ECTS - Theory of Differential Equations
Theory of Differential Equations (MATH562) Course Detail
| Course Name | Course Code | Season | Lecture Hours | Application Hours | Lab Hours | Credit | ECTS |
|---|---|---|---|---|---|---|---|
| Theory of Differential Equations | MATH562 | Area Elective | 3 | 0 | 0 | 3 | 5 |
| Pre-requisite Course(s) |
|---|
| N/A |
| Course Language | English |
|---|---|
| Course Type | Elective Courses |
| Course Level | Ph.D. |
| Mode of Delivery | Face To Face |
| Learning and Teaching Strategies | Lecture, Question and Answer. |
| Course Lecturer(s) |
|
| Course Objectives | The course aims to introduce and present Initial Value Problem: Existence and Uniqueness of Solutions; Continuation of Solutions; Continuous and Differential Dependence of Solutions. Linear Systems: Linear Homogeneous And Nonhomogeneous Systems with Constant and Variable Coefficients; Structure of Solutions of Systems with Constant and Periodic Coefficients; Higher Order Linear Differential Equations; Sturmian Theory, Stability: Lyapunov Stability and Instability. Lyapunov Functions; Lyapunov's Second Method; Quasilinear Systems. |
| Course Learning Outcomes |
The students who succeeded in this course;
|
| Course Content | IVP: existence and uniqueness, continuation and continuous dependence of solutions; linear systems: linear (non)homogeneous systems with constant and variable coefficients; structure of solutions of systems with periodic coefficients; higher order linear differential equations; Sturmian theory, stability: Lyapunov (in)stability, Lyapunov functions |
Weekly Subjects and Releated Preparation Studies
| Week | Subjects | Preparation |
|---|---|---|
| 1 | Initial Value Problem (IVP): Examples of (IVP) | Read related sections in references |
| 2 | Fundamental Theory: Preliminaries, Existence and Uniqueness of Solutions; | Read related sections in references |
| 3 | Continuation of Solutions; Continuity and Differentiability of Solutions with respect to parameters | Read related sections in references |
| 4 | Linear Systems: Preliminaries, Linear Homogeneous and Nonhomogeneous | Read related sections in references |
| 5 | Linear Systems with Constant and Variable Coefficients | Read related sections in references |
| 6 | Structure of Solutions of Systems with Constant and Periodic Coefficients; | Read related sections in references |
| 7 | Midterm | |
| 8 | Higher Order Linear Differential Equations; | Read related sections in references |
| 9 | Sturmian Theory: Sturm Comparison Theory, Sturm Oscillation Theory. | Read related sections in references |
| 10 | Stability: Definitions of Stability and Boundedness. | Read related sections in references |
| 11 | Lyapunov Stability and Instability | Read related sections in references |
| 12 | Lyapunov Functions; Lyapunav stability and Instability results. Lyapunov's Second Method;. | Read related sections in references |
| 13 | Quasilinear Systems; Linearization | Read related sections in references |
| 14 | Stability of an Equilibrium and Stable Manifold Theorem for Nonautonomous Differential Equations | Read related sections in references |
| 15 | Revision. | |
| 16 | Midterm |
Sources
| Course Book | 1. Richard K. Miller, Anthony N. Michel, Ordinary Differential Equations, 1982, Academic Press |
|---|---|
| Other Sources | 2. W. Kelley, A. Peterson, The Theory of Differential Equations Classical and Qualitative,2004, Prentice–Hall. |
| 3. C. A. Swanson, Comparison and Oscillation Theory, 1968, Academic Press. |
Evaluation System
| Requirements | Number | Percentage of Grade |
|---|---|---|
| Attendance/Participation | - | - |
| Laboratory | - | - |
| Application | - | - |
| Field Work | - | - |
| Special Course Internship | - | - |
| Quizzes/Studio Critics | - | - |
| Homework Assignments | 5 | 30 |
| Presentation | - | - |
| Project | - | - |
| Report | - | - |
| Seminar | - | - |
| Midterms Exams/Midterms Jury | 1 | 30 |
| Final Exam/Final Jury | 1 | 40 |
| Toplam | 7 | 100 |
| Percentage of Semester Work | 60 |
|---|---|
| Percentage of Final Work | 40 |
| Total | 100 |
Course Category
| Core Courses | X |
|---|---|
| Major Area Courses | |
| 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 | Ability to carry out advanced research activities, both individual and as a member of a team | |||||
| 2 | Ability to evaluate research topics and comment with scientific reasoning | |||||
| 3 | Ability to initiate and create new methodologies, implement them on novel research areas and topics | |||||
| 4 | Ability to produce experimental and/or analytical data in systematic manner, discuss and evaluate data to lead scintific conclusions | |||||
| 5 | Ability to apply scientific philosophy on analysis, modelling and design of engineering systems | |||||
| 6 | Ability to synthesis available knowledge on his/her domain to initiate, to carry, complete and present novel research at international level | |||||
| 7 | Contribute scientific and technological advancements on engineering domain of his/her interest area | |||||
| 8 | Contribute industrial and scientific advancements to improve the society through research activities | |||||
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 | 14 | 3 | 42 |
| Presentation/Seminar Prepration | |||
| Project | |||
| Report | |||
| Homework Assignments | 5 | 3 | 15 |
| Quizzes/Studio Critics | |||
| Prepration of Midterm Exams/Midterm Jury | 1 | 10 | 10 |
| Prepration of Final Exams/Final Jury | 1 | 10 | 10 |
| Total Workload | 77 | ||