MATH 207 | Course Introduction and Application Information - Department of Mathematics

Course Name

Introduction to Differential Equations I

Code	Semester	Theory (hour/week)	Application/Lab (hour/week)	Local Credits	ECTS
MATH 207	Fall	2	2	3	5

Prerequisites

	MATH 154 To get a grade of at least FD
or	MATH 110 To get a grade of at least FD

Course Language

English

Course Type

Required

Course Level

First Cycle

Mode of Delivery

face to face

Teaching Methods and Techniques of the Course

Problem Solving
Case Study
Q&A

National Occupation Classification

-

Course Coordinator

Doç. Dr. Sevin GÜMGÜM

Course Lecturer(s)

Assistant(s)

Course Objectives	This course is an introduction to the basic concepts, theory, methods and applications of ordinary differential equations. The aim of this course is to solve differential equations and to develop the basics of modeling of real life problems.
Learning Outcomes	The students who succeeded in this course; will be able to apply mathematical modelling in areas such as physics, engineering, biology or economics and interpret their solutions. will be able to solve first order ordinary differential equations and interpret their qualitative behaviour. will be able to find solutions of homogeneous and nonhomogeneous second order linear differential equations. will be able to solve higher order certain linear differential equations. will be able to find solutions of systems of linear diffrential equations. will be able to use the Laplace transform method to solve linear ordinary differential equations.
Course Description	In this course basic concepts of differential equations will be discussed.The types of first order ordinary differential equations will be given and the solution methods will be taught. Also, solution methods for higherorder ordinary differential equations will be analyzed.
Related Sustainable Development Goals

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

Week	Subjects	Related Preparation
1	Introduction, classification of differential equations, Mathematical Modelling.	R. Kent Nagle, Edward B. Saff and Arthur David Snider, ''Fundamentals of Differential Equations and Boundary Value Problems'’, (Pearson, 2011), Section 1.1
2	Separable Differential Equations. First Order Linear Differential Equations.	R. Kent Nagle, Edward B. Saff and Arthur David Snider, ''Fundamentals of Differential Equations and Boundary Value Problems'’, (Pearson, 2011), Section: 2.2, 2.3
3	Exact Differential Equations. Non- Exact Differential Equations.	R. Kent Nagle, Edward B. Saff and Arthur David Snider, ''Fundamentals of Differential Equations and Boundary Value Problems'’, (Pearson, 2011), Section 2.4, 2.5.
4	Bernoulli Differential Equations. Existence and uniqueness theorem.	R. Kent Nagle, Edward B. Saff and Arthur David Snider, ''Fundamentals of Differential Equations and Boundary Value Problems'’, (Pearson, 2011), Section 2.6, 13.2
5	Homogeneous, Non-homogeneous Constant Coefficient Second Order Differential Equations. The Method of Undetermined Coefficients.	R. Kent Nagle, Edward B. Saff and Arthur David Snider, ''Fundamentals of Differential Equations and Boundary Value Problems'’, (Pearson, 2011), Section 4.2, 4.4
6	Non-homogeneous Constant Coefficient Second Order Differential Equations. The Method of Undetermined Coefficients. Variation of parameters.	R. Kent Nagle, Edward B. Saff and Arthur David Snider, ''Fundamentals of Differential Equations and Boundary Value Problems'’, (Pearson, 2011), Section 4.4, 4.6
7	Homogeneous, Non-homogeneous Variable Coefficient Second Order Differential Equations.	R. Kent Nagle, Edward B. Saff and Arthur David Snider, ''Fundamentals of Differential Equations and Boundary Value Problems'’, (Pearson, 2011), Section 4.7
8	Higher order linear equations: General theory, Systems of Linear Differential Equations, Distinct eigenvalues.	R. Kent Nagle, Edward B. Saff and Arthur David Snider, ''Fundamentals of Differential Equations and Boundary Value Problems'’, (Pearson, 2011), Section 9.5-9.6
9	Midterm Exam	-
10	Systems of Linear Differential Equations, Distinct eigenvalues and Complex eigenvalues.	R. Kent Nagle, Edward B. Saff and Arthur David Snider, ''Fundamentals of Differential Equations and Boundary Value Problems'’, (Pearson, 2011), Section 9.5-9.6
11	Systems of Linear Differential Equations, Complex and repeated eigenvalues.	R. Kent Nagle, Edward B. Saff and Arthur David Snider, ''Fundamentals of Differential Equations and Boundary Value Problems'’, (Pearson, 2011), Section 9.5-9.6
12	Laplace Transforms: Definition of the Laplace Transform, Properties of the Laplace Transform, Inverse Laplace Transforms. Solving Initial Value Problems by Laplace Transforms.	R. Kent Nagle, Edward B. Saff and Arthur David Snider, ''Fundamentals of Differential Equations and Boundary Value Problems'’, (Pearson, 2011), Section 7.2, 7.3.,7.4, 7.5.
13	Laplace Transforms: Definition of the Laplace Transform, Properties of the Laplace Transform, Inverse Laplace Transforms. Solving Initial Value Problems by Laplace Transforms.	R. Kent Nagle, Edward B. Saff and Arthur David Snider, ''Fundamentals of Differential Equations and Boundary Value Problems'’, (Pearson, 2011), Section 7.2, 7.3.,7.4, 7.5.
14	Laplace Transform: Systems of Linear Differential Equations (Including Non-homogeneous Case)Series Solutions of Differential Equations.	R. Kent Nagle, Edward B. Saff and Arthur David Snider, ''Fundamentals of Differential Equations and Boundary Value Problems'’, (Pearson, 2011), Section 7.9
15	Semester review
16	Final exam

