Differential Equations (MATH276) Course Detail

Course Name	Course Code	Season	Lecture Hours	Application Hours	Lab Hours	Credit	ECTS
Differential Equations	MATH276	4. Semester	4	0	0	4	6

Pre-requisite Course(s)
MATH158 ve MATH152

Course Language	English
Course Type	Compulsory Departmental Courses
Course Level	Bachelor’s Degree (First Cycle)
Mode of Delivery	Face To Face
Learning and Teaching Strategies	Lecture, Question and Answer.
Course Coordinator
Course Lecturer(s)
Course Assistants
Course Objectives	The course is specifically designed for engineering students as this material is applicable to many fields. The purpose of this course is to provide an understanding of ordinary differential equations (ODE's), systems of ODE’s and to give methods for solving them. This course provides also a preliminary information about partial differential equations (PDE's).
Course Learning Outcomes	The students who succeeded in this course; be able to determine the existence and uniqueness of a solution and select the appropriate method for finding the solution. use appropriate methods for solution of first, second and higher order ODE’s. solve differential equations using power series and Laplace transform methods. solve linear systems of ODE’s by using elimination and Laplace transform methods. find Fourier series expansions of periodic functions. solve some elementary PDE’s such as heat, wave and Laplace equations by the method of separation of variables technique.
Course Content	First-order, higher-order linear ordinary differential equations, series solutions of differential equations, Laplace transforms, linear systems of ordinary differential equations, Fourier analysis and partial differential equations.

Weekly Subjects and Releated Preparation Studies

Week	Subjects	Preparation
1	First Order Ordinary Differential Equations: Preliminaries, pp. 1-5	pp. 1-5
2	Solutions, Existence-Uniqueness Theorem, Separable Equations, Linear Equations.	pp. 5-27
3	Bernoulli Equations, Homogeneous Equations, Exact Equations and Integrating Factors.	pp. 27-49
4	Substitutions, Higher Order Linear Ordinary Differential Equations: Basic Theory of Higher Order Linear Equations	pp. 49-98
5	Reduction of Order Method, Homogeneous Constant Coefficient Equations	pp. 98-113
6	Undetermined Coefficients Method, Variation of Parameters Method	pp. 113-125
7	Midterm
8	Cauchy-Euler Equations, Series Solutions of Ordinary Differential Equations: Power Series Solutions (Ordinary Point)	pp. 125-191
9	Power Series Solutions (Ordinary Point) (continued), Power Series Solutions (Regular-Singular Point)	pp. 191-221
10	Laplace Transforms: Basic Properties of the Laplace Transforms, Convolution	pp. 223-244
11	Solution of Differential Equations by the Laplace Transforms	pp. 244-255
12	Systems of Linear Ordinary Differential Equations: Solution of Systems of Linear ODE Using Elimination	pp. 257-291
13	Solution of Systems of Linear ODE Using Laplace Transforms	pp. 292-306
14	Fourier Analysis: Odd and Even Functions, Periodic Functions, Trigonometric Series, Fourier Series and Fourier Sine and Fourier Cosine Series for Functions of Any Period	pp. 319-333
15	Partial Differential Equations: Separation of Variables, Solution of Heat, Wave and Laplace Equations	pp. 307-319 and pp. 333-335
16	Final Exam

Sources

Course Book	1. Lectures on Differential Equations, E. Akyıldız, Y. Akyıldız, Ş.Alpay, A. Erkip and A.Yazıcı,, Matematik Vakfı Yayın No:1
Other Sources	2. Differential Equations, 2nd Edition, Shepley L. Ross, John Wiley and Sons, 1984.
	3. Advanced Engineering Mathematics, 8th Edition, Erwin Kreyszig, John Wiley and Sons, 1998.
	4. Ordinary Differential Equations Problem Book with Solutions, Rajeh Eid, Atılım University Publications 16, Ankara, Atılım University, 2005.

