Department of Mechanical Engineering

MATH 207 | Course Introduction and Application Information

Course Name

Introduction to Differential Equations I

Code	Semester	Theory (hour/week)	Application/Lab (hour/week)	Local Credits	ECTS
MATH 207	SPRING	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 (Core Course)
Course Level	First Cycle
Mode of Delivery	face to face
Teaching Methods and Techniques of the Course	Problem Solving Case Study Q&A
National Occupational Classification Code	-
Course Coordinator	Dr. Öğr. Üyesi Ayşe Beler
Course Lecturer(s)	Dr. Öğr. Üyesi Ayşe Beler Dr. Öğr. Üyesi Neslişah İmamoğlu Karabaş
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;

Name	Description	PC Sub	* Contribution Level
Name	Description	PC Sub	1	2	3	4	5
LO1	Will be able to apply mathematical modelling in areas such as physics, engineering, biology or economics and interpret their solutions.	1.1					X
LO2	will be able to define and classify differential equations, and establish the relationship between the initial value and the existence interval of the solution.	1.1					X
LO3	will be able to solve first order ordinary differential equations and interpret their qualitative behaviour.	1.1					X
LO4	will be able to find solutions of homogeneous and nonhomogeneous second order linear differential equations.	1.1					X
LO5	will be able to find solutions of systems of linear diffrential equations.	1.1					X
LO6	will be able to use the Laplace transform method to solve linear ordinary differential equations.	1.1					X

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 Managment Skills Courses
	Transferable Skill Courses

WEEKLY SUBJECTS AND RELATED PREPARATION STUDIES

Week	Subjects	Required Materials	Learning Outcome
1	Introduction, classification of differential equations, mathematical modeling, and the fundamentals of ecological mathematical models.	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	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	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, and distinct eigenvalues, with applications in ecosystem modeling and biodiversity dynamics.	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, Inverse Laplace Transforms	R. Kent Nagle, Edward B. Saff and Arthur David Snider, ''Fundamentals of Differential Equations and Boundary Value Problems'ʼ, (Pearson, 2011), Section 7.2, 7.3, 7.4	-
13	Solving Initial Value Problems by Laplace Transforms. Laplace transforms of discontinuous functions: Unit step functions, pulse functions and impulse functions.	R. Kent Nagle, Edward B. Saff and Arthur David Snider, ''Fundamentals of Differential Equations and Boundary Value Problems'ʼ, (Pearson, 2011), Section 7.5, 7.9	-
14	Laplace transforms of discontinuous functions: Unit step functions, pulse functions and impulse functions. Convolution Integral, Convolution theorem. Solutions of integro differential equations.	R. Kent Nagle, Edward B. Saff and Arthur David Snider, ''Fundamentals of Differential Equations and Boundary Value Problems'ʼ, (Pearson, 2011), Section 7.6, 7.8 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.

EVALUATION SYSTEM

Semester Activities	Number	Weighting	LO1	LO2	LO3	LO4	LO5	LO6
Quizzes / Studio Critiques	6	18	X	X	X	X	X	X
Midterm	1	32	X	X	X	X	X	X
Final Exam	1	50	X	X	X	X	X	X
Total	8	100

ECTS / WORKLOAD TABLE

Semester Activities	Number	Duration (Hours)	Workload
Participation	-	-	-
Theoretical Course Hours	16	2	32
Laboratory / Application Hours	16	2	32
Study Hours Out of Class	14	3	42
Field Work	-	-	-
Quizzes / Studio Critiques	6	2	12
Portfolio	-	-	-
Homework / Assignments	-	-	-
Presentation / Jury	-	-	-
Project	-	-	-
Seminar / Workshop	-	-	-
Oral Exams	-	-	-
Midterms	1	14	14
Final Exam	1	18	18
		Total	150

COURSE LEARNING OUTCOMES AND PROGRAM QUALIFICATIONS RELATIONSHIP

#	PC Sub	Program Competencies/Outcomes	* Contribution Level
#	PC Sub	Program Competencies/Outcomes	1	2	3	4	5
1	Engineering Knowledge: Knowledge of mathematics, science, basic engineering, computation, and related engineering discipline-specific topics; the ability to apply this knowledge to solve complex engineering problems.
	1	Mathematics					LO1 LO2 LO3 LO4 LO5 LO6
	2	Science
	3	Basic Engineering
	4	Computation
	5	Related engineering discipline-specific topics
	6	The ability to apply this knowledge to solve complex engineering problems
2	Problem Analysis: Ability to identify, formulate and analyze complex engineering problems using basic knowledge of science, mathematics and engineering, and considering the UN Sustainable Development Goals relevant to the problem being addressed.
3	Engineering Design: The ability to devise creative solutions to complex engineering problems; the ability to design complex systems, processes, devices or products to meet current and future needs, considering realistic constraints and conditions.
	1	Ability to design creative solutions to complex engineering problems
	2	Ability to design complex systems, processes, devices or products to meet current and future needs, considering realistic constraints and conditions
4	Use of Techniques and Tools: Ability to select and use appropriate techniques, resources, and modern engineering and computing tools, including estimation and modeling, for the analysis and solution of complex engineering problems, while recognizing their limitations.
5	Research and Investigation: Ability to use research methods to investigate complex engineering problems, including literature research, designing and conducting experiments, collecting data, and analyzing and interpreting results.
	1	Literature research for the study of complex engineering problems
	2	Designing experiments
	3	Ability to use research methods, including conducting experiments, collecting data. analyzing and interpreting results
6	Global Impact of Engineering Practices: Knowledge of the impacts of engineering practices on society, health and safety, economy, sustainability, and the environment, within the context of the UN Sustainable Development Goals; awareness of the legal implications of engineering solutions.
	1	Knowledge of the impacts of engineering practices on society, health and safety, economy, sustainability, and the environment, within the context of the UN Sustainable Development Goals
	2	Awareness of the legal implications of engineering solutions
7	Ethical Behavior: Acting in accordance with the principles of the engineering profession, knowledge about ethical responsibility; awareness of being impartial, without discrimination, and being inclusive of diversity.
	1	Acting in accordance with the principles of the engineering profession, knowledge about ethical responsibility ethical responsibility
	2	Awareness of being impartial and inclusive of diversity, without discriminating on any subject
8	Individual and Teamwork: Ability to work effectively, individually and as a team member or leader on interdisciplinary and multidisciplinary teams (face-to-face, remote or hybrid).
	1	Ability to work individually and within the discipline
	2	Ability to work effectively as a team member or leader in multidisciplinary teams (face-to-face, remote or hybrid)
9	Verbal and Written Communication: Taking into account the various differences of the target audience (such as education, language, profession) on technical issues.
	1	Ability to communicate verbally
	2	Ability to communicate effectively in writing
10	Project Management: Knowledge of business practices such as project management and economic feasibility analysis; awareness of entrepreneurship and innovation.
	1	Knowledge of business practices such as project management and economic feasibility analysis
	2	Awareness of entrepreneurship and innovation
11	Lifelong Learning: Lifelong learning skills that include being able to learn independently and continuously, adapting to new and developing technologies, and thinking questioningly about technological changes.

*1 Lowest, 2 Low, 3 Average, 4 High, 5 Highest

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