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 | Acquires skills to use the advanced theoretical and applied knowledge obtained at the mathematics bachelors program to do further academic and scientific research in both mathematics-based graduate programs and public or private sectors. | X | ||||
| 2 | Transplants and applies the theoretical and applicable knowledge gained in their field to the secondary education by using suitable tools and devices. | X | ||||
| 3 | Acquires the skill of choosing, using and improving problem solving techniques which are needed for modeling and solving current problems in mathematics or related fields by using the obtained knowledge and skills. | X | ||||
| 4 | Acquires analytical thinking and uses time effectively in the process of deduction. | X | ||||
| 5 | Acquires basic software knowledge necessary to work in the computer science related fields and together with the skills to use information technologies effectively. | X | ||||
| 6 | Obtains the ability to collect data, to analyze, interpret and use statistical methods necessary in decision making processes. | X | ||||
| 7 | Acquires the level of knowledge to be able to work in the mathematics and related fields and keeps professional knowledge and skills up-to-date with awareness in the importance of lifelong learning. | X | ||||
| 8 | Takes responsibility in mathematics related areas and has the ability to work affectively either individually or as a member of a team. | X | ||||
| 9 | Has proficiency in English language and has the ability to communicate with colleagues and to follow the innovations in mathematics and related fields. | X | ||||
| 10 | Has the ability to communicate ideas with peers supported by qualitative and quantitative data. | X | ||||
| 11 | Has professional and 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 | ||