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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, orbits and fixed points 3 One and more dimensional linear systems 4 Almost lineer systems 5 Nonlineer systems-stability of fixed points 6 Stability by linearization 7 Applications, some population models 8 Stability by the direct methods: Energy and Lyapunov s method 9 Midterm 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 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 + FIN * 0.60 *** Resit Exam is Not Administered in Institutions Where Resit is not Applicable.

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)

Email: guzin.gokmen@deu.edu.tr, Tel: (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 4 48 Preparation for midterm exam 1 30 30 Preparation for final exam 1 30 30 Final 1 2 2 Midterm 1 2 2 TOTAL WORKLOAD (hours) 164

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