Industrial Engineering (English) Preview
Bachelor	TR-NQF-HE: Level 6	QF-EHEA: First Cycle	EQF-LLL: Level 6

Course Introduction and Application Information

Course Code:

MATH205

Course Name:

Differential Equations

Semester:

Fall

Course Credits:

ECTS

Language of instruction:

English

Course Condition:

Does the Course Require Work Experience?:

Type of course:

Compulsory Courses

Course Level:

Bachelor

TR-NQF-HE:6. Master`s Degree

QF-EHEA:First Cycle

EQF-LLL:6. Master`s Degree

Mode of Delivery:

Face to face

Course Coordinator:

Dr. Öğr. Üy. FUNDA ÖZDEMİR

Course Lecturer(s):

Assist. Prof. Dr. FUNDA ÖZDEMIR

Course Assistants:

Course Objective and Content

Course Objectives:	To make the students know mainly the concepts ordinary differential equations, their solution methods, and their applications in modeling and simulating engineering systems.
Course Content:	Introduction to ordinary differential equations, first order differential equations, second order linear equations, higher order linear equations; series solutions of second order linear equations; the Laplace transform, systems of first order linear equations.

Learning Outcomes

The students who have succeeded in this course;
1) Solve first-order separable and linear differential equations.
2) Find the fundamental solution and the general solution of certain second order linear differential equations.
3) Use the Laplace transform method to solve linear ordinary differential equations.
4) Find the particular solution to a nonhomogeneous linear system of ordinary differential equations.
5) Solve higher-order certain linear differential equations and systems of differential equations.
6) Apply mathematical modelling in areas such as physics, engineering, biology or economics.

Course Flow Plan

Week	Subject	Related Preparation
1)	Introduction, classification of differential equations
2)	First order differential equations: linear equations, method of integrating factors, separable equations, difference between linear and nonlinear equations
3)	Exact equations and integrating factors, existence and uniqueness theorem
4)	Second order linear equations: homogeneous equations with constant coefficients, fundamental solutions of linear homogeneous equations, linear independence, Wronskian.
5)	Complex roots, repeated roots; reduction of order
6)	Nonhomogeneous equations: method of undetermined coefficients, variation of parameters
7)	Higher order linear equations: general theory, homogeneous equations with constant coefficients, method of undetermined coefficients, variation of parameters.
8)	Midterm Exam
9)	The Laplace transform: definitions, solution of initial value problems
10)	Step functions, solution of differential equations with discontinuous forcing functions
11)	Impulse functions, the convolution integral
12)	Systems of first order linear equations: introduction, linear independence, eigenvalues, eigenvectors
13)	Complex eigenvalues, fundamental matrices, repeated eigenvalues, nonhomogeneous linear systems
14)	Series Solutions: power series, series solutions near an ordinary point

Sources

Course Notes / Textbooks:	Boyce, William E.; DiPrima, Richard C., Meade, Douglas B., Elementary Differential Equations and Boundary Value Problems, 12th Edition, Wiley-Blackwell, 2021.
References:	Lecture notes

Course - Program Learning Outcome Relationship

Course Learning Outcomes	1	2	3	4	5	6
Program Outcomes
1) Adequate knowledge in mathematics, science and industrial engineering; the ability to use theoretical and practical knowledge in these areas in complex engineering problems.	3	3	3	3	3	3
2) Ability to identify, formulate, and solve complex industrial engineering problems; ability to select and apply appropriate analysis and modeling methods for this purpose.
3) Ability to design a complex industrial system, process, device or product to meet specific requirements under realistic constraints and conditions; ability to apply modern design methods for this purpose.
4) Ability to develop, select and use modern techniques and tools necessary for the analysis and solution of complex problems encountered in industrial engineering applications; ability to use information technologies effectively.
5) Ability to design, conduct experiments, collect data, analyze and interpret results for the study of complex engineering problems or industrial engineering research topics.
6) Ability to work effectively within and multidisciplinary teams; individual study skills.
7) Ability to communicate effectively orally and in writing; knowledge of at least one foreign language; ability to write effectice reports and understand written reports, to prepare design and production reports, to make effective presentations, to give and receive clear and understandable instructions.
8) Awareness of the necessity of lifelong learning; ability to access information, to follow developments in science and technology and to renew continuously.
9) To act in accordance with ethical principles, professional and ethical responsibility; information on the standards used in engineering applications.
10) Information on business practices such as project management, risk management and change management; awareness of entrepreneurship and innovation; information about sustainable development.
11) Knowledge of the effects of industrial engineering practices on health, environment and safety in the universal and social scale and the problems of the era reflected in industrial engineering; awareness of the legal consequences of industrial engineering solutions.

Course - Learning Outcome Relationship

No Effect	1 Lowest	2 Average	3 Highest

	Program Outcomes	Level of Contribution
1)	Adequate knowledge in mathematics, science and industrial engineering; the ability to use theoretical and practical knowledge in these areas in complex engineering problems.	3
2)	Ability to identify, formulate, and solve complex industrial engineering problems; ability to select and apply appropriate analysis and modeling methods for this purpose.
3)	Ability to design a complex industrial system, process, device or product to meet specific requirements under realistic constraints and conditions; ability to apply modern design methods for this purpose.
4)	Ability to develop, select and use modern techniques and tools necessary for the analysis and solution of complex problems encountered in industrial engineering applications; ability to use information technologies effectively.
5)	Ability to design, conduct experiments, collect data, analyze and interpret results for the study of complex engineering problems or industrial engineering research topics.
6)	Ability to work effectively within and multidisciplinary teams; individual study skills.
7)	Ability to communicate effectively orally and in writing; knowledge of at least one foreign language; ability to write effectice reports and understand written reports, to prepare design and production reports, to make effective presentations, to give and receive clear and understandable instructions.
8)	Awareness of the necessity of lifelong learning; ability to access information, to follow developments in science and technology and to renew continuously.
9)	To act in accordance with ethical principles, professional and ethical responsibility; information on the standards used in engineering applications.
10)	Information on business practices such as project management, risk management and change management; awareness of entrepreneurship and innovation; information about sustainable development.
11)	Knowledge of the effects of industrial engineering practices on health, environment and safety in the universal and social scale and the problems of the era reflected in industrial engineering; awareness of the legal consequences of industrial engineering solutions.

Assessment & Grading

Semester Requirements	Number of Activities	Level of Contribution
Midterms	1	% 40
Final	1	% 60
total		% 100
PERCENTAGE OF SEMESTER WORK		% 40
PERCENTAGE OF FINAL WORK		% 60
total		% 100

Workload and ECTS Credit Calculation

Activities	Number of Activities	Preparation for the Activity	Spent for the Activity Itself	Completing the Activity Requirements	Workload
Course Hours	13	0	3		39
Study Hours Out of Class	13	0	4		52
Midterms	1	18	2		20
Final	1	25	2		27
Total Workload					138