COURSE UNIT TITLE

: OSCILLATION THEORY

DEGREE PROGRAMMES

Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS
MAT 5056 OSCILLATION THEORY ELECTIVE 3 0 0 7

Offered By

Graduate School of Natural and Applied Sciences

Level of Course Unit

Second Cycle Programmes (Master's Degree)

Course Coordinator

PROFESSOR DOCTOR BAŞAK KARPUZ

Offered to

Mathematics (English)
Mathematics (English)

Course Objective

The aim of this course is to introduce fundamental concepts of applied mathematics and build relations between other theoretical fields of mathematics.

Learning Outcomes of the Course Unit

1   Will be able to understand the reason behind the oscillatory behavior of solutions of differential equations
2   Will be able to use the concept of characteristic equation
3   Will be able to analyze the character of solutions of differential equations
4   Will be able to utilize the Laplace transform
5   Will be able to understand asymptotic behavior of solutions of differential equations

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description
1 Some basic existence and uniqueness theorems
2 The Laplace transform
3 Oscillation of first-order autonomous delay differential equations
4 Oscillation of first-order delay differential equations with variable arguments I
5 Oscillation of first-order delay differential equations with variable arguments II
6 Oscillation of first-order delay differential equations with positive and negative coefficients
7 Linearized oscillation of first-order delay differential equations
8 Generalizations on the oscillation of first-order equations
9 Oscillation of first-order differential equations with neutral terms
10 Oscillation of second-order differential equations I
11 Oscillation of second-order differential equations II
12 Oscillation of higher-order delay differential equations I
13 Oscillation of higher-order delay differential equations II
14 Oscillation of higher-order delay differential equations III

Recomended or Required Reading

Textbooks:
Györi, I.; Ladas, G.Oscillation Theory of Delay Differential Equations with Applications. The Clarendon Press, Oxford University Press, New York, 1991.

Supplementary Books:
Agarwal, Ravi P.; Berezansky, Leonid; Braverman, Elena; Domoshnitsky, Alexander. Nonoscillation Theory of Functional Differential Equations with Applications.Springer, New York, 2012.
Agarwal, Ravi P.; Bohner, Martin; Grace, Said R.; O'Regan, Donal. Discrete Oscillation Theory. Hindawi Publishing Corporation, New York, 2005.
Agarwal, Ravi P.; Bohner, Martin; Li, Wan-Tong. Nonoscillation and Oscillation: Theory for Functional Differential Equations.Monographs and Textbooks in Pure and Applied Mathematics, 267. Marcel Dekker, Inc., New York, 2004.
Agarwal, Ravi P.; Grace, Said R.; O'Regan, Donal. Oscillation Theory for Difference and Functional Differential Equations.Kluwer Academic Publishers, Dordrecht, 2000.
Erbe, L. H.; Kong, Qingkai; Zhang, B. G. Oscillation Theory for Functional-Differential Equations.Monographs and Textbooks in Pure and Applied Mathematics, 190. Marcel Dekker, Inc., New York, 1995.
Ladde, G. S.; Lakshmikantham, V.; Zhang, B. G. Oscillation Theory of Differential Equations with Deviating Arguments.Monographs and Textbooks in Pure and Applied Mathematics, 110. Marcel Dekker, Inc., New York, 1987
Swanson, C. A. Comparison and Oscillation Theory of Linear Differential Equations. Mathematics in Science and Engineering, Vol. 48. Academic Press, New York-London, 1968.

Planned Learning Activities and Teaching Methods

Lecture Notes, Presentations, Problem Solving

Assessment Methods

SORTING NUMBER SHORT CODE LONG CODE FORMULA
1 MTE MIDTERM EXAM
2 FIN FINAL EXAM
3 FCG FINAL COURSE GRADE MTE * 0.40 + FIN * 0.60
4 RST RESIT
5 FCGR FINAL COURSE GRADE (RESIT) MTE * 0.40 + RST * 0.60


Further Notes About Assessment Methods

None

Assessment Criteria

To be announced.

Language of Instruction

English

Course Policies and Rules

Attendance to at least 70% for the lectures is an essential requirement of this course and is the responsibility of the student.
It is necessary that attendance to the lecture and homework delivery must be on time.
Any unethical behavior that occurs either in presentations or in exams will be dealt with as outlined in school policy.
You can find the graduate policy at http://web.fbe.deu.edu.tr

Contact Details for the Lecturer(s)

e-mail: basak.karpuz@deu.edu.tr
Office: 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 14 3 42
Preparations before/after weekly lectures 14 4 56
Preparation for midterm exam 1 31 31
Preparation for final exam 1 37 37
Midterm 1 3 3
Final 1 4 4
TOTAL WORKLOAD (hours) 173

Contribution of Learning Outcomes to Programme Outcomes

PO/LOPO.1PO.2PO.3PO.4PO.5PO.6PO.7PO.8PO.9PO.10PO.11
LO.15544455553
LO.25534455553
LO.35544555453
LO.45544555453
LO.55553355453

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

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