Information Package / Course Catalogue - Adnan Menderes University

General Information Unit Staff Academic Information Programme Outcomes Course Structure Diagram Contact Information

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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 Assessment	Count	Percent
Midterm Examination	1	%40
Final Examination	1	%60

Workload Calculation

Activities	Count	Preparation	Time	Total Work Load (hours)
Lecture - Theory	14	2	4	84
Midterm Examination	1	25	2	27
Final Examination	1	38	2	40
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	4
OÇ-2	5
OÇ-3	4
OÇ-4	4			4
OÇ-5	5			4

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