Course Information
SemesterCourse Unit CodeCourse Unit TitleT+P+LCreditNumber of ECTS CreditsLast Updated Date
3MMT220Differential Equations4+2+05712.11.2025

 
Course Details
Language of Instruction Turkish
Level of Course Unit Bachelor's Degree
Department / Program Computer Engineering
Type of Program Formal Education
Type of Course Unit Compulsory
Course Delivery Method Face To Face
Objectives of the Course The aim of this course is to introduce the types of differential equations encountered in engineering fields and to teach the methods for solving these equations. Since the course covers differential equation applications specific to each engineering discipline, students develop the ability to understand differential equations relevant to their own field and solve related problems more effectively.
Course Content Basic concepts related to differential equations and the classification of differential equations, first-order differential equations (equations separable by variables, differential equations that can be made separable by variables, homogeneous differential equations, differential equations that can be made homogeneous, exact differential equations, integration factor method, linear differential equations, linearizable differential equations, Bernoulli differential equation, Riccati differential equation, special types of differential equations, Clairaut differential equation, Lagrange differential equation), second-order differential equations (second-order differential equations without dependent variables, second-order differential equations without independent variables, order reduction method in differential equations), high-order linear (first-order) differential equations (general solution of right-hand side constant coefficient linear differential equations, Wronski determinant, general solution of right-hand side constant coefficient linear differential equations, method of undetermined coefficients, method of variation of Lagrange constants (parameters)), Cauchy-Euler differential equation, systems of differential equations (elimination method, Cramer's rule) Laplace transform, inverse Laplace transform, inverse Laplace transform using the method of partial fractions, solution of linear differential equations with constant coefficients using the Laplace transform, convolution, application of the convolution theorem to integral equations, solution of systems of differential equations using the Laplace transform.
Course Methods and Techniques
Prerequisites and co-requisities None
Course Coordinator None
Name of Lecturers Asist Prof.Dr. Fatma Zehra UZEKMEK
Assistants None
Work Placement(s) No

Recommended or Required Reading
Resources Türker, E. S. ve Başarır, M., 2003, Çözümlü Problemlerle Diferansiyel Denklemler, Değişim Kitabevi, Sakarya.
Çengel, Y. A. ve Palm, W. J. (Türkçesi: Tahsin Engin), 2012, Mühendisler ve Fen Bilimciler İçin Diferansiyel Denklemler, Güven Kitabevi, İzmir.
Bronson, R.,1993, (Türkçesi: Hilmi Hacısalihoğlu), Diferansiyel Denklemler, Schaum´s Outlines, Nobel Kitabevi, Ankara.
Edwards, C. H.ve Penney, D. E., (Türkçesi: Ömer Akın) 2008, Diferansiyel Denklemler ve Sınır Değer Problemleri,
William E. Boyce-Richard C. Diprima, Elementary Differential Equations and boundary Value Problems, 12th Edition
Peter V.O’Neil , The University of Alabama at Birmingham: Advanced Engineerimg Mathematics, 7th Edition.
Mehmet Çağlıyan, Nisa Çelik, Setenay Doğan, Adi Diferensiyel Denklemler, Dora Yayınları.
Course Notes Lectures, Question-Answer, Problem Solving
Exams 1 Ara Sınav, 1 Final Sınavı

Course Category
Mathematics and Basic Sciences %100
Engineering %30

Planned Learning Activities and Teaching Methods
Activities are given in detail in the section of "Assessment Methods and Criteria" and "Workload Calculation"

Assessment Methods and Criteria
In-Term Studies Quantity Percentage
Mid-terms 1 % 50
Final examination 1 % 50
Total
2
% 100

 
ECTS Allocated Based on Student Workload
Activities Quantity Duration Total Work Load
Course Duration 14 4 56
Hours for off-the-c.r.stud 14 6 84
Mid-terms 1 2 2
Practice 14 2 28
Final examination 1 2 2
Total Work Load   Number of ECTS Credits 7 172

 
Course Learning Outcomes: Upon the successful completion of this course, students will be able to:
NoLearning Outcomes
1 Develops a command of the terminology related to differential equations; learns the concepts of order, degree, and linearity; derives the differential equation corresponding to a family of curves by using mathematical knowledge; and applies analytical thinking and analysis skills to solve initial and boundary value problems.
2 Analyzes differential equations and systems of differential equations using mathematical analysis methods; identifies and applies appropriate solution techniques by utilizing problem-solving and modeling skills.
3 Solves differential equations and systems of equations by using the Laplace transform; thereby applies mathematical and fundamental engineering knowledge and gains the ability to transfer abstract mathematical methods to engineering problems to produce solutions.

 
Weekly Detailed Course Contents
WeekTopicsStudy MaterialsMaterials
1 Basic concepts related to differential equations and the classification of differential equations, equations separable in variables
2 Differential equations that can be separated into variables, homogeneous differential equations, differential equations that can be made homogeneous
3 Exact differential equations, integration factor method
4 Linear differential equations, differential equations that can be linearized, Bernoulli differential equation, Riccati differential equation
5 Riccati differential equation, special type differential equations, Clairaut differential equation
6 Lagrange differential equation, second-order differential equations without dependent variables, second-order differential equations without independent variables, order reduction method in differential equations.
7 Higher-order linear differential equations, the general solution of linear differential equations with constant coefficients on the right-hand side, the Wronski determinant.
8 MIDTERM EXAM
9 The general solution of right-hand side constant coefficient linear differential equations, method of undetermined coefficients.
10 Method of parameter variation, Cauchy-Euler differential equation, systems of differential equations (elimination method, Cramer's rule).
11 Laplace transform, inverse Laplace transform.
12 The inverse Laplace transform using the method of partial fractions, convolution, application of the convolution theorem to integral equations, and the solution of linear differential equations with constant coefficients using the Laplace transform.
13 Solving differential equations using the Laplace transform, solving systems of differential equations using the Laplace transform.
14 Applications related to differential equations and differential equation systems.
15 FINAL EXAM

 
Contribution of Learning Outcomes to Programme Outcomes
P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 P11
All 5
C1 5
C2 5 3
C3 5 3

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