COURSE UNIT TITLE

: NONLINEAR-DYNAMICS AND CHAOS-II

DEGREE PROGRAMMES

Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS
PHY 5136 NONLINEAR-DYNAMICS AND CHAOS-II ELECTIVE 3 0 0 8

Offered By

Graduate School of Natural and Applied Sciences

Level of Course Unit

Second Cycle Programmes (Master's Degree)

Course Coordinator

PROFESSOR DOCTOR GÜL GÜLPINAR

Offered to

PHYSICS
PHYSICS

Course Objective

At the end of this course, students should have a clear idea of the mathematical foundations of this area. The student will also be equipped with a set of analytical and numerical tools for analysing bifurcations, chaos and other nonlinear effects in systems arising from applications. This includes the analysis and classification of low-dimensional effects and also methods for reducing high-dimensional and non-standard dynamical systems to canonical low-dimensional models.

Learning Outcomes of the Course Unit

1   Explore the basic concepts of nonlinear dynamics using the 'simple' pendulum and adaptations of it.
2   Be able to analyse simple one and two-dimensional nonlinear systems.
3   Be able to analyse identify attractors of those nonlinear systems, and to characterise their stability.
4   Be able to understand and apply the basic numerical methods relevant for nonlinear systems.
5   Be able to demonstrate an understanding of what constitutes chaotic behaviour and explain why this imposes limits on predictability.
6   Be able to survey applications of the ideas in several areas of physics, and in other disciplines.
7   Be able to describe the concept of a fractal and explain the idea of a non-integer dimension.

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description
1 Introduction
2 General features of dynamical systems
3 Continuous Dynamical Systems
4 Continuous Dynamical Systems (cont.)
5 Discrete Dynamical systems
6 Discrete Dynamical systems (cont.)
7 Discrete Dynamical systems (cont.)
8 Non-linear waves
9 Non-linear waves (cont.)
10 Modeling of nonlinear Dynamics-1
11 Control of non-linear dynamics
12 Quantum Nonlinear Dynamics

Recomended or Required Reading

Textbook:
Strogatz, S., Nonlinear Dynamics and Chaos. Boulder, CO: Westview Press, 1994. ISBN:
9780201543445..
References:
1 Baker, G. L., and J. P. Gollub., Chaotic Dynamics, 2nd ed. Cambridge, UK: Cambridge
University Press, 1996. ISBN: 9780521471060.
2. Berge, P., Y. Pomeau, and C. Vidal. Order within Chaos. New York, NY: John Wiley &
Sons, 1987. ISBN: 9780471849674.
3. Beltrami, E. Mathematics for Dynamic Modeling. Boston, MA: Academic Press, 1987.
ISBN: 9780120855551.
4. Gleick, James. Chaos: Making a New Science / James Gleick. New York, NY: Viking,
1987. ISBN: 9780670811786.

Planned Learning Activities and Teaching Methods

1. Lecturing
2.Question-Answer
3.Discussing
4.Homework

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


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

Further Notes About Assessment Methods

None

Assessment Criteria

1. The homework and mid-term exams of the student is assessed as the achievement of them in the semester.
2. At %40 score of final examination is added directly to the others.

Language of Instruction

English

Course Policies and Rules

1. It is obligated to continue at least 70% of lessons.
2. If the student don t make the homework and attend mid-terms, he does not access the final exam

Contact Details for the Lecturer(s)

gul.gulpinar@deu.edu.tr

Office Hours

Wednesday and Friday between 11:00-12:00 a.m.

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours)
Lecture 14 3 42
Preparations for final exam 1 10 10
Preparations for mid-term exam 1 5 5
Preparations for homework 7 7 49
Preparations for presentations 8 4 32
Weekly preparations before/after course 14 4 56
Final Exam 1 3 3
Mid-term Exam 2 2 4
TOTAL WORKLOAD (hours) 201

Contribution of Learning Outcomes to Programme Outcomes

PO/LOPO.1PO.2PO.3PO.4PO.5PO.6PO.7PO.8PO.9PO.10
LO.15
LO.245343
LO.3445
LO.454253
LO.5314
LO.6535
LO.74452

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

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