COURSE UNIT TITLE

: DIFERENTIAL EQUATIONS I

DEGREE PROGRAMMES

Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS
MAT 2039 DIFERENTIAL EQUATIONS I COMPULSORY 4 0 0 7

Offered By

Mathematics

Level of Course Unit

First Cycle Programmes (Bachelor's Degree)

Course Coordinator

ASSOCIATE PROFESSOR MELTEM ADIYAMAN

Offered to

Mathematics (Evening)
Mathematics

Course Objective

This course is an introduction to the basic concepts, theory, methods and applications of ordinary differential equations. It aims to develop the basics of modeling at an introductory level and to learn the methods to solution of first and higher order differential equations.

Learning Outcomes of the Course Unit

1   will be able to classify the differential equations.
2   will be able to use solution methods of first order ordinary differential equations
3   will be able to understand explicit methods of solving higher order linear differential equations
4   will be able to solve nonhomogeneous differentail equations
5   will be able to analyze series solutions of linear differential equations
6   will be able to solve linear equations by Laplace method

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:Explicit solution,implicit solution, Initial Value Problem, Existence of Solution
2 First Order Ordinary Differential Equations: Seperable Differential Equations, Exact Differential Equations
3 Integrating factors and NonExact Differential Equations, Bernoulli equations
4 First order homogeneous equations,special substitutions,Riccati equation, Applications of first order equations
5 Theory of Higher Order Linear Differential Equations, Linear Dependence and Independence, Representation of Solutions for Homogeneous and Nonhomogeneous Case
6 Reduction of Order. Homogeneous Linear Equations with Constant Coefficients
7 Solution of Nonhomogeneous Differential Equations: Method of Undetermined Coefficients
8 Midterm, Method of Variation of Parameters
9 CauchyEuler Differential Equations, Laplace Transforms: Definition of the Laplace Transform, Properties of the Laplace Transform.
10 Inverse Laplace Transforms. Solving Initial Value Problems by Laplace Transforms
11 Series Solutions of Differential Equations. Power Series Solutions: Series Solutions around an Ordinary Point
12 Systems of Linear Differential Equations: Differential Operators and an Operator Method and laplace transformation method
13 Analyze and convergence of Fourier Series for periodic functions
14 Fourier sine and cosine series

Recomended or Required Reading

Textbook(s): "Fundamentals of Differential Equations and Boundary Value Problems (6. edition) by Nagle, Saff and Snider, Pearson,Addison Wesley
Supplementary Book(s): Introduction to Ordinary Differential Equations by Shepley L. Ross. Fourth Edition, John Wiley and Sons
Materials: Course presentation slayts

Planned Learning Activities and Teaching Methods

Lecture notes
Presentation
Problem solving

Assessment Methods

SORTING NUMBER SHORT CODE LONG CODE FORMULA
1 VZ Vize
2 FN Final
3 BNS BNS VZ * 0.40 + FN * 0.60
4 BUT Bütünleme Notu
5 BBN Bütünleme Sonu Başarı Notu VZ * 0.40 + BUT * 0.60


Further Notes About Assessment Methods

None

Assessment Criteria

Midterm, Final

Language of Instruction

English

Course Policies and Rules

1. Attending at least 70 percent of lectures is mandatory.
2. Plagiarism of any type will result in disciplinary action

Contact Details for the Lecturer(s)

meltem.evrenosoglu@deu.edu.tr

Office Hours

To be announced.

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 midterm exam 1 30 30
Preparation for final exam 1 38 38
Final 1 2 2
Midterm 1 2 2
TOTAL WORKLOAD (hours) 170

Contribution of Learning Outcomes to Programme Outcomes

PO/LOPO.1PO.2PO.3PO.4PO.5PO.6PO.7PO.8PO.9PO.10PO.11PO.12PO.13
LO.13333
LO.233434
LO.334545
LO.434545
LO.534545
LO.633555

CONTACT INFORMATION
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Phone: +90(232) 412 12 12 - Fax: +90 (232) 464 81 35

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