- University
- Academic
- Schools/Vocational Schools
- Vocational School of Justice
- Vocational School
- Department of Banking and Insurance (Turkish)
- Department of Computer Programming (Turkish)
- Department of Foreign Trade (Turkish)
- Department of Real Estate Management (Turkish)
- Department of Graphic Design (Turkish)
- Department of Interior Design (Turkish)
- Department of Construction Technology (Turkish)
- Department of Occupational Health and Safety (Turkish)
- Department of Architectural Restoration (Turkish)
- Department of Furniture and Decoration (Turkish)
- Department of Accounting and Tax Applications (Turkish)
- Department of Marketing (Turkish)
- Department of Radio and Tv Programming (Turkish)
- Department of Civil Aviation Cabin Services (Turkish)
- Department of Civil Aviation Transportation Management (Turkish)
- Department of Tourism and Hotel Management (Turkish)
- Department of Applied English Translation
- Vocational School Of Health Services
- Department of Child Development (Turkish)
- Department of Physiotherapy (Turkish)
- Department of Paramedic (Turkish)
- Department of Opticianry (Turkish)
- Department of Medical Documentation and Secreteriat (Turkish)
- Department of Medical Imaging Techniques (Turkish)
- Department of Medical Laboratory Techniques (Turkish)
- Department of Elderly Care (Turkish)
- School of Applied Management Sciences
- School of Foreign Languages
- Faculties
- Faculty of Arts and Sciences
- Faculty of Fine Arts and Design
- Faculty of Law
- Faculty of Communication
- Faculty of Business
- Faculty of Engineering
- Department of Computer Engineering
- Department of Biomedical Engineering
- Department of Electrical and Electronics Engineering
- Department of Industrial Engineering
- Department of Food Engineering
- Department of Genetics and Bioengineering
- Department of Aerospace Engineering
- Department of Civil Engineering
- Department of Mechanical Engineering
- Department of Mechatronics Engineering
- Department of Software Engineering
- Faculty of Health Sciences
- Medicine
- Graduate School
- Graduate Programs in Economics
- Graduate Programs in Law
- Graduate Programs in Communication
- Graduate Programs in Business Administration
- Graduate Programs in Logistics Management
- Programs in the Field of Mathematics
- Graduate Programs in Architecture
- Graduate Programs in Engineering
- M.SC. in Computer Engineering (With Thesis)
- M.SC. in Computer Engineering (Without Thesis)
- Ph.D. In Computer Engineering
- M.SC. in Bioengineering (With Thesis)
- M.SC. in Electrical and Electronics Engineering (With Thesis)
- M.SC. in Electrical and Electronics Engineering (Without Thesis)
- Ph.D. In Electrical-Electronics Engineering
- M.SC. In Industrial Engineering (With Thesis)
- Mechanical Engineering Master's Program with Thesis (English)
- Graduate Programs in Psychology
- Health Field
- Graduate Programs in Political Science and International Relations
- Master's Programs in Sustainable Energy
- Programs in Design Studies
- Graduate Programs in Foreign Languages
- Research Centers
- Common Courses
- Schools/Vocational Schools
- Research
- Campus
- INTERNATIONAL
- Contact
M.SC. in Computer Engineering (Without Thesis)
EEE 612 | Course Introduction and Application Information
| Course Name |
Chaos and Fractals
|
|
Code
|
Semester
|
Theory
(hour/week) |
Application/Lab
(hour/week) |
Local Credits
|
ECTS
|
|
EEE 612
|
Fall/Spring
|
3
|
0
|
3
|
7.5
|
| Prerequisites |
None
|
|||||
| Course Language |
English
|
|||||
| Course Type |
Elective
|
|||||
| Course Level |
Third Cycle
|
|||||
| Mode of Delivery | - | |||||
| Teaching Methods and Techniques of the Course | - | |||||
| National Occupation Classification | - | |||||
| Course Coordinator | ||||||
| Course Lecturer(s) | - | |||||
| Assistant(s) | - | |||||
| Course Objectives | The course aims the students: i) to know basic concepts on chaotic systems and fractal sets and ii) to use this knowledge in engineering applications. | |||||||||||||||||||||||||||||||||||||||||||||
| Learning Outcomes |
|
|||||||||||||||||||||||||||||||||||||||||||||
| Course Description | A unification of chaotic dynamics and fractal sets in a dynamical system and set theory background. Sensitive dependency and topological transitivity in invariant sets. From stable fixed points to period doubling, and entrance to chaos. Symbolic dynamics and examples for strange attractors. From cantor set to classical fractals. Self-similarity and fractal dimension. Image encoding by iterated function systems. Randomness in fractal construction. Chaotification. Engineering applications of chaos and fractals. | |||||||||||||||||||||||||||||||||||||||||||||
