COMPUTER ENGINEERING
Bachelor	TR-NQF-HE: Level 6	QF-EHEA: First Cycle	EQF-LLL: Level 6

Ders Genel Tanıtım Bilgileri

Course Code:

MAT2062

Ders İsmi:

Differential Equations

Ders Yarıyılı:

Spring

Ders Kredileri:

Theoretical	Practical	Credit	ECTS
3	0	3	6

Language of instruction:

English

Ders Koşulu:

Ders İş Deneyimini Gerektiriyor mu?:

Type of course:

Non-Departmental Elective

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. Üyesi GÜLSEMAY YİĞİT

Course Lecturer(s):

Course Assistants:

Dersin Amaç ve İçeriği

Course Objectives:

This course covers the fundamental concepts of an introductory level of elementary differential equations with basic concepts, theory, solution methods and applications. Main goal is to develop the basics of modeling at an introductory level and connect this step to the theoretical and methodological resource of mathematics.

Course Content:

In this course basic concepts of elementary differential equations will be covered. The solution techniques for the different types of first order differential equations will be given and the solution methods will be taught. The higher order linear differential equations and solution methods will be discussed. The systems of linear equations will be covered with different techniques. Finally, the Laplace Transform method will be taught to solve linear differential equations.

Learning Outcomes

The students who have succeeded in this course;

Learning Outcomes

1 - Knowledge
Theoretical - Conceptual
2 - Skills
Cognitive - Practical
3 - Competences
Communication and Social Competence
Learning Competence
Field Specific Competence
Competence to Work Independently and Take Responsibility

Ders Akış Planı

Week	Subject	Related Preparation
1)	Classification of differential equations, Explicit solution, implicit solution, Initial Value Problems, Integrals as General and Particular Solutions.
2)	Existence and Uniqueness of Solution. Separable Differential Equations.
3)	First Order Linear Differential Equations.
4)	Substitutions methods. Homogeneous Differential Equations. Bernoulli Differential Equations.
5)	Exact Differential Equations.
6)	Population models. Reducible second order equations.
7)	Theory of Higher Order Linear Differential Equations, Existence and Uniqueness Theorem, Linear Dependence and Independence, Representation of Solutions for Homogeneous and Nonhomogeneous Cases.
8)	Homogeneous Linear Equations with Constant Coefficients. Euler Equations.
9)	Solution of Nonhomogeneous Linear Differential Equations. Method of Undetermined Coefficients.
10)	Solution of Nonhomogeneous Linear Differential Equations. Method of Variation of Parameters.
11)	Theory of Systems of Linear Differential Equations.
12)	The Eigenvalue Method for Systems of Linear Differential Equations.
13)	Laplace Transforms: Definition of the Laplace Transform, Properties of the Laplace Transform. Inverse Laplace Transform.
14)	Solution of Differential Equations by using Laplace Transform.

Sources

Course Notes / Textbooks:	Differential Equations with Boundary Value Problems by C. Henry Edwards & D. E.Penney, sixth edition
References:	Introduction to Ordinary Differential Equations” by Shepley L. Ross. Fourth Edition, John Wiley and Sons.

Ders - Program Öğrenme Kazanım İlişkisi

Ders Öğrenme Kazanımları
Program Outcomes
1) Adequate knowledge in mathematics, science and computer engineering; the ability to use theoretical and practical knowledge in these areas in complex engineering problems.
2) Ability to identify, formulate, and solve complex engineering problems; ability to select and apply appropriate analysis and modeling methods for this purpose.
3) Ability to design a complex 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 computer 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 computer engineering research topics.
6) Ability to work effectively within and multi-disciplinary teams; individual study skills.
7) Ability to communicate effectively in verbal and written Turkish; knowledge of at least one foreign language; ability to write active 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 engineering practices on health, environment and safety in the universal and social scale and the problems of the era reflected in engineering; awareness of the legal consequences of engineering solutions.

Ders - Öğrenme Kazanımı İlişkisi

No Effect	1 Lowest	2 Low	3 Average	4 High	5 Highest

	Program Outcomes	Level of Contribution
1)	Adequate knowledge in mathematics, science and computer engineering; the ability to use theoretical and practical knowledge in these areas in complex engineering problems.
2)	Ability to identify, formulate, and solve complex engineering problems; ability to select and apply appropriate analysis and modeling methods for this purpose.	2
3)	Ability to design a complex system, process, device or product to meet specific requirements under realistic constraints and conditions; ability to apply modern design methods for this purpose.	3
4)	Ability to develop, select and use modern techniques and tools necessary for the analysis and solution of complex problems encountered in computer 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 computer engineering research topics.	3
6)	Ability to work effectively within and multi-disciplinary teams; individual study skills.	2
7)	Ability to communicate effectively in verbal and written Turkish; knowledge of at least one foreign language; ability to write active 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 engineering practices on health, environment and safety in the universal and social scale and the problems of the era reflected in engineering; awareness of the legal consequences of engineering solutions.

Öğrenme Etkinliği ve Öğretme Yöntemleri

Ölçme ve Değerlendirme Yöntemleri ve Kriterleri

Assessment & Grading

Semester Requirements	Number of Activities	Level of Contribution
Quizzes	2	% 20
Midterms	1	% 35
Final	1	% 45
Total		% 100
PERCENTAGE OF SEMESTER WORK		% 55
PERCENTAGE OF FINAL WORK		% 45
Total		% 100