Evaluation System

Requirements	Number	Percentage of Grade
Attendance/Participation	-	-
Laboratory	-	-
Application	-	-
Field Work	-	-
Special Course Internship	-	-
Quizzes/Studio Critics	-	-
Homework Assignments	-	-
Presentation	-	-
Project	-	-
Report	-	-
Seminar	-	-
Midterms Exams/Midterms Jury	2	60
Final Exam/Final Jury	1	40
Toplam	3	100

Percentage of Semester Work	60
Percentage of Final Work	40
Total	100

Course Category

Core Courses	X
Major Area Courses
Supportive Courses
Media and Managment Skills Courses
Transferable Skill Courses

The Relation Between Course Learning Competencies and Program Qualifications

#	Program Qualifications / Competencies	Level of Contribution
#	Program Qualifications / Competencies	1	2	3	4	5
1	Adequate knowledge of mathematics, physical sciences and the subjects specific to engineering disciplines; the ability to apply theoretical and practical knowledge of these areas in the solution of complex engineering problems.					X
2	The ability to define, formulate, and solve complex engineering problems; the ability to select and apply proper analysis and modeling methods for this purpose.
3	The ability to design a complex system, process, device or product under realistic constraints and conditions in such a way as to meet the specific requirements; the ability to apply modern design methods for this purpose.
4	The ability to select, and use modern techniques and tools needed to analyze and solve complex problems encountered in engineering practices; the ability to use information technologies effectively.
5	The ability to design experiments, conduct experiments, gather data, and analyze and interpret results for investigating complex engineering problems or research areas specific to engineering disciplines.
6	The ability to work efficiently in inter-, intra-, and multi-disciplinary teams; the ability to work individually.
7	(a) Sözlü ve yazılı etkin iletişim kurma becerisi; etkin rapor yazma ve yazılı raporları anlama, tasarım ve üretim raporları hazırlayabilme, etkin sunum yapabilme, açık ve anlaşılır talimat verme ve alma becerisi. (b) En az bir yabancı dil bilgisi; bu yabancı dilde etkin rapor yazma ve yazılı raporları anlama, tasarım ve üretim raporları hazırlayabilme, etkin sunum yapabilme, açık ve anlaşılır talimat verme ve alma becerisi.
8	Recognition of the need for lifelong learning; the ability to access information, follow developments in science and technology, and adapt and excel oneself continuously.
9	Acting in conformity with the ethical principles; professional and ethical responsibility and knowledge of the standards employed in engineering applications.
10	Knowledge of business practices such as project management, risk management, and change management; awareness of entrepreneurship and innovation; knowledge of sustainable development.
11	Knowledge of the global and social effects of engineering practices on health, environment, and safety issues, and knowledge of the contemporary issues in engineering areas; awareness of the possible legal consequences of engineering practices.
12	(a) Knowledge of (i) fluid mechanics, (ii) heat transfer, (iii) manufacturing process, (iv) electronics and control, (v) vehicle components design, (vi) vehicle dynamics, (vii) vehicle propulsion/drive and power systems, (viii) technical laws and regulations in automotive engineering field, and (ix) vehicle verification tests. (b) The ability to merge and apply these knowledge in solving multi-disciplinary automotive problems.
13	The ability to make use of theoretical, experimental, and simulation methods, and computer aided design techniques in automotive engineering field.
14	The ability to work in the field of vehicle design and manufacturing.

ECTS/Workload Table

Activities	Number	Duration (Hours)	Total Workload
Course Hours (Including Exam Week: 16 x Total Hours)
Laboratory
Application
Special Course Internship
Field Work
Study Hours Out of Class	14	4	56
Presentation/Seminar Prepration
Project
Report
Homework Assignments
Quizzes/Studio Critics
Prepration of Midterm Exams/Midterm Jury	2	10	20
Prepration of Final Exams/Final Jury	1	10	10
Total Workload			86