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

  • 一階線性微分方程組的解題技巧與理論分析
  • 非線性系統的局部穩定性分析以及生物應用
  • 非線性系統的廣域分析理論
  • 課程進度 Progress Description

    進度說明 Progress Description
    1Systems of First Order Equations
    29/21中秋節放假;Systems of First Order Equations
    3Systems of First Order Equations
    4Systems of First Order Equations
    5Stability of Nonlinear Systems
    6Stability of Nonlinear Systems
    7Stability of Nonlinear Systems
    8Stability of Nonlinear Systems
    9Applications to Biology
    10Applications to Biology
    11Method of Lyapunov
    12Method of Lyapunov
    13Method of Lyapunov
    14Two Dimensional Systems
    15Two Dimensional Systems
    16Chaos and Strange Attractors;12/31開國紀念日補假
    17Chaos and Strange Attractors
    18Final Exam
     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.

    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
    3.本課程是否可歸認為學術倫理課程? 否
    Is this course recognized as an academic ethics course? In the course how many hours are regarding academic ethics topics? No
    4.本課程是否屬進入社區實踐課程? 否
    Is this course recognized as a Community engagement and Service learning course? Which community will be engaged? No