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

本課程將初步介紹波茲曼方程的數學理論, 其中包含波茲曼collision operator及傳輸方程的基本性質, 並介紹最近的研究方向. 基本背景要求為高等微積分, 線性代數及大學部微分方程.
This course will introduce mathematical properties of the Boltzmann equation, including Boltzmann collision operator and transport equation. Moreover, we will introduce some recent research directions. The background of this course is advanced calculus, linear algebra and undergraduate level of DE.

課程學習目標 Course Objectives

  • 對氣體動力學有基本認識
  • 熟悉分析技巧
  • 訓練學生研究能力
  • 課程進度 Course Outline

    週次 Week進度說明 Progress Description
    1Boltzmann Collision Operator
    2Boltzmann Collision Operator
    3Boltzmann Collision Operator
    4Boltzmann Collision Operator
    5Transport equation (Decay estimate)
    6Transport equation (Maximum Principle)
    7Transport equation (Averaging Lemma)
    8Transport equation (Averaging Lemma)
    9Transport equation (Phase Mixing)
    10Transport equation (Phase Mixing)
    11Transport equation (Nonlocal Problem)
    12Transport equation (Nonlocal Problem)
    13Linear Boltzmann Equation(Homogeneous case)
    14Linear Boltzmann Equation(inhomogeneous case in a torus)
    15Linear Boltzmann Equation(inhomogeneous case in a torus)
    16Linear Boltzmann Equation(inhomogeneous case in whole space)
    17Presentation
    18Presentation
     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?