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 Coordinator
Course Lecturer(s)
Course Assistants
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; students are expected to know and understand various ideas, concepts and methods from ordinary differential equations and how these ideas may be used in, or are connected to, the fields of engineering and mathematics. students will be able to learn how they can construct a Lyapunov function to determine the stability/instability of ordinary differential equations (ODE) and construct a new ODE to determine the oscillation/nonoscillation of an ODE.
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
#	Program Qualifications / Competencies	1	2	3	4	5
1	Alanında, bağımsız olarak, bir problem kurgulayabilir, çözüm yöntemi geliştirerek problemi çözebilir ve sonuçları değerlendirebilir				X
2	Matematiğin temel alanlarında ve kendi uzmanlığı olarak seçtiği alanda gerekli alt yapıyı oluşturur.				X
3	Matematik literatürünü ve özel olarak kendi araştırma konusu ile ilgili ulusal ve uluslararası güncel yayınları takip edebilir ve bunlardan kendi araştırma konusu ile ilgili olanları çalışmalarında kullanabilir				X
4	Bilimsel etik değerleri ve kuralları dikkate alır ve mesleki ve toplumsal yaşamda kullanabilir					X
5	Kendi çalışmalarının sonuçlarını veya belli bir konudaki güncel çalışmaları ve bulguları, çeşitli bilimsel toplantılarda topluluk önünde Türkçe ve İngilizce olarak sunabilir ve tartışmalara katılabilir.					X
6	Gerek bireysel, gerek bir çalışma grubunun üyesi olarak çalışabilme becerisini geliştirir				X
7	Yaratıcı ve eleştirel düşünme, problem çözme, özgün bir çalışma üretme becerisini geliştirir. Bilimsel gelişmeleri takip eder, özümsediği bilgilerin analiz, sentez ve değerlendirmesini yapabilir.				X
8	Kazandığı bilgi, beceri ve yetkinlikleri yaşam boyu geliştirmeye açık olur.					X
9	Alanında özümsediği bilgiyi ve problem çözme yeteneğini disiplinler arası çalışmalarda uygulayabilir; karşılaşılan problemleri matematiksel modellerle ifade ederek, matematiksel bakış açısı ile farklı çözüm yöntemleri önerir.			X
10	Matematik temelli yazılımları, bilişim ve iletişim teknolojilerini bilimsel amaçlı kullanabilir.					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	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