DIFFERENTIAL EQUATIONS PROGRAMME COURSE DESCRIPTION

Code	Name of the Course Unit	Semester	In-Class Hours (T+P)	Credit	ECTS Credit
MAT203	DIFFERENTIAL EQUATIONS	4	4	3	5

GENERAL INFORMATION
Language of Instruction :	Turkish
Level of the Course Unit :	BACHELOR'S DEGREE, TYY: + 6.Level, EQF-LLL: 6.Level, QF-EHEA: First Cycle
Type of the Course :	Compulsory
Mode of Delivery of the Course Unit	-
Coordinator of the Course Unit	Prof. OSMAN KOPMAZ
Instructor(s) of the Course Unit
Course Prerequisite	No

OBJECTIVES AND CONTENTS
Objectives of the Course Unit:	This is one of the basic calculus course of the sequence which serves as the foundation of all advanced subjects in applied and theoretical mathematics.
Contents of the Course Unit:	First order equations: separable, linear, homogeneous exact equations, orthogonal and oblique trajectories, applications. Higher order linear differential equations: Reduction of order, method of undetermine coefficients, method of variation of parameters, Cauchy-Euler equations, operator methods, applications. Power series solutions: ordinary points, regular singular points. The Laplace Transform: basic properties, solution of initial value problems, convolution integral, solution of various equations. Systems of linear differential epuations: Brief discussion of theory of linear systems, solving linear systems; by operator method, by Laplace transform. Introduction to Partial Differential equations: Separation of variables.

KEY LEARNING OUTCOMES OF THE COURSE UNIT (On successful completion of this course unit, students/learners will or will be able to)
Learning all the solution methods of First order Differential Equations involving functions of one variable.
Learning the solution methods of first order higher order differential equations
Learning the solution methods of linear differential equations
Learning the solution methods of higher order differential equations

WEEKLY COURSE CONTENTS AND STUDY MATERIALS FOR PRELIMINARY & FURTHER STUDY
Week	Preparatory	Topics(Subjects)	Method
1	-	Preliminaries. Solutions. Existence-Uniqueness Theorem. Separable Equations. Linear Equations. Homogeneous Equations.	-
2	-	Exact Equations and Integrating Factors.Substitutions. Approximate solutions (2.6.1 and 2.6.2). Application	-
3	-	Basic Theory of Higher Order Linear Equations.	-
4	-	Reduction of Order. Homogeneous Constant Coefficient Equations.	-
5	-	Undetermined Coefficients. Variation of Parameters.	-
6	-	The Cauchy-Euler equation. Operator Method.	-
7	-	Power Series Solutions (ordinary points).	-
8	-	MID-TERM EXAM	-
9	-	Power Series Solutions (regular singular points)	-
10	-	The Laplace Transform. Basic Properties. Convolution.	-
11	-	Solution of Differential Equations by the Laplace Transform.	-
12	-	Solutions of Systems of Linear Differential Equations by the Laplace Transform.	-
13	-	Solutions of Systems of Linear Differential Equations by Elimination: simple elimination and operator method.	-
14	-	Introduction to Partial Differential Equations	-
15	-	Introduction to Partial Differential Equations	-
16	-	FINAL EXAM	-
17	-	FINAL EXAM	-

SOURCE MATERIALS & RECOMMENDED READING
Shepley L. Ross, Differential Equations.
Prof Dr Metin Başarır, Prof Dr Eyüp Sabri Türker, Differential Equations with Solved Problems, Değişim Publications
Schaum's Series, Differential Equations, Nobel Publishing.
Prof. Dr. Mustafa Bayram, Differential Equations.
Nagle, Saff, Snider, Fundamentals of Differential Equations.

ASSESSMENT
Assessment & Grading of In-Term Activities	Number of Activities	Degree of Contribution (%)	Description

Level of Contribution
0	1	2	3	4	5

KNOWLEDGE
Theoretical
	Programme Learning Outcomes	Level of Contribution
		0	1	2	3	4	5
1	Ability to apply mathematics, science and engineering knowledge.						5

KNOWLEDGE
Factual
	Programme Learning Outcomes	Level of Contribution
		0	1	2	3	4	5
1	Ability to apply mathematics, science and engineering knowledge.						5

SKILLS
Cognitive
	Programme Learning Outcomes	Level of Contribution
		0	1	2	3	4	5
1	Ability to design experiments, conduct experiments, collect data, analyze and interpret results.	0

SKILLS
Practical
	Programme Learning Outcomes	Level of Contribution
		0	1	2	3	4	5
1	A system, product or process has economic, environmental, social, political, ethical, health and safety, under realistic constraints and conditions such as feasibility and sustainability, Ability to design to meet requirements.		1

OCCUPATIONAL
Autonomy & Responsibility
	Programme Learning Outcomes	Level of Contribution
		0	1	2	3	4	5
1	Ability to work in teams with different disciplines		1

OCCUPATIONAL
Learning to Learn
	Programme Learning Outcomes	Level of Contribution
		0	1	2	3	4	5
1	Ability to identify, formulate and solve engineering problems					4

OCCUPATIONAL
Communication & Social
	Programme Learning Outcomes	Level of Contribution
		0	1	2	3	4	5
1	Awareness of having professional and ethical responsibilities.		1
2	Ability to communicate effectively verbally and in writing.		1

OCCUPATIONAL
Occupational and/or Vocational
	Programme Learning Outcomes	Level of Contribution
		0	1	2	3	4	5
1	The ability to have a comprehensive education to understand the impact of engineering solutions on global and social dimensions.		1
2	Awareness of the necessity of lifelong learning and the ability to do so.	0
3	The ability to have knowledge about current/contemporary issues.		1
4	Ability to use the techniques required for engineering applications and modern engineering and calculation equipment.				3

WORKLOAD & ECTS CREDITS OF THE COURSE UNIT
Workload for Learning & Teaching Activities
Type of the Learning Activites	Learning Activities (# of week)	Duration (hours, h)	Workload (h)
Lecture & In-Class Activities	14	3	42
Preliminary & Further Study	14	3	42
Land Surveying	0	0	0
Group Work	0	0	0
Laboratory	0	0	0
Reading	3	4	12
Assignment (Homework)	6	5	30
Project Work	0	0	0
Seminar	0	0	0
Internship	0	0	0
Technical Visit	0	0	0
Web Based Learning	0	0	0
Implementation/Application/Practice	0	0	0
Practice at a workplace	0	0	0
Occupational Activity	0	0	0
Social Activity	0	0	0
Thesis Work	0	0	0
Field Study	0	0	0
Report Writing	0	0	0
Final Exam	1	1	1
Preparation for the Final Exam	0	0	0
Mid-Term Exam	1	1	1
Preparation for the Mid-Term Exam	0	0	0
Short Exam	0	0	0
Preparation for the Short Exam	0	0	0
TOTAL	39	0	128