have an oral and written communication ability in at least one of the common foreign languages ("European Language Portfolio Global Scale", Level B2) | X | ||||
| 9 | Has software and hardware knowledge in the area of expertise, and has proficient information and communication technology knowledge | X | ||||
| 10 | Follows scientific, cultural, and ethical criteria in collecting, interpreting and announcing data in the research area and has the ability to teach. | X | ||||
| 11 | Has professional ethical consciousness and responsibility which takes into account the universal and social dimensions in the process of data collection, interpretation, implementation and declaration of results in mathematics and its applications. | X | ||||
ECTS/Workload Table
| Activities | Number | Duration (Hours) | Total Workload |
|---|---|---|---|
| Course Hours (Including Exam Week: 16 x Total Hours) | |||
| Laboratory | |||
| Application | |||
| Special Course Internship | |||
| Field Work | |||
| Study Hours Out of Class | 16 | 5 | 80 |
| Presentation/Seminar Prepration | |||
| Project | |||
| Report | |||
| Homework Assignments | |||
| Quizzes/Studio Critics | |||
| Prepration of Midterm Exams/Midterm Jury | 2 | 16 | 32 |
| Prepration of Final Exams/Final Jury | |||
| Total Workload | 112 | ||