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Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS MAT 4030 DIFERENCE EQUATIONS ELECTIVE 4 0 0 7

Offered By

Mathematics

Level of Course Unit

First Cycle Programmes (Bachelor's Degree)

Course Coordinator

PROFESSOR DOCTOR BAŞAK KARPUZ

Offered to

Mathematics (Evening) Mathematics

Course Objective

Difference equations is a rich field, both interesting and useful. The goal is to present an overview of the various facets of difference equations that can be studied by elementary mathematical methods

Learning Outcomes of the Course Unit

1   will be able to learn the difference calculus 2   will be able to learn the usage in the linear equations 3   will be able to learn the usage in the nonlinear equations 4   will be able to learn the stability theory for difference equations 5   will be able to apply difference calculus to dynamical systems

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description 1 The difference calculus 2 The difference operator, summation, generating functions 3 First order linear difference equations 4 Equations with variable coefficients 5 The z-transform 6 Initial value problems for linear systems 7 Stability of linear systems 8 Midterm 9 Stability of nonlinear systems, chaotic behavior 10 Asymptotic methods, linear equations 11 Asymptotic methods tononlinear equations 12 The self adjoint second order linear equations 13 Sturmian theory 14 Application of methods

Recomended or Required Reading

Textbook(s): Difference Equation, W. G. Kelley and A.C. Peterson (Academic Press Inc) Supplementary Book(s): References: Materials: Course presentation slayts

Planned Learning Activities and Teaching Methods

Lecture notes, presentation, solving problems

Assessment Methods

SORTING NUMBER SHORT CODE LONG CODE FORMULA 1 MTE MIDTERM EXAM 2 ASG ASSIGNMENT 3 FINS FINAL EXAM 4 FCG FINAL COURSE GRADE MTE * 0.30 + ASG * 0.20 + FIN * 0.50 5 RST RESIT 6 FCGR FINAL COURSE GRADE (RESIT) MTE * 0.30 + ASG * 0.20 + RST * 0.50

Further Notes About Assessment Methods

None

Assessment Criteria

To be announced.

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)

e-Mail: basak.karpuz@deu.edu.tr Phone: 0 232 301 85 76

Office Hours

To be announced

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours) Lectures 13 4 52 Preparations before/after weekly lectures 12 2 24 Preparing assignments 5 10 50 Preparation for midterm exam 1 15 15 Preparation for final exam 1 20 20 Final 1 2 2 Midterm 1 2 2 TOTAL WORKLOAD (hours) 165

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 4 3 2 3 4 4 4 4 5 LO.2 4 3 2 3 4 4 4 4 5 LO.3 4 3 2 3 4 4 4 4 5 LO.4 4 3 3 4 4 4 4 5 LO.5 3 3 3 4 4 4 4 5