Mechanical Engineering

Course Code	Course Name	Year	Period	Semester	T+A+L	Credit	ECTS
99600007	Differential Equations	2	Autumn	3	4+0+0	4	5

Course Type	Compulsory
Course Cycle	Bachelor's (First Cycle) (TQF-HE: Level 6 / QF-EHEA: Level 1 / EQF-LLL: Level 6)
Course Language	English
Methods and Techniques	Anlatım
Mode of Delivery	Face to Face
Prerequisites	-
Coordinator	-
Instructor(s)	Asst. Prof. Nurten URLU ÖZALAN
Instructor Assistant(s)	-

Name and Surname	Room	E-Mail Address	Internal	Meeting Hours
Asst. Prof. Nurten URLU ÖZALAN	A-130	[email protected]	7880	Friday 10:00-12:00

Basic Vocational Courses	X
Specialization / Field Courses
Support Courses
Transferable Skills Courses
Humanities, Communication and Management Skills Courses

Relationship Levels
Lowest	Low	Medium	High	Highest
1	2	3	4	5

#	Program Learning Outcomes	Level
P1	Adequate knowledge of mathematics, science and mechanical engineering disciplines; Ability to use theoretical and applied knowledge in these fields in solving complex engineering problems.	5
P2	Ability to identify, formulate and solve complex Mechanical Engineering problems; ability to select and apply appropriate analysis and modeling methods for this purpose.	5

Upon the successful completion of this course, students will be able to:
No	Learning Outcomes	Outcome Relationship	Measurement Method **
O1	Knows the engineering applications of basic mathematical knowledge and theorems.	P.1.7	1
O2	Know Differential Equations, solution methods and engineering applications	P.2.36	1
** Written Exam: 1, Oral Exam: 2, Homework: 3, Lab./Exam: 4, Seminar/Presentation: 5, Term Paper: 6, Application: 7

Week	Topics
1	Equations, Definition and Classification of Equations, Difference Scale and Scale, Solutions of Difference Equations: Integral Curve, Open-Open Solution, Special Solution, General Solution, Unique Solution, Initial Value Problem. Obtaining of Differential Equations
2	Definition and Classification of Differential Equations, Order and Degree of Differential Equation, Solutions of Differential Equations: Integral Curve, Closed-Open Solution, Special Solution, General Solution, Singular Solution, Initial Value Problem. Derivation of Differential Equations
3	First Order Differential Equations: Separable Difference by Variables, Differential Differences with Variables, Difference Equations, Homogeneous Functions, Homogeneous Difference Equations, Homogeneous Hale Insoluble Difference Equations.
4	First Order Differential Equations: Differential Equations Separable in Their Variables, Differential Equations Transformable into Differential Equations Separable in Their Variables, Homogeneous Functions, Homogeneous Differential Equations, Differential Equations Transformable into Homogeneous Equations.
5	Linear Equations, Integral Multipliers Method, Parameter Change Method.
6	Second Order Linear Differential Equations: Homogeneous Differential Equations with Constant Coefficients, Characteristic Equation, General Solutions of Linear Homogeneous Equations, Linear Independence and Wronskian Determinant.
7	Second Order Linear Difference Equations: Equations with Constant Coefficient Homogeneous Difference, Characteristic Equation, General Solutions of Linear Homogeneous Equations, Linear Independence and Wronskian Determinancy.
8	Complex Roots of Characteristic Equation, Real Roots, Repeated Roots, Order Reduction, Inhomogeneous Equations.
9	Complex Roots of the Characteristic Equation, Real Roots, Repeating Roots, Order Drop, Nonhomogeneous Equations.
10	Method of Indeterminate Coefficients, Method of Variation of Parameters (Constant), Some Special Second Order Differential Equations: Differential Equations without Dependent Variable, Differential Equations without Independent Variable. Variable Coefficient Euler Differential Equation
11	Indeterminate Coefficients Method, Variation Method of Parameters (Constant), Some Special Second Order Differential Equations: Difference Variables, Difference Equations without Independent Variables. Euler Equation Equation with Variable Coefficient
12	Laplace transform, Definition of Laplace Transform
13	Laplace transformation, Definition of Laplace Transformation,
14	Initial Value Problems Solution with Laplace Transformation.

Resources

Differential Equations and Linear Algebra, Stephan W. Goode& Scott A. Annin Pearson Education Inc. (Pearson Printice Hall) 2007.

In-Term Studies	Quantity	Percentage
Attendance	-	-
Laboratory	-	-
Practice	-	-
Course Specific Internship (If Any)	-	-
Homework	-	-
Presentation	-	-
Projects	-	-
Seminar	-	-
Quiz	-	-
Midterms	1	40 (%)
Final Exam	1	60 (%)
Total		100 (%)

	Quantity	Duration	Total Work Load
Course Week Number and Time	14	4	56
Out-of-Class Study Time (Pre-study, Library, Reinforcement)	14	3	42
Midterms	1	20	20
Quiz	0	0	0
Homework	0	0	0
Practice	0	0	0
Laboratory	0	0	0
Project	0	0	0
Workshop	0	0	0
Presentation/Seminar Preparation	0	0	0
Fieldwork	0	0	0
Final Exam	1	30	30
Other	0	0	0
Total Work Load:			148
Total Work Load / 30			4,93
Course ECTS Credits:			5

Relationship Levels
Lowest	Low	Medium	High	Highest
1	2	3	4	5

#	Learning Outcomes	P1	P2
O1	Knows the engineering applications of basic mathematical knowledge and theorems.	5	-
O2	Know Differential Equations, solution methods and engineering applications	-	5