ILAS Seminar-E2 :Chaos theory
| Numbering Code | U-LAS70 10002 SE50 | Year/Term | 2022 ・ First semester | |
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| Number of Credits | 2 | Course Type | seminar | |
| Target Year | Mainly 1st year students | Target Student | For all majors | |
| Language | English | Day/Period | Wed.5 | |
| Instructor name | DECHANT，Andreas (Graduate School of Science Senior Lecturer) | |||
| Outline and Purpose of the Course | This seminar introduces various fascinating aspects of chaos. While “chaos” often has the connotation of something complicated and uncontrollable, we will see that chaotic behavior can emerge from seemingly simple situations. We will discover that chaos can be, in its own way, very ordered. Perhaps even more surprisingly, chaos can actually be a source of stability. Along the way, we will familiarize ourselves with some of the necessary mathematical tools to describe chaotic behavior. Finally, we will discuss where chaos occurs in physics and everyday phenomena. Throughout the seminar, we will perform several simple experiments on a computer and learn to recognize chaotic behavior. | |||
| Course Goals |
- Understanding the connection between non-linearity and chaos. - Becoming familiar with the basic mathematical theory of chaos. - Recognizing chaotic phenomena in daily life and physics. - Being able to write simple computer programs to visualize chaotic behavior. |
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| Schedule and Contents |
Week 1-2: Dynamical systems and phase-space description. Week 3-6: Using the Julia programming language to visualize dynamical systems. Week 7-9: Bifurcations: the route to chaos. Week 10: The Lyapunov exponent: chaotic or not? Week 11-12: Self-similarity and Feigenbaum constants: order in chaos. Week 13-14: Chaos in physics. Week 15：Final written examination Week 16：Feedback |
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| Evaluation Methods and Policy | The students will be graded based on their participation in class (20%), worksheets and programming assignments (40%) and a final written examination (40%). Students will need at least 60% in total to pass. | |||
| Course Requirements | Basic programming skills are helpful but not required. | |||
| Study outside of Class (preparation and review) | The students will occasionally be asked to complete assignments or simple programming exercises. | |||
| Textbooks | Textbooks/References | No textbook, handouts will be provided. | ||
