# 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 3 0 0 3 6
Pre-requisite Course(s)
Math 262 (Ordinary Differential Equations) and Math 231 (Linear Algebra I) or Math 275 (Linear Algebra)
Course Language English N/A Bachelor’s Degree (First Cycle) Face To Face Lecture, Question and Answer. 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. The students who succeeded in this course; know other aspects of ordinary differential equations such as existence-uniqueness theorems, initial and boundary value problems, eigenvalue problems. prove the existence theorem and to learn continuation of solution and dependence on initial value. transform differential equations to systems of higher order ODE and to use the vector notation, Wronskian identity. learn oscillation and comparison theorems. 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 2. Differential Equations, Second Edition, by Shepley L. Ross, John 3. Lectures on Differential Equations, Yılmaz Akyıldız and Ali Yazıcı.

### Evaluation System

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 40 100

### Course Category

Core Courses X

### 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

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