MATH 207 | Course Introduction and Application Information - Department of Genetics and Bioengineering

Course Name

Introduction to Differential Equations I

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

Elective

Course Level

First Cycle

Mode of Delivery

-

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

#	Content	PC Sub	* Contribution Level
#	Content	PC Sub	1	2	3	4	5
1	will be able to classify the differential equations.
2	will be able to use solution methods of first order ordinary differential equations.
3	will be able to solve higher order linear differential equations with constant coefficients.
4	will be able to use the Laplace transform method of linear differential equations.
5	will be able to analyze series solutions of linear differential equations.
6	will be able to solve systems of linear differential equations.
7	will be able to analyze approximate methods of solving first-order equations by using the method of succesive approximations and the Euler method.

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.

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

Week	Subjects	Related Preparation	Learning Outcome
1	Description and Classification of differential equations. 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 1.1, 2.2, 2.3
2	Description and Classification of differential equations. 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: 1.1, 2.2, 2.3
3	Exact Differential Equations. Non- Exact Differential Equations. Bernoulli Differential Equations. Numerical Solutions to IVPs	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. 3.6
4	Numerical Solutions to IVPs. Explicit Euler, Improved Euler, Heunn's Method	R. Kent Nagle, Edward B. Saff and Arthur David Snider, ''Fundamentals of Differential Equations and Boundary Value Problems'’, (Pearson, 2011), Section 3.6
5	Homogeneous Constant 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 4.2
6	Non-homogeneous Constant Coefficient Second Order Differential Equations. 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
7	Systems of Linear Differential Equations/ Matrix Exponential	R. Kent Nagle, Edward B. Saff and Arthur David Snider, ''Fundamentals of Differential Equations and Boundary Value Problems'’, (Pearson, 2011), Section 9.5-9.8
8	Midterm
9	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.
10	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.
11	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
12	Power Series Solutions: Series Solutions around an Ordinary Point.	R. Kent Nagle, Edward B. Saff and Arthur David Snider, ''Fundamentals of Differential Equations and Boundary Value Problems'’, (Pearson, 2011), Section 8.3
13	Series Solutions around a Singular Point.	R. Kent Nagle, Edward B. Saff and Arthur David Snider, ''Fundamentals of Differential Equations and Boundary Value Problems'’, (Pearson, 2011), Section 8.3
14	Review
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	LO 1	LO 2	LO 3	LO 4	LO 5	LO 6	LO 7
Participation
Laboratory / Application
Field Work
Quizzes / Studio Critiques	2	15
Portfolio
Homework / Assignments
Presentation / Jury
Project
Seminar / Workshop
Oral Exams
Midterm	1	40
Final Exam	1	45
Total

Weighting of Semester Activities on the Final Grade	3	55
Weighting of End-of-Semester Activities on the Final Grade	1	45
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

#	PC Sub	Program Competencies/Outcomes	* Contribution Level
#	PC Sub	Program Competencies/Outcomes	1	2	3	4	5
1	To have adequate knowledge in Mathematics, Science and Genetics and Bioengineering; to be able to use theoretical and applied information in these areas on complex engineering problems.		-	-	-	-	-
2	To be able to identify, define, formulate, and solve complex Genetics and Bioengineering problems; to be able to select and apply proper analysis and modeling methods for this purpose.		-	-	-	-	-
3	To be able to design a complex system, process, device or product under realistic constraints and conditions, in such a way as to meet the requirements; to be able to apply modern design methods for this purpose.		-	-	-	-	-
4	To be able to devise, select, and use modern techniques and tools needed for analysis and solution of complex problems in Genetics and Bioengineering applications; to be able to use information technologies effectively.		-	-	-	-	-
5	To be able to design and conduct experiments, gather data, analyze and interpret results for investigating complex engineering problems or Genetics and Bioengineering research topics.		-	-	-	-	-
6	To be able to work efficiently in Genetics and Bioengineering disciplinary and multi-disciplinary teams; to be able to work individually.		-	-	-	-	-
7	To be able to communicate effectively in Turkish, both orally and in writing; to be able to author and comprehend written reports, to be able to prepare design and implementation reports, to present effectively, to be able to give and receive clear and comprehensible instructions.		-	-	-	-	-
8	To have knowledge about global and social impact of Genetics and Bioengineering practices on health, environment, and safety; to have knowledge about contemporary issues as they pertain to engineering; to be aware of the legal ramifications of Genetics and Bioengineering solutions.		-	-	-	-	-
9	To be aware of ethical behavior, professional and ethical responsibility; to have knowledge about standards utilized in Genetics and Bioengineering applications.		-	-	-	-	-
10	To have knowledge about industrial practices such as project management, risk management, and change management; to have awareness of entrepreneurship and innovation; to have knowledge about sustainable development.		-	-	-	-	-
11	To be able to collect data in the area of Genetics and Bioengineering, and to be able to 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 recognize the need for lifelong learning; to be able to access information, to be able to stay current with developments in science and technology; to be able to relate the knowledge accumulated throughout the human history to Genetics and Bioengineering.		-	-	-	-	-