Dokuz Eylül University Information Package / Courses Catalog

Description of Individual Course Units

Course Unit Code	Course Unit Title	Type Of Course	D	U	L	ECTS
MAT 4033	NONLINEAR DIFERENTIAL EQUATIONS AND DYNMC. SYST.	ELECTIVE	4	0	0	7

Offered By

Mathematics

Level of Course Unit

First Cycle Programmes (Bachelor's Degree)

Course Coordinator

DOCTOR MELTEM ALTUNKAYNAK

Offered to

Mathematics (Evening)
Mathematics

Course Objective

In this course dynamical systems which are formulated by nonlinear equations are given. Exact (analytical) solution to these problems may or may not be obtained. In this case behaviour of solutions and stability of the system are discussed. Periodic and chaotic behaviours are also introduced.

Learning Outcomes of the Course Unit

1	will be able to obtain and classify the critical points of dynamical systems.
2	will be able to apply the theory to simple modelling problems.
3	will be able to discuss the stability of a dynamical system.
4	will be able to describe how a phase portrait changes as a parameter changes in the system.
5	will be able to determine the behaviour of the solutions to dynamical system.

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week	Subject	Description
1	Some remarks on differential equations
2	Dynamical systems,phase space.
3	Orbits and fixed points
4	One and more dimensional linear systems
5	Almost lineer systems
6	Nonlineer systems-stability of fixed points
7	Stability by linearization
8	Applications, some population models
9	Stability by the direct methods: Energy and Lyapunov's method
10	Gradient Systems
11	Periodic solutions, limit cycles
12	Poincare-Bendixson theorem
13	The Hopf Bifurcation
14	Lorenz system and Chaos

Recomended or Required Reading

Textbook(s): Invitation to Dynamical Systems. Edward R. Scheinerman
Supplementary Book(s): Dynamical Systems with Applications using Mathematica. Stephen Lynch.
Materials: Presentations of lectures

Planned Learning Activities and Teaching Methods

Lecture notes, Solving problems

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

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

Further Notes About Assessment Methods

None

Assessment Criteria

Evaluation of exams.

Language of Instruction

English

Course Policies and Rules

Any unethical behavior that occurs either in presentations or in exams will be dealt with as outlined in school policy. You can find the undergraduate policy at https://fen.deu.edu.tr/en/

Contact Details for the Lecturer(s)

Email: meltem.topcuoglu@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	4	56
Preparation for midterm exam	1	25	25
Preparation for final exam	1	25	25
Final	1	2	2
Midterm	1	2	2
TOTAL WORKLOAD (hours)			166

Contribution of Learning Outcomes to Programme Outcomes

PO/LO	PO.1	PO.3	PO.7	PO.12	PO.13
LO.1	4	3
LO.2			5
LO.3		5		4
LO.4		5			4
LO.5				5

COURSE UNIT TITLE

DEGREE PROGRAMMES

Description of Individual Course Units

Offered By

Level of Course Unit

Course Coordinator

Offered to

Course Objective

Learning Outcomes of the Course Unit

Mode of Delivery

Prerequisites and Co-requisites

Recomended Optional Programme Components

Course Contents

Recomended or Required Reading

Planned Learning Activities and Teaching Methods

Assessment Methods

Further Notes About Assessment Methods

Assessment Criteria

Language of Instruction

Course Policies and Rules

Contact Details for the Lecturer(s)

Office Hours

Work Placement(s)

Workload Calculation

Contribution of Learning Outcomes to Programme Outcomes

CONTACT INFORMATION