# COURSE UNIT TITLE

: DIFFERENTIAL EQUATIONS

#### Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS
MAT 2505 DIFFERENTIAL EQUATIONS COMPULSORY 4 0 0 6

#### Offered By

Faculty of Engineering

#### Level of Course Unit

First Cycle Programmes (Bachelor's Degree)

#### Course Coordinator

ASISTANT PROFESSOR MEHMET EMRE ÇEK

#### Offered to

Electrical and Electronics Engineering

#### Course Objective

To teach the fundamentals and main methods and techniques of differential equations.

#### Learning Outcomes of the Course Unit

 1 To be able to to express the fundamental concepts of differential equations. 2 To be able to understand and use the concept of construction of a general solution for basic differential equations and systems. 3 To be able to use the linear algebra methods for solving system of the first order differential equations. 4 To be able to apply the direct and the inverse Laplace transformations of elementary functions. 5 To be able to apply the Laplace transform for solving initial value problems for differential equations. 6 To be able to use main methods for solving classical differential equations.

Face -to- Face

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#### Course Contents

 Week Subject Description 1 Classification of differential equations, their origins and applications, particular, general and singular solutions, Initial value and initial boundary value problems. 2 First order ordinary differential equations; solving separable and homogeneous equations. Linear equations, integrating factors. 3 Solving exact equations, Bernoulli equation. Methods of special transformations and grouping 4 Second order linear ordinary differential equations with constant coefficients: homogeneous and non-homogeneous equations, linearly independent solutions of homogeneous linear equations, a general solution. 5 Wronskian and its properties, finding a general solution of the homogeneous linear differential equation with constant coefficients. 6 Cauchy-Euler s equation, non-homogeneous linear differential equations: finding a particular and general Cauchy-Euler s equation, non-homogeneous linear differential equations: finding a particular and general solutions of non-homogeneous linear differential equations. 7 Visa I, Variation of parameters method. Reduction of the order method. 8 Higher order linear ordinary differential equations with constant coefficients: homogeneous and non-homogeneous equations, linearly independent solutions of homogeneous linear equations, a general solution. 9 Finding a particular and general solutions of non-homogeneous n-order linear differential equations. Variation of parameters method. 10 Linearly independent and linearly dependent vector functions. System of the first order two ordinary differential equations. Finding a general solution of homogeneous system with constant coefficients: characteristic equation, distinct, repeated and complex roots. 11 System of the first order n ordinary differential equations. Finding a general solution of homogeneous system of n differential equations with constant coefficients: characteristic equation, distinct, repeated and complex roots. 12 Solution of the system in the case when the matrix of the coefficients is symmetric. Fundamental matrix. Finding a general solution of non-homogeneous system by fundamental matrix: examples. 13 Visa II, The Laplace transform and properties, Laplace transform of elementary functions, formulae for Laplace transform of derivatives and integral, Laplace transform of the convolution of two functions, the inverse Laplace transform: examples. Solving initial value problems for ordinary differential equations and systems with constant coefficients by the Laplace transform method. 14 Boundary value Problems and Eigenvalue Problems for the second order differential equations with constant coefficients. Regular Sturm-Liouville Eigenvalue Problems : Finding Eigenvalues and Eigenfunctions.

Main Source: Goode S.W., Differential Equations and Linear Algebra, Prentice Hall, New Jersey, 2002

Supplementary Sources: Ross S.L., Introduction to Ordinary Differential Equations, Blaisdell Publishing Company, 2001
Boyce W.E. DiPrima R.C., Elementary Differential Equations and Boundary Value Problems, John Wiley and Sons, 1998

Other Lecture materials: PDF files of lecture notes of Prof. Dr. Valery Yakhno

Lectures
Homeworks
Examinations

#### Assessment Methods

 SORTING NUMBER SHORT CODE LONG CODE FORMULA 1 MTE1 MIDTERM EXAM 1 2 MTE2 MIDTERM EXAM 2 3 FIN FINAL EXAM 4 FCG FINAL COURSE GRADE MTE1 * 0.25 + MTE2 * 0.25 + FIN * 0.50 5 RST RESIT 6 FCG FINAL COURSE GRADE MTE 1 * 0.25 + MTE 2 * 0.25 + RST * 0.50

*** Resit Exam is Not Administered in Institutions Where Resit is not Applicable.

None

To be announced.

English

To be announced.

#### Contact Details for the Lecturer(s)

emre.cek@deu.edu.tr

To be announced.

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