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

微分方程是用來描述科學和工程現象的重要工具。本課程係介紹線性常微分方程式,主要包含:微分方程解的存在唯一性,解微分方程的技巧,方程解的定性分析,微分方程的近似解與數值解。
Differential equations are important tools to understand phenomena in science and engineer. This course is aimed to introduce linear ordinary differential equations (ODEs). The topics include: existence and uniqueness of solutions of ODEs, techniques of solving ODEs, qualitative analysis of ODEs, approximated solutions and numerical solutions of ODEs.

課程學習目標 Course Objectives

  • basic knowledge of the Differential equations
  • the behavior of their solutions
  • some elementary methods for solving different types of equations
  • 課程進度 Course Outline

    週次 Week進度說明 Progress Description
    1Ch1: Introduction
    2Ch2: First Order Differential Equations
    3Ch2: First Order Differential Equations
    4Ch2: First Order Differential Equations
    5Ch3: Second Order Linear Equations
    6春假
    7Ch3: Second Order Linear Equations
    8Ch3: Second Order Linear Equations
    9Ch4: Higher Order Linear Equations
    10Ch4: Higher Order Linear Equations
    11Ch4: Higher Order Linear Equations
    12Ch5: Series Solutions of Second Order Linear Equations
    13Ch5: Series Solutions of Second Order Linear Equations
    14Ch5: Series Solutions of Second Order Linear Equations
    15Ch6: The Laplace Transform
    16Ch6: The Laplace Transform
    17Ch7: Systems of Linear Equations
    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?
    Is this course recognized as an academic ethics course? In the course how many hours are regarding academic ethics topics?
    4.本課程是否屬進入社區實踐課程?
    Is this course recognized as a Community engagement and Service learning course? Which community will be engaged?