MATH 601 | Course Introduction and Application Information - M.SC. in Computer Engineering (Without Thesis)

Course Name

Differential Equations

Code	Semester	Theory (hour/week)	Application/Lab (hour/week)	Local Credits	ECTS
MATH 601	Fall/Spring	3	0	3	7.5

Prerequisites	None
Course Language	English
Course Type	Elective
Course Level	Third Cycle
Mode of Delivery	-
Teaching Methods and Techniques of the Course	Problem Solving Case Study Q&A
National Occupation Classification	-
Course Coordinator	Dr. Öğr. Üyesi JAMİLA KALANTAROVA
Course Lecturer(s)	Dr. Öğr. Üyesi JAMİLA KALANTAROVA
Assistant(s)	Araş. Gör. Ayşe BELER

Course Objectives

This course aims to give the analysis of linear and nonlinear systems, existence and uniqueness of solutions and stability theory.

Learning Outcomes

The students who succeeded in this course;

will be able to analyze, transform, use in the models and solve the second order differential equations
will be able to solve Systems of Linear differential equations.
will be able to analyze the methods of nonlinear differential equations.
will be able to solve Hamiltonian Systems.
will be able to determine Stability of linear and nonlinear systems.

Course Description

This course contains the results of linear equations and systems, perturbations of linear systems, the existence and uniqueness of nonlinear initial value problems and the stability theory of linear and nonlinear equations. It also includes the boundary value problems.

Course Category	Core Courses
	Major Area Courses
	Supportive Courses
	Media and Management Skills Courses
	Transferable Skill Courses

Week	Subjects	Related Preparation	Learning Outcome
1	Initial-value problems, Picard existence theorem.	John R Graef, Johnny Henderson, Lingju Kong and Xueyan Sherry Liu, ‘’ Ordinary Differential Equations and Boundary Value Problems: Volume I: Advanced Ordinary Differential Equations’’, (World Scientific, 2018), Section 1.2, 1.3
2	Peano existence theorem.	John R Graef, Johnny Henderson, Lingju Kong and Xueyan Sherry Liu, ‘’ Ordinary Differential Equations and Boundary Value Problems: Volume I: Advanced Ordinary Differential Equations’’, (World Scientific, 2018), Section: 1.4
3	Continiuity of solutions.	John R Graef, Johnny Henderson, Lingju Kong and Xueyan Sherry Liu, ‘’ Ordinary Differential Equations and Boundary Value Problems: Volume I: Advanced Ordinary Differential Equations’’, (World Scientific, 2018), Section 2.1, 2.3, 2.4
4	Continuous dependance of solutions on initial conditions, Continuity of solutions wrt Parameter	John R Graef, Johnny Henderson, Lingju Kong and Xueyan Sherry Liu, ‘’ Ordinary Differential Equations and Boundary Value Problems: Volume I: Advanced Ordinary Differential Equations’’, (World Scientific, 2018), Section 2.3, 2.4
5	Linear systems of differential equations	John R Graef, Johnny Henderson, Lingju Kong and Xueyan Sherry Liu, ‘’ Ordinary Differential Equations and Boundary Value Problems: Volume I: Advanced Ordinary Differential Equations’’, (World Scientific, 2018), Section 5.1
6	Stability Theory: First order systems	John R Graef, Johnny Henderson, Lingju Kong and Xueyan Sherry Liu, ‘’ Ordinary Differential Equations and Boundary Value Problems: Volume I: Advanced Ordinary Differential Equations’’, (World Scientific, 2018), Section 7.1
7	Stability Theory: Lyapunov’s method	R. Kent Nagle, Edward B. Saff and Arthur David Snider, ''Fundamentals of Differential Equations and Boundary Value Problems'’, (Pearson, 2011), Section 12.5
8	Stability Theory: Higher order systems	R. Kent Nagle, Edward B. Saff and Arthur David Snider, ''Fundamentals of Differential Equations and Boundary Value Problems'’, (Pearson, 2011), Section: 12.7
9	Perturbated Linear Systems	John R Graef, Johnny Henderson, Lingju Kong and Xueyan Sherry Liu, ‘’ Ordinary Differential Equations and Boundary Value Problems: Volume I: Advanced Ordinary Differential Equations’’, (World Scientific, 2018), Section 8.1
10	Comparison theorems	John R Graef, Johnny Henderson, Lingju Kong and Xueyan Sherry Liu, ‘’ Ordinary Differential Equations and Boundary Value Problems: Volume I: Advanced Ordinary Differential Equations’’, (World Scientific, 2018), Section 4.1
11	Diffrential inequalities	John R Graef, Johnny Henderson, Lingju Kong and Xueyan Sherry Liu, ‘’ Ordinary Differential Equations and Boundary Value Problems: Volume I: Advanced Ordinary Differential Equations’’, (World Scientific, 2018), Section 4.1
12	Diffrential inequalities: Applications	John R Graef, Johnny Henderson, Lingju Kong and Xueyan Sherry Liu, ‘’ Ordinary Differential Equations and Boundary Value Problems: Volume I: Advanced Ordinary Differential Equations’’, (World Scientific, 2018), Section 4.1
13	Boundary value problems	R. Kent Nagle, Edward B. Saff and Arthur David Snider, ''Fundamentals of Differential Equations and Boundary Value Problems'’, (Pearson, 2011), Section. 11.3
14	Boundary value problems	R. Kent Nagle, Edward B. Saff and Arthur David Snider, ''Fundamentals of Differential Equations and Boundary Value Problems'’, (Pearson, 2011), Section. 11.4,11.7
15	Semester Review	Nonlinear Ordinary Differential Equations, D.W.Jordan & P.Smith,Oxford, Fourth Edition
16	Final Exam

