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

這門課主要是介紹基本的複變數函數的理論。主要的內容包括複數系、解析函數、初等函數、複數積分、解析函數的數列表示、留數理論、保角映射以及 Fourier 和 Laplace 轉換。除了基礎理論,我們也將簡單介紹一些在物理或工程方面的應用。
This course provides the mathematical foundations needed for understanding and working with the modern analysis. The main topics are complex number system, analytic functions, integrations, conformal mappings and some integral transformations. Some applications in physics and engineering will also be included.

課程學習目標 Course Objectives

  • Properties of Analytic Functions
  • Isolated Singularities of an Analytic Function and The Residue Theorem
  • Conformal Mapping and the Riemann Mapping Theorem
  • 課程進度 Progress Description

    進度說明 Progress Description
    1The Complex Numbers
    2The Complex Numbers Function of the Complex Variable z
    3Function of the Complex Variable z
    4Analytic Functions
    5Line Integrals and Entire Functions
    6Properties of Entire Functions
    7Properties of Analytic Functions
    8Properties of Analytic Functions
    9Simply Connected Domains
    10Midterm (11/23 19:00-21:00 數學系 3174 教室)
    11Isolated Singularities of an Analytic Function
    12The Residue Theorem
    13Applications of the Residue Theorem to the Evaluation of Integrals and Sums
    14Applications of the Residue Theorem to the Evaluation of Integrals and Sums
    15Applications of the Residue Theorem to the Evaluation of Integrals and Sums
    16Introduction to Conformal Mapping
    17Introduction to Conformal Mapping
    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