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

本課程主要是介紹一階偏微分方程及二階線性偏微分方程。我們將學習一些解偏微分方程的古典方法,如特徵線方法、分離變數法、傅立葉轉換法、拉普拉斯轉換法、格林函數方法。
This course provides an introduction to the first-order PDEs and the second-order linear PDEs. We will study the classical approach to solve PDEs, such as the method of characteristics, the separation of variables technique, Fourier transform, Laplace transform, and Green's function methods.

課程學習目標 Course Objectives

  • We expect to grab the basic idea and concept of PDE.
  • Learn various properties of important types of PDE.
  • Learn some PDEs from physics.
  • 課程進度 Progress Description

    進度說明 Progress Description
    1Introduction
    2Preliminaries
    3Conservation Equations and Characteristics
    4Conservation Equations and Characteristics
    5The Wave Equation
    6The Wave Equation
    7The Wave Equation
    8Midterm Exam.
    9Separation of Variables and Fourier Series
    10Separation of Variables and Fourier Series
    11The Heat Equation
    12The Heat Equation
    13Function Spaces
    14Function Spaces
    15Fourier Series
    16Fourier Series
    17Maximum Principles
    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