PAÜ .:. Eğitim Öğretim Bilgi Sistemi

COURSE INFORMATION

Course Code	Course Title	L+P Hour	Semester	ECTS
MAT 219	DIFFERENTIAL EQUATIONS	2 + 2	3rd Semester	6

COURSE DESCRIPTION

Course Level	Bachelor's Degree
Course Type	Compulsory
Course Objective	The aim of this course is to teach ordinary differential equations from both physical and mathematical points of view.
Course Content	Basic Concepts, First Order Differential Equations and Applications, Higher Order Linear Differential Equations with Constant and Variable Coefficients, Higher Order Nonlinear Differential Equations, Systems of Linear Differential Equations, Power Series Solutions.
Prerequisites	No the prerequisite of lesson.
Corequisite	No the corequisite of lesson.
Mode of Delivery	Face to Face

COURSE LEARNING OUTCOMES

1	Knows the basic informations.
2	Learns the First Order Differential Equations and Applications.
3	Knows the Higher Order Linear Differential Equations with Constant and Variable Coefficients.
4	Learns the Higher Order Nonlinear Differential Equations.
5	Solves the systems of linear equations.
6	Finds the serial solutions.

COURSE'S CONTRIBUTION TO PROGRAM

	PO 01	PO 02	PO 03	PO 04	PO 05	PO 06	PO 07	PO 08	PO 09	PO 10	PO 11	PO 12	PO 13	PO 14	PO 15	PO 16	PO 17	PO 18	PO 19	PO 20
LO 001	5	5	5	3	3	1	1	1	1	1	3	3	1
LO 002	5	5	5	3	3	1	1	1	1	1	3	3	1
LO 003	5	5	5	3	3	1	1	1	1	1	3	3	1
LO 004	5	5	5	3	3	1	1	1	1	1	3	3	1
LO 005	5	5	5	3	3	1	1	1	1	1	3	3	1
LO 006	5	5	5	3	3	1	1	1	1	1	3	3	1
Sub Total	30	30	30	18	18	6	6	6	6	6	18	18	6
Contribution	5	5	5	3	3	1	1	1	1	1	3	3	1	0	0	0	0	0	0	0

ECTS ALLOCATED BASED ON STUDENT WORKLOAD BY THE COURSE DESCRIPTION

Activities	Quantity	Duration (Hour)	Total Work Load (Hour)
Course Duration (14 weeks/theoric+practical)	14	4	56
Hours for off-the-classroom study (Pre-study, practice)	14	3	42
Mid-terms	1	25	25
Final examination	1	33	33
Total Work Load ECTS Credit of the Course			156 6

COURSE DETAILS

Select Year

	Course Term	No	Instructors
Details	2023-2024 Fall	13	UĞUR YÜCEL

Course Details

Course Code	Course Title	L+P Hour	Course Code	Language Of Instruction	Course Semester
MAT 219	DIFFERENTIAL EQUATIONS	2 + 2	13	Turkish	2023-2024 Fall

Course Coordinator	E-Mail	Phone Number	Course Location	Attendance
Prof. Dr. UĞUR YÜCEL	uyucel@pau.edu.tr		MUH A0210	%80

Goals		The aim of this course is to teach ordinary differential equations from both physical and mathematical points of view.
Content		Basic Concepts, First Order Differential Equations and Applications, Higher Order Linear Differential Equations with Constant and Variable Coefficients, Higher Order Nonlinear Differential Equations, Systems of Linear Differential Equations, Power Series Solutions.

Topics

Weeks	Topics
1	Basic Concepts: Definition of a differential equation, classifications, solution of a differential equation
2	First order differential equations: Seperable Equations, Homogeneous Equations, Linear Equations
3	First order differential equations: Bernoulli Equation, Exact differential equations, Integrating factor, Ricatti Equation
4	Applications of First-Order Differential Equations: Orthogonal trajectories, Growth and Decay, Cooling, Applications of nonlinear equations
5	First Order and Higher Degree Differential Equations
6	Some Higher-Order Non-Linear Differential Equations
7	Linear Differential Equations of Higher-Order
8	Solutions of Linear Equations, Homogeneous Linear Equations
9	The Method of Undetermined Coefficients, The Variation of Parameters Method
10	Cauchy-Euler Differential Equation
11	Applications of Second-Order Differential Equations
12	Systems of Differential Equations: Examples of Systems, Operator Method, First Order Systems, First Order Linear Systems, Matrix Formulation
13	Systems of Differential Equations: Basic Theory of Systems of First Order Linear Equations, Eigenvalue-Eigenvector Method for Solving First Order Linear Systems with Constant Coefficients
14	Power Series: Series Solutions about Ordinary Points

Materials

Materials are not specified.

Resources

Course Assessment

Assesment Methods	Percentage (%)	Assesment Methods Title
Final Exam	60	Final Exam
Midterm Exam	40	Midterm Exam

L+P: Lecture and Practice
PQ: Program Learning Outcomes
LO: Course Learning Outcomes

Prospective Student