Course Notes/Textbooks	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.
Suggested Readings/Materials	Shepley L. Ross, ''Introduction to Ordinary Differential Equations'', Fourth Edition, (John Wiley and Sons,1989), ISBN-13: 978-0471032953.

Semester Activities	Number	Weigthing
Participation
Laboratory / Application
Field Work
Quizzes / Studio Critiques	2	20
Portfolio
Homework / Assignments
Presentation / Jury
Project
Seminar / Workshop
Oral Exams
Midterm	1	30
Final Exam	1	50
Total

Weighting of Semester Activities on the Final Grade	3	50
Weighting of End-of-Semester Activities on the Final Grade	1	50
Total

Semester Activities	Number	Duration (Hours)	Workload
Theoretical Course Hours (Including exam week: 16 x total hours)	16	2	32
Laboratory / Application Hours (Including exam week: '.16.' x total hours)	16	2	32
Study Hours Out of Class	14	3	42
Field Work			0
Quizzes / Studio Critiques	2	4	8
Portfolio			0
Homework / Assignments			0
Presentation / Jury			0
Project			0
Seminar / Workshop			0
Oral Exam			0
Midterms	1	16	16
Final Exam	1	20	20
		Total	150

#	Program Competencies/Outcomes	* Contribution Level
#	Program Competencies/Outcomes	1	2	3	4	5
1	To be able to have a grasp of basic mathematics, applied mathematics or theories and applications of statistics.	-	-	-	-	X
2	To be able to use advanced theoretical and applied knowledge, interpret and evaluate data, define and analyze problems, develop solutions based on research and proofs by using acquired advanced knowledge and skills within the fields of mathematics or statistics.	-	-	-	-	-
3	To be able to apply mathematics or statistics in real life phenomena with interdisciplinary approach and discover their potentials.	-	-	-	X	-
4	To be able to evaluate the knowledge and skills acquired at an advanced level in the field with a critical approach and develop positive attitude towards lifelong learning.	-	-	X	-	-
5	To be able to share the ideas and solution proposals to problems on issues in the field with professionals, non-professionals.	-	-	-	-	-
6	To be able to take responsibility both as a team member or individual in order to solve unexpected complex problems faced within the implementations in the field, planning and managing activities towards the development of subordinates in the framework of a project.	-	-	-	-	-
7	To be able to use informatics and communication technologies with at least a minimum level of European Computer Driving License Advanced Level software knowledge.	-	-	-	-	-
8	To be able to act in accordance with social, scientific, cultural and ethical values on the stages of gathering, implementation and release of the results of data related to the field.	-	-	-	-	-
9	To be able to possess sufficient consciousness about the issues of universality of social rights, social justice, quality, cultural values and also environmental protection, worker's health and security.	-	-	-	-	-
10	To be able to connect concrete events and transfer solutions, collect data, analyze and interpret results using scientific methods and having a way of abstract thinking.	-	-	-	-	-
11	To be able to collect data in the areas of Mathematics or Statistics and communicate with colleagues in a foreign language.	-	-	-	-	-
12	To be able to speak a second foreign language at a medium level of fluency efficiently.	-	-	-	-	-
13	To be able to relate the knowledge accumulated throughout the human history to their field of expertise.	-	-	-	-	-