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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

ASSOCIATE PROFESSOR MEHMET EMRE ÇEK

Offered to

Aerospace Engineering 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.

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

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 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 9 Higher order linear ordinary differential equations with constant coefficients: homogeneous and non-homogeneous equations, linearly independent solutions of homogeneous linear equations, a general solution. 10 Finding a particular and general solutions of non-homogeneous n-order linear differential equations. Variation of parameters method. 11 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. 12 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. 13 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. 14 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.

Recomended or Required Reading

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

Planned Learning Activities and Teaching Methods

Lectures Examinations

Assessment Methods

SORTING NUMBER SHORT CODE LONG CODE FORMULA 1 MTE MIDTERM EXAM 2 FIN FINAL EXAM 3 FCG FINAL COURSE GRADE MTE * 0.50 + FIN * 0.50 4 RST RESIT 5 FCGR FINAL COURSE GRADE (RESIT) MTE * 0.50 + RST * 0.50

Further Notes About Assessment Methods

None

Assessment Criteria

To be announced.

Language of Instruction

English

Course Policies and Rules

To be announced.

Contact Details for the Lecturer(s)

emre.cek@deu.edu.tr

Office Hours

Office Hour will be announced during the term.

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours) Lectures 14 4 56 Preparations before/after weekly lectures 14 3 42 Preparation for final exam 1 12 12 Preparation for midterm exam 1 12 12 Treatment of Examinations (Quiz + Midterm + Final) 2 15 30 Preparation for quiz etc. 0 0 0 Final 1 2 2 Midterm 1 2 2 Quiz etc. 0 0 0 TOTAL WORKLOAD (hours) 156

Contribution of Learning Outcomes to Programme Outcomes

PO/LO PO.1 PO.2 PO.3 PO.4 PO.5 PO.6 PO.7 PO.8 PO.9 PO.10 PO.11 PO.12 PO.13 LO.1 5 5 4 4 LO.2 5 5 4 4 LO.3 5 5 4 4 LO.4 5 5 4 4 LO.5 5 5 4 4 LO.6 5 5 4 4