GASTRONOMY AND CULINARY ARTS
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
Fall

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) - Possess advanced level theoretical and practical knowledge supported by textbooks with updated information, practice equipments and other resources.
2) Use of advanced theoretical and practical knowledge within the field. -Interpret and evaluate data, define and analyze problems, develop solutions based on research and proofs by using acquired advanced knowledge and skills within the field.
3) Inform people and institutions, transfer ideas and solution proposals to problems in written and orally on issues in the field. - Share the ideas and solution proposals to problems on issues in the field with professionals and non-professionals by the support of qualitative and quantitative data. -Organize and implement project and activities for social environment with a sense of social responsibility. -Monitor the developments in the field and communicate with peers by using a foreign language at least at a level of European Language Portfolio B1 General Level. -Use informatics and communication technologies with at least a minimum level of European Computer Driving License Advanced Level software knowledge.
4) Evaluate the knowledge and skills acquired at an advanced level in the field with a critical approach. -Determine learning needs and direct the learning. -Develop positive attitude towards lifelong learning.
5) Act in accordance with social, scientific, cultural and ethic values on the stages of gathering, implementation and release of the results of data related to the field. - 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.
6) Conduct studies at an advanced level in the field independently. - Take responsibility both as a team member and individually 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

Ders - Öğrenme Kazanımı İlişkisi

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

	Program Outcomes	Level of Contribution
1)	- Possess advanced level theoretical and practical knowledge supported by textbooks with updated information, practice equipments and other resources.	2
2)	Use of advanced theoretical and practical knowledge within the field. -Interpret and evaluate data, define and analyze problems, develop solutions based on research and proofs by using acquired advanced knowledge and skills within the field.	4
3)	Inform people and institutions, transfer ideas and solution proposals to problems in written and orally on issues in the field. - Share the ideas and solution proposals to problems on issues in the field with professionals and non-professionals by the support of qualitative and quantitative data. -Organize and implement project and activities for social environment with a sense of social responsibility. -Monitor the developments in the field and communicate with peers by using a foreign language at least at a level of European Language Portfolio B1 General Level. -Use informatics and communication technologies with at least a minimum level of European Computer Driving License Advanced Level software knowledge.	5
4)	Evaluate the knowledge and skills acquired at an advanced level in the field with a critical approach. -Determine learning needs and direct the learning. -Develop positive attitude towards lifelong learning.	3
5)	Act in accordance with social, scientific, cultural and ethic values on the stages of gathering, implementation and release of the results of data related to the field. - 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.	3
6)	Conduct studies at an advanced level in the field independently. - Take responsibility both as a team member and individually 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	3

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