Information Package / Course Catalogue
Differential Equations
Course Code: MAT253
Course Type: Required
Couse Group: First Cycle (Bachelor's Degree)
Education Language: English
Work Placement: N/A
Theory: 4
Prt.: 0
Credit: 4
Lab: 0
ECTS: 6
Objectives of the Course

To introduce the basic concepts required to understand, construct, solve and interpret differential equations, to teach methods to solve differential equations of various types, and to give an ability to apply knowledge of mathematics on engineering problems.

Course Content

Introduction to differential equations, first order differential equations, second order linear equations, solutions for system of linear differential equations

Name of Lecturer(s)
Lec. Ahmet GENÇ
Prof. Hülya İNCEBOZ
Prof. İnci ERHAN
Learning Outcomes
1.Classify differential equations according to certain features
2.Solve first order linear equations and nonlinear equations of certain types and interpret the solutions
3.Understand the conditions for the existence and uniqueness of solutions for the linear differential equations
4.Solve second and higher order linear differential equations with constant coefficients and construct all solutions from the linearly independent solutions
5.To be able to solve higher order linear differential equations
Recommended or Required Reading
1.Introduction to Ordinary Differential Equations 4 th. Edition, Shepley L. Ross, Wiley, 1989
2.Çözümlü Diferansiyel Denklem Problemleri, Doç. Dr. Cevdet Cerit, İ.T.Ü. Fen-Edebiyat Fakültesi, 2009
Weekly Detailed Course Contents
Week 1 - Theoretical
Introduction to differential equations, Definitions, Classifications of differential equations, solutions, The elimination of arbitrary constants, initial and value problems, Solutions and the existence uniqueness theorem
Week 2 - Theoretical
First-Order Equations for Which Exact Solutions are Obtainable
Week 3 - Theoretical
Linear Equations and Bernoulli Equations, Special Integrating Factors and Transformations
Week 4 - Theoretical
Applications of First-Order Equations
Week 5 - Theoretical
Explicit Methods of Solving Higher-Oreder Linear Differential Equations, Basic Theory of Linear Differential Equations, The Homogeneous Linear Equation with Constant Coefficients
Week 6 - Theoretical
The Method of Undetermined Coeeficients, Variation of parameters, The Cauchy-Euler Equation
Week 7 - Theoretical
Applications of Second-Order Linear Equation with Constant Coefficients
Week 8 - Theoretical
Series Solutions of Linear Differential Equations
Week 9 - Theoretical
Solutions About Singular Points; The Method of Frobenius, Bessel’s Equations and Bessel Functions
Week 10 - Theoretical
System of of Linear Differential Equations, Differential operators and an Operator Method
Week 11 - Theoretical
Basic Theory of Linear system in Normal Form: Two Equations in Two Unknown Functions, homogeneous Linear Systems with Constant Coefficient: Two Equations in Two Unknown Functions
Week 12 - Theoretical
Matrices and Vectors, Matrix Method for Homogeneous Linear Systems with Constant Coefficients
Week 13 - Theoretical
Laplace Transforms
Week 14 - Theoretical
Sabit Katsayılı Lineer Diferansiyel Denklemlerin Laplace Dönüşümü Çözümü, Lineer Sistemlerin Laplace Dönüşümü Çözümü
Assessment Methods and Criteria
Type of AssessmentCountPercent
Midterm Examination1%40
Final Examination1%60
Workload Calculation
ActivitiesCountPreparationTimeTotal Work Load (hours)
Lecture - Theory142484
Midterm Examination125227
Final Examination138240
TOTAL WORKLOAD (hours)151
Contribution of Learning Outcomes to Programme Outcomes
PÇ-1
PÇ-2
PÇ-3
PÇ-4
PÇ-5
PÇ-6
PÇ-7
PÇ-8
PÇ-9
PÇ-10
PÇ-11
OÇ-1
5
4
5
4
5
4
5
5
4
5
4
OÇ-2
4
5
4
5
4
5
4
5
5
4
5
OÇ-3
5
4
5
4
5
4
4
5
4
5
4
OÇ-4
5
5
5
4
5
4
5
4
5
4
5
OÇ-5
4
5
4
5
4
5
4
5
4
5
4
Adnan Menderes University - Information Package / Course Catalogue
2026