|
|
Core Courses | |
| Major Area Courses | ||
| Supportive Courses | ||
| Media and Management Skills Courses | ||
| Transferable Skill Courses |
WEEKLY SUBJECTS AND RELATED PREPARATION STUDIES
| Week | Subjects | Related Preparation | Learning Outcome |
| 1 | Historical remarks. First examples of chaotic systems and fractal sets in nature and engineering. | Chaos and Fractals: New Frontiers of Science, Heinz-Otto Peitgen, Hartmut Jürgens, Dietmar Saupe, 2nd Edition, Springer, ISBN-10: 0387202293, ISBN-13: 978-0387202297. Lecture Notes. | |
| 2 | Nonlinear dynamics: From equilibrium to chaos. Multiple equilibria. Limit cycle. Quasi periodic trajectories. Almost periodicity. Period doubling. | Chaos and Fractals: New Frontiers of Science, Heinz-Otto Peitgen, Hartmut Jürgens, Dietmar Saupe, 2nd Edition, Springer, ISBN-10: 0387202293, ISBN-13: 978-0387202297. Lecture Notes. | |
| 3 | Definition of chaos. Invariant set. Sensitive dependence on initial conditions. Denseness of periodic and aperiodic trajectories. Topological transitivity. | Chaos and Fractals: New Frontiers of Science, Heinz-Otto Peitgen, Hartmut Jürgens, Dietmar Saupe, 2nd Edition, Springer, ISBN-10: 0387202293, ISBN-13: 978-0387202297. Lecture Notes. | |
| 4 | Liapunov exponents. Identification of chaos by numerical methods. | Chaos and Fractals: New Frontiers of Science, Heinz-Otto Peitgen, Hartmut Jürgens, Dietmar Saupe, 2nd Edition, Springer, ISBN-10: 0387202293, ISBN-13: 978-0387202297. Lecture Notes. | |
| 5 | Analysis of discrete time chaotic systems: Logistic map. Fixed point. Contraction mapping. Bifurcation. | Chaos and Fractals: New Frontiers of Science, Heinz-Otto Peitgen, Hartmut Jürgens, Dietmar Saupe, 2nd Edition, Springer, ISBN-10: 0387202293, ISBN-13: 978-0387202297. Lecture Notes. | |
| 6 | Analysis of continuous time chaotic systems: Lorenz system. Circuit realizations of Lorenz system. Rössler system. | Chaos and Fractals: New Frontiers of Science, Heinz-Otto Peitgen, Hartmut Jürgens, Dietmar Saupe, 2nd Edition, Springer, ISBN-10: 0387202293, ISBN-13: 978-0387202297. Lecture Notes. | |
| 7 | Chua’s chaotic circuit and its hardware realizations | Chaos and Fractals: New Frontiers of Science, Heinz-Otto Peitgen, Hartmut Jürgens, Dietmar Saupe, 2nd Edition, Springer, ISBN-10: 0387202293, ISBN-13: 978-0387202297. Lecture Notes. | |
| 8 | Bifurcation: Pitchfork, saddle-node, Hopf, homoclinic and heteroclinic bifurcations. | Chaos and Fractals: New Frontiers of Science, Heinz-Otto Peitgen, Hartmut Jürgens, Dietmar Saupe, 2nd Edition, Springer, ISBN-10: 0387202293, ISBN-13: 978-0387202297. Lecture Notes. | |
| 9 | 1. Midterm | ||
| 10 | Fractal set examples from nature. | Chaos and Fractals: New Frontiers of Science, Heinz-Otto Peitgen, Hartmut Jürgens, Dietmar Saupe, 2nd Edition, Springer, ISBN-10: 0387202293, ISBN-13: 978-0387202297. Lecture Notes. | |
| 11 | Definition of fractal set. Self-similarity. Fractal dimension. Box counting dimension. Hausdorff dimension. | Chaos and Fractals: New Frontiers of Science, Heinz-Otto Peitgen, Hartmut Jürgens, Dietmar Saupe, 2nd Edition, Springer, ISBN-10: 0387202293, ISBN-13: 978-0387202297. Lecture Notes. | |
| 12 | Construction of fractal sets by Iterated Function Systems. Contraction mapping. | Chaos and Fractals: New Frontiers of Science, Heinz-Otto Peitgen, Hartmut Jürgens, Dietmar Saupe, 2nd Edition, Springer, ISBN-10: 0387202293, ISBN-13: 978-0387202297. Lecture Notes. | |
| 13 | 2. Midterm | ||
| 14 | Engineering applications of chaotic systems. Secure communication by synchronized chaotic systems. Chaotification. Chaotic liquid mixing. | Chaos and Fractals: New Frontiers of Science, Heinz-Otto Peitgen, Hartmut Jürgens, Dietmar Saupe, 2nd Edition, Springer, ISBN-10: 0387202293, ISBN-13: 978-0387202297. Lecture Notes. | |
| 15 | Engineering applications of fractal sets. Fractal image compression. | Chaos and Fractals: New Frontiers of Science, Heinz-Otto Peitgen, Hartmut Jürgens, Dietmar Saupe, 2nd Edition, Springer, ISBN-10: 0387202293, ISBN-13: 978-0387202297. Lecture Notes. | |
| 16 | Review of the Semester |
| Course Notes/Textbooks | The textbook referenced above and lecture notes |
| Suggested Readings/Materials | Related Books and Research Papers |
