1. FIRST CYCLE - BACHELOR'S DEGREE
  2. FACULTY OF EDUCATION
  3. DEPARTMENT OF MATHEMATICS AND SCIENCE TEACHING DEPARTMENT
  4. 133 ELEMENTARY MATHEMATICS EDUCATION
Course Information Course Learning Outcomes Course's Contribution To Program ECTS Workload Course Details
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COURSE INFORMATION
Course CodeCourse TitleL+P HourSemesterECTS
IMO 3108DIFFERENTIAL EQUATIONS3 + 06th Semester4

COURSE DESCRIPTION
Course Level Bachelor's Degree
Course Type Compulsory
Course Objective This course aims to inform prospective teachers about the classification of differential equations, find different solutions to ordinary differential equations, teach general solutions of ordinary differential equations, obtain special solutions that satisfy initial conditions, have them practice first and second-order ordinary differential equations, to develop a positive attitude towards differential equations course.
Course Content The concept of a differential equation, classifications of differential equations, initial value problems, general solutions, separable differential equations, homogenous differential equations, homogenization of differential equations, exact differential equations, integration factors, and equations that can be converted to exact differential equations, first-order linear differential equations, Bernoulli and Riccati equations. Second-order differential equations and their applications. Higher-order differential equations, and linear differential equations and solutions.
Prerequisites No the prerequisite of lesson.
Corequisite No the corequisite of lesson.

COURSE LEARNING OUTCOMES
1Identifies the differential equations.
2Classifies the differential equations.
3Identifies the first order differential equations and solves.
4Learns some application areas of first-order differential equations.
5Identifies the second-order differential equations types.
6Finds the solutions of the homogenous linear equations with constant coefficients.
7Finds the solutions of the nonhomogenous linear equations with constant coefficients.
8Learns some application areas of second-order differential equations.
9 Develop positive attitudes toward Differential Equations.

COURSE'S CONTRIBUTION TO PROGRAM
PO 01PO 02PO 03PO 04PO 05PO 06PO 07PO 08PO 09PO 10PO 11PO 12PO 13PO 14
LO 00154     5      
LO 00254     5      
LO 003       55     
LO 00455      4     
LO 00555            
LO 006       55     
LO 007       55     
LO 00855      4     
LO 009            5 
Sub Total2523     2523   5 
Contribution33000003300010

ECTS ALLOCATED BASED ON STUDENT WORKLOAD BY THE COURSE DESCRIPTION
ActivitiesQuantityDuration (Hour)Total Work Load (Hour)
Course Duration (14 weeks/theoric+practical)14228
Hours for off-the-classroom study (Pre-study, practice)14342
Assignments144
Mid-terms11212
Final examination11818
Total Work Load

ECTS Credit of the Course





104

4
COURSE DETAILS
 Select Year   


 Course TermNoInstructors
Details 2025-2026 Spring1İSMET AYHAN
Details 2024-2025 Spring1İSMET AYHAN


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Course Details
Course Code Course Title L+P Hour Course Code Language Of Instruction Course Semester Mode of Delivery
IMO 3108 DIFFERENTIAL EQUATIONS 3 + 0 1 Turkish 2025-2026 Spring Face to Face
Course Coordinator  E-Mail  Phone Number  Course Location Attendance
Prof. Dr. İSMET AYHAN iayhan@pau.edu.tr EGT A0232-02 %70
Goals This course aims to inform prospective teachers about the classification of differential equations, find different solutions to ordinary differential equations, teach general solutions of ordinary differential equations, obtain special solutions that satisfy initial conditions, have them practice first and second-order ordinary differential equations, to develop a positive attitude towards differential equations course.
Content The concept of a differential equation, classifications of differential equations, initial value problems, general solutions, separable differential equations, homogenous differential equations, homogenization of differential equations, exact differential equations, integration factors, and equations that can be converted to exact differential equations, first-order linear differential equations, Bernoulli and Riccati equations. Second-order differential equations and their applications. Higher-order differential equations, and linear differential equations and solutions.
Topics
WeeksTopics
1 Basic Concept related to Diferential Equations and Mathematical and Physical Applications
2 First order Diferential Equations, Seperable Differential Equations, Homogen Differential Equations
3 Homogeneous and homogenizable differential equations
4 Exact differential equations and integration factor
5 Linear and Bernoulli Differential Equations
6 Riccati, Clairaut, Lagrange, Differential Equations
7 Orthogonal Trajectories, applications of 1st order differential equations
8 Applications of 1st order differential equations
9 Midterm
10 2nd order differential equations that do not include one of the variables
11 2nd order linear differential equations with constant coefficients
12 Higher order linear differential equations with constant coefficients
13 Linear differential equations with variable coefficients, Euler-Cauchy differential equation,Applications of 2nd order differential equations
14 Applications of 2nd order differential equations
Materials
Materials are not specified.
Resources
ResourcesResources Language
Ahmet Karedeniz, Yüksek Matematik cilt 3, Çağlayan Kitapevi, İstanbul.Türkçe
Course Assessment
Assesment MethodsPercentage (%)Assesment Methods Title
Final Exam60Final Exam
Midterm Exam40Midterm Exam
L+P: Lecture and Practice
PQ: Program Learning Outcomes
LO: Course Learning Outcomes