基本素養 Basic Literacy

核心能力 Competence

掌握連續與逼進的能力
Ability to handle continuity phenomena and approximations.
處理數字及符號運算的能力
Ability to operate with symbols and digits.
透視形像與空間的能力
Ability to visualize space, shape, and images.
利用計算機處理數學的能力
Ability of using computer to do mathematics.
應用隨機理論的能力
Ability to apply stochastic mathematics.
處理大量數據的能力
Ability to handle large amount of data.
處理離散型數學的能力
Ability to do mathematics relating to discrete models.
獨立研究的能力
Ability to do independent studies of mathematics.
使用計算機的能力
Abilities to use computer as a tool.

課程概述 Course Description

大自然的現象往往隨時間充滿複雜的變化,且對應的微分方程也是非線性的。本課程係非線性常微分方程的定性分析,主要包含:線性系統的穩定性分析,非線性系統解的局部與廣域分析,分歧理論與混沌。
Most natural phenomena involve complicated changes in time, and the corresponding differential equations are nonlinear. This course is aimed to the qualitative study of nonlinear ordinary differential equations (ODEs). The topics include: stability analysis of linear systems, local and global theory of solutions of nonlinear systems, bifurcation theory and chaos.

課程學習目標 Course Objectives

Dynamical systems is the study of the long-term behavior of an object (function or sequence) whose dynamical law (evolution or iteration equation) is given. Dynamical systems originated in late 19th century with the study of the orbits of the solar system. In 20th century it develops into a rich and powerful field with applications to physics, biology, meteorology, economics, and more. The mathematical core of the theory is the study of the global orbit structure (stability, periodicity or ergodicity) of the flows or maps. This course is aimed to be the further study on differential equations and an introduction to dynamical systems.

課程進度 Course Outline

週次 Week進度說明 Progress Description
1First Order Equation
2First Order Equation
3Planar Linear Systems
4Planar Linear Systems
5Higher Dimensional Linear Systems
6Higher Dimensional Linear Systems
7Existence and Uniqueness Theory
8Existence and Uniqueness Theory
9Local Theory of Nonlinear Systems
10Local Theory of Nonlinear Systems
11Global Theory of Nonlinear Systems
12Global Theory of Nonlinear Systems
13Discrete Dynamical Systems
14Discrete Dynamical Systems
15Selected Topics or Applications
16Selected Topics or Applications
17Selected Topics or Applications
18Selected Topics or Applications
 以上每週進度教師可依上課情況做適度調整。The schedule may be subject to change.

課程學習融入下列議題或具有下列內涵的程度
Immersing the Following Issues or Contents

議題或內容 Issues or Contents關聯性 Correlation
生命教育 Life Education 間接相關 Indirect correlation
服務學習 Service Learning 無相關 No correlation
性別平等 Gender Equity 無相關 No correlation
環境安全 Environmental Safety 間接相關 Indirect correlation
環境保護 Environmental Protection 間接相關 Indirect correlation
智慧財產權 Intellectual Property 無相關 No correlation
法治教育 Law-Related Education 無相關 No correlation
人權教育 Human Rights Education 無相關 No correlation

有關課程其他調查 Other Surveys of Courses

1.本課程是否規劃業界教師參與教學或演講? 否
Is there any industry specialist invited in this course? How many times? No
2.本課程是否規劃含校外實習(並非參訪)? 否
Are there any internships involved in the course? How many hours? No