EVALUATION SYSTEM
| Semester Activities | Number | Weighting | LO 1 | LO 2 | LO 3 | LO 4 |
| Participation | ||||||
| Laboratory / Application | ||||||
| Field Work | ||||||
| Quizzes / Studio Critiques | ||||||
| Portfolio | ||||||
| Homework / Assignments |
2
|
10
|
||||
| Presentation / Jury | ||||||
| Project |
2
|
30
|
||||
| Seminar / Workshop | ||||||
| Oral Exams | ||||||
| Midterm |
2
|
30
|
||||
| Final Exam |
1
|
30
|
||||
| Total |
| Weighting of Semester Activities on the Final Grade |
70
|
|
| Weighting of End-of-Semester Activities on the Final Grade |
30
|
|
| Total |
ECTS / WORKLOAD TABLE
| Semester Activities | Number | Duration (Hours) | Workload |
|---|---|---|---|
| Theoretical Course Hours (Including exam week: 16 x total hours) |
16
|
3
|
48
|
| Laboratory / Application Hours (Including exam week: '.16.' x total hours) |
16
|
0
|
|
| Study Hours Out of Class |
15
|
3
|
45
|
| Field Work |
0
|
||
| Quizzes / Studio Critiques |
0
|
||
| Portfolio |
0
|
||
| Homework / Assignments |
2
|
15
|
30
|
| Presentation / Jury |
0
|
||
| Project |
2
|
20
|
40
|
| Seminar / Workshop |
0
|
||
| Oral Exam |
0
|
||
| Midterms |
2
|
15
|
30
|
| Final Exam |
1
|
32
|
32
|
| Total |
225
|
COURSE LEARNING OUTCOMES AND PROGRAM QUALIFICATIONS RELATIONSHIP
|
#
|
PC Sub | Program Competencies/Outcomes |
* Contribution Level
|
||||
|
1
|
2
|
3
|
4
|
5
|
|||
| 1 | Accesses information in breadth and depth by conducting scientific research in Computer Engineering, evaluates, interprets and applies information. |
-
|
-
|
-
|
X
|
-
|
|
| 2 | Is well-informed about contemporary techniques and methods used in Computer Engineering and their limitations. |
-
|
-
|
X
|
-
|
-
|
|
| 3 | Uses scientific methods to complete and apply information from uncertain, limited or incomplete data, can combine and use information from different disciplines. |
-
|
-
|
-
|
X
|
-
|
|
| 4 | Is informed about new and upcoming applications in the field and learns them whenever necessary. |
-
|
-
|
-
|
-
|
X
|
|
| 5 | Defines and formulates problems related to Computer Engineering, develops methods to solve them and uses progressive methods in solutions. |
-
|
-
|
-
|
-
|
X
|
|
| 6 | Develops novel and/or original methods, designs complex systems or processes and develops progressive/alternative solutions in designs. |
-
|
-
|
-
|
X
|
-
|
|
| 7 | Designs and implements studies based on theory, experiments and modelling, analyses and resolves the complex problems that arise in this process. |
-
|
-
|
-
|
X
|
-
|
|
| 8 | Can work effectively in interdisciplinary teams as well as teams of the same discipline, can lead such teams and can develop approaches for resolving complex situations, can work independently and takes responsibility. |
-
|
-
|
X
|
-
|
-
|
|
| 9 | Engages in written and oral communication at least in Level B2 of the European Language Portfolio Global Scale. |
-
|
-
|
X
|
-
|
-
|
|
| 10 | Communicates the process and the results of his/her studies in national and international venues systematically, clearly and in written or oral form. |
-
|
-
|
X
|
-
|
-
|
|
| 11 | Is knowledgeable about the social, environmental, health, security and law implications of Computer Engineering applications, knows their project management and business applications, and is aware of their limitations in Computer Engineering applications. |
-
|
-
|
X
|
-
|
-
|
|
| 12 | Highly regards scientific and ethical values in data collection, interpretation, communication and in every professional activity. |
-
|
X
|
-
|
-
|
-
|
|
*1 Lowest, 2 Low, 3 Average, 4 High, 5 Highest
Success Stories of Izmir University of Economics Students
Sami Eyidilli
Department of Business Administration
Department of Business Administration
Academic Career
Merve Akça
Psychology
Psychology
International Career
Aslı Nur TİMUR YORDANOV
CIU Lead Sustainable Energy Architect
CIU Lead Sustainable Energy Architect
Professional
Alper GÜLER
Qreal 3D Technologies
Qreal 3D Technologies
Entrepreneur
NEW GÜZELBAHÇE CAMPUS
DetailsGLOBAL CAREER
As Izmir University of Economics transforms into a world-class university, it also raises successful young people with global competence.
More..CONTRIBUTION TO SCIENCE
Izmir University of Economics produces qualified knowledge and competent technologies.
More..VALUING PEOPLE
Izmir University of Economics sees producing social benefit as its reason for existence.
More..
You are one step ahead with your graduate education at Izmir University of Economics.