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 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.
獨立研究與撰寫論文的能力
Ability to do independent researches and to write thesis.
使用計算機的能力
Abilities to use computer as a tool.

課程概述 Course Description

本課程為數值偏微分方程的入門課程。主要在教導學生如何發展有限差分法對偏微分方程求解,同時分析數值方法的穩定性與收斂性。本課程中將教授有限差分法解各種不同類型問題包含:橢圓方程問題、擴散方程問題、對流方程問題。
This course provides an introduction to solve partial differential equations numerically. The course covers the finite difference approximation, elliptic equations, Fourier analysis of linear PDEs, diffusion equations, advection equations.

課程學習目標 Course Objectives

  • 介紹有限元素法求解偏微分方程式
  • 介紹有限差分法求解偏微分方程式
  • 微分方程式簡介
  • 課程進度 Course Outline

    週次 Week進度說明 Progress Description
    1Introduction to FEM elliptic problems
    2Introduction to FEM elliptic problems
    3Introduction to FEM elliptic problems
    4Abstract formulation of the finite element method for elliptic problems
    5Abstract formulation of the finite element method for elliptic problems
    6Abstract formulation of the finite element method for elliptic problems
    7Abstract formulation of the finite element method for elliptic problems
    8放假
    9Some finite element space
    10Some finite element space
    11Approximation theory for FEM. Error estimates for elliptic problems
    12Approximation theory for FEM. Error estimates for elliptic problems
    13Approximation theory for FEM. Error estimates for elliptic problems
    14Some applications to elliptic problems
    15FEM for parabolic problems
    16FEM for parabolic problems
    17Hyperbolic problems
    18Hyperbolic problems
     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?
    Is there any industry specialist invited in this course? How many times?
    2.本課程是否規劃含校外實習(並非參訪)?
    Are there any internships involved in the course? How many hours?
    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?