Course Notes/Textbooks	John R Graef, Johnny Henderson, Lingju Kong and Xueyan Sherry Liu, ‘’ Ordinary Differential Equations and Boundary Value Problems: Volume I: Advanced Ordinary Differential Equations’’, (World Scientific, 2018), ISBN: 9811221359,9789811221354,9813236450,9789813236455.
Suggested Readings/Materials	Kent Nagle, Edward B. Saff and Arthur David Snider, “Fundamentals of Differential Equations and Boundary Value Problems” 6th Edition, (Pearson, 2011), ISBN-13: 978-0321747747.

Semester Activities	Number	Weigthing
Participation
Laboratory / Application
Field Work
Quizzes / Studio Critiques
Portfolio
Homework / Assignments
Presentation / Jury
Project
Seminar / Workshop
Oral Exams
Midterm	2	60
Final Exam	1	40
Total

Weighting of Semester Activities on the Final Grade	2	60
Weighting of End-of-Semester Activities on the Final Grade	1	40
Total

Semester Activities	Number	Duration (Hours)	Workload
Theoretical Course Hours (Including exam week: 16 x total hours)	16	3	48
Laboratory / Application Hours (Including exam week: '.16.' x total hours)	16		0
Study Hours Out of Class	15	6	90
Field Work			0
Quizzes / Studio Critiques			0
Portfolio			0
Homework / Assignments			0
Presentation / Jury			0
Project			0
Seminar / Workshop			0
Oral Exam			0
Midterms	2	25	50
Final Exam	1	37	37
		Total	225

#	PC Sub	Program Competencies/Outcomes	* Contribution Level
#	PC Sub	Program Competencies/Outcomes	1	2	3	4	5
1	Accesses information in breadth and depth by conducting scientific research in Computer Engineering, evaluates, interprets and applies information.		-	-	-	X	-
2	Is well-informed about contemporary techniques and methods used in Computer Engineering and their limitations.		-	-	X	-	-
3	Uses scientific methods to complete and apply information from uncertain, limited or incomplete data, can combine and use information from different disciplines.		-	-	-	X	-
4	Is informed about new and upcoming applications in the field and learns them whenever necessary.		-	-	-	-	X
5	Defines and formulates problems related to Computer Engineering, develops methods to solve them and uses progressive methods in solutions.		-	-	-	-	X
6	Develops novel and/or original methods, designs complex systems or processes and develops progressive/alternative solutions in designs.		-	-	-	X	-
7	Designs and implements studies based on theory, experiments and modelling, analyses and resolves the complex problems that arise in this process.		-	-	-	X	-
8	Can work effectively in interdisciplinary teams as well as teams of the same discipline, can lead such teams and can develop approaches for resolving complex situations, can work independently and takes responsibility.		-	-	X	-	-
9	Engages in written and oral communication at least in Level B2 of the European Language Portfolio Global Scale.		-	-	X	-	-
10	Communicates the process and the results of his/her studies in national and international venues systematically, clearly and in written or oral form.		-	-	X	-	-
11	Is knowledgeable about the social, environmental, health, security and law implications of Computer Engineering applications, knows their project management and business applications, and is aware of their limitations in Computer Engineering applications.		-	-	X	-	-
12	Highly regards scientific and ethical values in data collection, interpretation, communication and in every professional activity.		-	X	-	-	-

MATH 601 | Course Introduction and Application Information

WEEKLY SUBJECTS AND RELATED PREPARATION STUDIES

EVALUATION SYSTEM

ECTS / WORKLOAD TABLE

COURSE LEARNING OUTCOMES AND PROGRAM QUALIFICATIONS RELATIONSHIP

NEW GÜZELBAHÇE CAMPUS

GLOBAL CAREER

CONTRIBUTION TO SCIENCE

VALUING PEOPLE

BENEFIT TO SOCIETY