＜概要/Course Content Summary＞
"Nonlinearity" plays a crucial role in various field of modern science.
This course examines simplified dynamical models to clarify the nature of nonlinearity.
This course provides the skills to analyze complex phenomena appearing in various fields.
Prerequisities: Introductory physics and mathematics are used throughout.
The mathematical prerequisite is infinitesimal [differential， integral] calculus， Taylor series， differential equations， partial derivatives， Jacobian matrix， divergence theorem，and linear algebra， such as eigenvalues and eigenvectors.
＜到達目標/Goals,Aims＞
Through the cource， student will be able to:
-define what "nonlinear" is.
-understand the theory and concept of "nonlinear".
-appreciate the rich structure of "nonlinear".
-describe and analyse complex phenomena.
＜授業計画/Schedule＞
（実施回/
Week）
|
（内容/
Contents）
|
（授業時間外の学習/
Assignments）
|
|
（実施回/ Week）
1-2
|
（内容/ Contents）
orientation， student survey
What is "nonlinear" ?
linear theory， true nonlinearity， singularity， criticality， dynamical system
|
（授業時間外の学習/ Assignments）
preparing for or reviewing nonlinearity
|
|
（実施回/ Week）
3-5
|
（内容/ Contents）
One-dimensional system
dynamical system, linearization and stability, graphical method
|
（授業時間外の学習/ Assignments）
preparing for or reviewing dynamical system
|
|
（実施回/ Week）
6-9
|
（内容/ Contents）
Bifurcation
stability, existence and uniqueness, phase portrait, non-dimensionalization,
|
（授業時間外の学習/ Assignments）
preparing for or reviewing bifurcation
|
|
（実施回/ Week）
10-12
|
（内容/ Contents）
Two-dimensional system
matrix and category, dynamics and bifurcation
|
（授業時間外の学習/ Assignments）
preparing for or reviewing two-dimensional system
|
|
（実施回/ Week）
13-14
|
（内容/ Contents）
Chaos
chaos and randomness， maps and flows， symmetry and invariance
|
（授業時間外の学習/ Assignments）
preparing for or reviewing chaos
|
|
（実施回/ Week）
15
|
（内容/ Contents）
Summary
check your understanding about nonlinear physics
|
（授業時間外の学習/ Assignments）
preparing for your classwork
|
The progress and contents may be changed according to the student's understanding
＜成績評価基準/Evaluation Criteria＞
|
平常点(出席，クラス参加，グループ作業の成果等)
|
30%
|
Attendance， Participation， efforts
|
|
期末レポート試験・論文
|
40%
|
Understanding of the lectured subjects
|
|
提出物
|
30%
|
Homework assignments
|
|
